diff --git a/solution/0400-0499/0480.Sliding Window Median/README.md b/solution/0400-0499/0480.Sliding Window Median/README.md index c20104e9a6835..d13650be743e3 100644 --- a/solution/0400-0499/0480.Sliding Window Median/README.md +++ b/solution/0400-0499/0480.Sliding Window Median/README.md @@ -68,25 +68,25 @@ tags: 我们可以使用两个优先队列(大小根堆)维护当前窗口中的元素,其中一个优先队列存储当前窗口中较小的一半元素,另一个优先队列存储当前窗口中较大的一半元素。这样,当前窗口的中位数就是两个优先队列的堆顶元素的平均值或其中的一个。 -我们设计一个类 `MedianFinder`,用于维护当前窗口中的元素。该类包含以下方法: +我们设计一个类 $\textit{MedianFinder}$,用于维护当前窗口中的元素。该类包含以下方法: -- `add_num(num)`:将 `num` 加入当前窗口中。 +- `add_num(num)`:将 $\textit{num}$ 加入当前窗口中。 - `find_median()`:返回当前窗口中元素的中位数。 -- `remove_num(num)`:将 `num` 从当前窗口中移除。 -- `prune(pq)`:如果堆顶元素在延迟删除字典 `delayed` 中,则将其从堆顶弹出,并从该元素的延迟删除次数中减一。如果该元素的延迟删除次数为零,则将其从延迟删除字典中删除。 -- `rebalance()`:如果较小的一半元素的数量比较大的一半元素的数量多 2 个,则将较大的一半元素的堆顶元素加入较小的一半元素中;如果较小的一半元素的数量比较大的一半元素的数量少,则将较大的一半元素的堆顶元素加入较小的一半元素中。 +- `remove_num(num)`:将 $\textit{num}$ 从当前窗口中移除。 +- `prune(pq)`:如果堆顶元素在延迟删除字典 $\textit{delayed}$ 中,则将其从堆顶弹出,并从该元素的延迟删除次数中减一。如果该元素的延迟删除次数为零,则将其从延迟删除字典中删除。 +- `rebalance()`:如果较小的一半元素的数量比较大的一半元素的数量多 $2$ 个,则将较大的一半元素的堆顶元素加入较小的一半元素中;如果较小的一半元素的数量比较大的一半元素的数量少,则将较大的一半元素的堆顶元素加入较小的一半元素中。 -在 `add_num(num)` 方法中,我们先考虑将 `num` 加入较小的一半元素中,如果 `num` 大于较大的一半元素的堆顶元素,则将 `num` 加入较大的一半元素中。然后我们调用 `rebalance()` 方法,使得两个优先队列的大小之差不超过 $1$。 +在 `add_num(num)` 方法中,我们先考虑将 $\textit{num}$ 加入较小的一半元素中,如果 $\textit{num}$ 大于较大的一半元素的堆顶元素,则将 $\textit{num}$ 加入较大的一半元素中。然后我们调用 `rebalance()` 方法,使得两个优先队列的大小之差不超过 $1$。 -在 `remove_num(num)` 方法中,我们将 `num` 的延迟删除次数加一。然后我们将 `num` 与较小的一半元素的堆顶元素进行比较,如果 `num` 小于等于较小的一半元素的堆顶元素,则更新较小的一半元素的大小,并且调用 `prune()` 方法,使得较小的一半元素的堆顶元素不在延迟删除字典中。否则,我们更新较大的一半元素的大小,并且调用 `prune()` 方法,使得较大的一半元素的堆顶元素不在延迟删除字典中。 +在 `remove_num(num)` 方法中,我们将 $\textit{num}$ 的延迟删除次数加一。然后我们将 $\textit{num}$ 与较小的一半元素的堆顶元素进行比较,如果 $\textit{num}$ 小于等于较小的一半元素的堆顶元素,则更新较小的一半元素的大小,并且调用 `prune()` 方法,使得较小的一半元素的堆顶元素不在延迟删除字典中。否则,我们更新较大的一半元素的大小,并且调用 `prune()` 方法,使得较大的一半元素的堆顶元素不在延迟删除字典中。 在 `find_median()` 方法中,如果当前窗口的大小为奇数,则返回较小的一半元素的堆顶元素;否则,返回较小的一半元素的堆顶元素与较大的一半元素的堆顶元素的平均值。 在 `prune(pq)` 方法中,如果堆顶元素在延迟删除字典中,则将其从堆顶弹出,并从该元素的延迟删除次数中减一。如果该元素的延迟删除次数为零,则将其从延迟删除字典中删除。 -在 `rebalance()` 方法中,如果较小的一半元素的数量比较大的一半元素的数量多 2 个,则将较大的一半元素的堆顶元素加入较小的一半元素中;如果较小的一半元素的数量比较大的一半元素的数量少,则将较大的一半元素的堆顶元素加入较小的一半元素中。 +在 `rebalance()` 方法中,如果较小的一半元素的数量比较大的一半元素的数量多 $2$ 个,则将较大的一半元素的堆顶元素加入较小的一半元素中;如果较小的一半元素的数量比较大的一半元素的数量少,则将较大的一半元素的堆顶元素加入较小的一半元素中。 -时间复杂度 $O(n \times \log n)$,空间复杂度 $O(n)$。其中 $n$ 为数组 `nums` 的长度。 +时间复杂度 $O(n \times \log n)$,空间复杂度 $O(n)$。其中 $n$ 为数组 $\textit{nums}$ 的长度。 @@ -449,4 +449,822 @@ func (h *hp) Pop() any { + + +### 方法二:有序集合 + +我们可以用两个有序集合来维护当前窗口中的元素,其中有序集合 $l$ 存储当前窗口中较小的一半元素,有序集合 $r$ 存储当前窗口中较大的一半元素。 + +遍历数组 $\textit{nums}$,对于每个元素 $x$,我们将其加入有序集合 $r$,然后将有序集合 $r$ 的最小值加入有序集合 $l$。如果有序集合 $l$ 的大小比有序集合 $r$ 的大小大于 $1$,我们将有序集合 $l$ 的最大值加入有序集合 $r$。 + +如果当前窗口元素总数为 $k$,大小为奇数,则有序集合 $l$ 的最大值就是中位数;如果当前窗口的大小为偶数,则有序集合 $l$ 的最大值和有序集合 $r$ 的最小值的平均值就是中位数。然后,我们将窗口的最左边元素移除,继续遍历数组。 + +时间复杂度 $O(n \log k)$,空间复杂度 $O(k)$。其中 $n$ 为数组 $\textit{nums}$ 的长度。 + + + +#### Python3 + +```python +from sortedcontainers import SortedList + + +class Solution: + def medianSlidingWindow(self, nums: List[int], k: int) -> List[float]: + l = SortedList() + r = SortedList() + ans = [] + for i, x in enumerate(nums): + r.add(x) + l.add(r.pop(0)) + while len(l) - len(r) > 1: + r.add(l.pop()) + j = i - k + 1 + if j >= 0: + ans.append(l[-1] if k & 1 else (l[-1] + r[0]) / 2) + if nums[j] in l: + l.remove(nums[j]) + else: + r.remove(nums[j]) + return ans +``` + +#### Java + +```java +class Solution { + public double[] medianSlidingWindow(int[] nums, int k) { + TreeMap l = new TreeMap<>(); + TreeMap r = new TreeMap<>(); + int n = nums.length; + double[] ans = new double[n - k + 1]; + int lSize = 0, rSize = 0; + for (int i = 0; i < n; ++i) { + r.merge(nums[i], 1, Integer::sum); + int x = r.firstKey(); + if (r.merge(x, -1, Integer::sum) == 0) { + r.remove(x); + } + l.merge(x, 1, Integer::sum); + ++lSize; + while (lSize - rSize > 1) { + x = l.lastKey(); + if (l.merge(x, -1, Integer::sum) == 0) { + l.remove(x); + } + r.merge(x, 1, Integer::sum); + --lSize; + ++rSize; + } + int j = i - k + 1; + if (j >= 0) { + ans[j] = k % 2 == 1 ? l.lastKey() : ((double) l.lastKey() + r.firstKey()) / 2; + if (l.containsKey(nums[j])) { + if (l.merge(nums[j], -1, Integer::sum) == 0) { + l.remove(nums[j]); + } + --lSize; + } else { + if (r.merge(nums[j], -1, Integer::sum) == 0) { + r.remove(nums[j]); + } + --rSize; + } + } + } + return ans; + } +} +``` + +#### C++ + +```cpp +class Solution { +public: + vector medianSlidingWindow(vector& nums, int k) { + multiset l, r; + int n = nums.size(); + vector ans; + for (int i = 0; i < n; ++i) { + r.insert(nums[i]); + l.insert(*r.begin()); + r.erase(r.begin()); + while (l.size() - r.size() > 1) { + r.insert(*l.rbegin()); + l.erase(prev(l.end())); + } + int j = i - k + 1; + if (j >= 0) { + ans.push_back(k % 2 ? *l.rbegin() : ((double) *l.rbegin() + *r.begin()) / 2); + auto it = l.find(nums[j]); + if (it != l.end()) { + l.erase(it); + } else { + r.erase(r.find(nums[j])); + } + } + } + return ans; + } +}; +``` + +#### Go + +```go +func medianSlidingWindow(nums []int, k int) (ans []float64) { + l := redblacktree.New[int, int]() + r := redblacktree.New[int, int]() + merge := func(st *redblacktree.Tree[int, int], x, v int) { + c, _ := st.Get(x) + if c+v == 0 { + st.Remove(x) + } else { + st.Put(x, c+v) + } + } + lSize, rSize := 0, 0 + for i, x := range nums { + merge(r, x, 1) + x = r.Left().Key + merge(r, x, -1) + merge(l, x, 1) + lSize++ + for lSize-rSize > 1 { + x = l.Right().Key + merge(l, x, -1) + merge(r, x, 1) + lSize-- + rSize++ + } + if j := i - k + 1; j >= 0 { + if k%2 == 1 { + ans = append(ans, float64(l.Right().Key)) + } else { + ans = append(ans, float64(l.Right().Key+r.Left().Key)/2) + } + if x = nums[j]; x <= l.Right().Key { + merge(l, x, -1) + lSize-- + } else { + merge(r, x, -1) + rSize-- + } + } + } + return +} +``` + +#### TypeScript + +```ts +function medianSlidingWindow(nums: number[], k: number): number[] { + const l = new TreapMultiSet((a, b) => a - b); + const r = new TreapMultiSet((a, b) => a - b); + const n = nums.length; + const ans: number[] = []; + for (let i = 0; i < n; ++i) { + r.add(nums[i]); + l.add(r.shift()!); + while (l.size - r.size > 1) { + r.add(l.pop()!); + } + const j = i - k + 1; + if (j >= 0) { + ans[j] = k % 2 ? l.last()! : (l.last()! + r.first()!) / 2; + if (nums[j] <= l.last()!) { + l.delete(nums[j]); + } else { + r.delete(nums[j]); + } + } + } + return ans; +} + +type CompareFunction = ( + a: T, + b: T, +) => R extends 'number' ? number : boolean; + +interface ITreapMultiSet extends Iterable { + add: (...value: T[]) => this; + has: (value: T) => boolean; + delete: (value: T) => void; + + bisectLeft: (value: T) => number; + bisectRight: (value: T) => number; + + indexOf: (value: T) => number; + lastIndexOf: (value: T) => number; + + at: (index: number) => T | undefined; + first: () => T | undefined; + last: () => T | undefined; + + lower: (value: T) => T | undefined; + higher: (value: T) => T | undefined; + floor: (value: T) => T | undefined; + ceil: (value: T) => T | undefined; + + shift: () => T | undefined; + pop: (index?: number) => T | undefined; + + count: (value: T) => number; + + keys: () => IterableIterator; + values: () => IterableIterator; + rvalues: () => IterableIterator; + entries: () => IterableIterator<[number, T]>; + + readonly size: number; +} + +class TreapNode { + value: T; + count: number; + size: number; + priority: number; + left: TreapNode | null; + right: TreapNode | null; + + constructor(value: T) { + this.value = value; + this.count = 1; + this.size = 1; + this.priority = Math.random(); + this.left = null; + this.right = null; + } + + static getSize(node: TreapNode | null): number { + return node?.size ?? 0; + } + + static getFac(node: TreapNode | null): number { + return node?.priority ?? 0; + } + + pushUp(): void { + let tmp = this.count; + tmp += TreapNode.getSize(this.left); + tmp += TreapNode.getSize(this.right); + this.size = tmp; + } + + rotateRight(): TreapNode { + // eslint-disable-next-line @typescript-eslint/no-this-alias + let node: TreapNode = this; + const left = node.left; + node.left = left?.right ?? null; + left && (left.right = node); + left && (node = left); + node.right?.pushUp(); + node.pushUp(); + return node; + } + + rotateLeft(): TreapNode { + // eslint-disable-next-line @typescript-eslint/no-this-alias + let node: TreapNode = this; + const right = node.right; + node.right = right?.left ?? null; + right && (right.left = node); + right && (node = right); + node.left?.pushUp(); + node.pushUp(); + return node; + } +} + +class TreapMultiSet implements ITreapMultiSet { + private readonly root: TreapNode; + private readonly compareFn: CompareFunction; + private readonly leftBound: T; + private readonly rightBound: T; + + constructor(compareFn?: CompareFunction); + constructor(compareFn: CompareFunction, leftBound: T, rightBound: T); + constructor( + compareFn: CompareFunction = (a: any, b: any) => a - b, + leftBound: any = -Infinity, + rightBound: any = Infinity, + ) { + this.root = new TreapNode(rightBound); + this.root.priority = Infinity; + this.root.left = new TreapNode(leftBound); + this.root.left.priority = -Infinity; + this.root.pushUp(); + + this.leftBound = leftBound; + this.rightBound = rightBound; + this.compareFn = compareFn; + } + + get size(): number { + return this.root.size - 2; + } + + get height(): number { + const getHeight = (node: TreapNode | null): number => { + if (node == null) return 0; + return 1 + Math.max(getHeight(node.left), getHeight(node.right)); + }; + + return getHeight(this.root); + } + + /** + * + * @complexity `O(logn)` + * @description Returns true if value is a member. + */ + has(value: T): boolean { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): boolean => { + if (node == null) return false; + if (compare(node.value, value) === 0) return true; + if (compare(node.value, value) < 0) return dfs(node.right, value); + return dfs(node.left, value); + }; + + return dfs(this.root, value); + } + + /** + * + * @complexity `O(logn)` + * @description Add value to sorted set. + */ + add(...values: T[]): this { + const compare = this.compareFn; + const dfs = ( + node: TreapNode | null, + value: T, + parent: TreapNode, + direction: 'left' | 'right', + ): void => { + if (node == null) return; + if (compare(node.value, value) === 0) { + node.count++; + node.pushUp(); + } else if (compare(node.value, value) > 0) { + if (node.left) { + dfs(node.left, value, node, 'left'); + } else { + node.left = new TreapNode(value); + node.pushUp(); + } + + if (TreapNode.getFac(node.left) > node.priority) { + parent[direction] = node.rotateRight(); + } + } else if (compare(node.value, value) < 0) { + if (node.right) { + dfs(node.right, value, node, 'right'); + } else { + node.right = new TreapNode(value); + node.pushUp(); + } + + if (TreapNode.getFac(node.right) > node.priority) { + parent[direction] = node.rotateLeft(); + } + } + parent.pushUp(); + }; + + values.forEach(value => dfs(this.root.left, value, this.root, 'left')); + return this; + } + + /** + * + * @complexity `O(logn)` + * @description Remove value from sorted set if it is a member. + * If value is not a member, do nothing. + */ + delete(value: T): void { + const compare = this.compareFn; + const dfs = ( + node: TreapNode | null, + value: T, + parent: TreapNode, + direction: 'left' | 'right', + ): void => { + if (node == null) return; + + if (compare(node.value, value) === 0) { + if (node.count > 1) { + node.count--; + node?.pushUp(); + } else if (node.left == null && node.right == null) { + parent[direction] = null; + } else { + // 旋到根节点 + if ( + node.right == null || + TreapNode.getFac(node.left) > TreapNode.getFac(node.right) + ) { + parent[direction] = node.rotateRight(); + dfs(parent[direction]?.right ?? null, value, parent[direction]!, 'right'); + } else { + parent[direction] = node.rotateLeft(); + dfs(parent[direction]?.left ?? null, value, parent[direction]!, 'left'); + } + } + } else if (compare(node.value, value) > 0) { + dfs(node.left, value, node, 'left'); + } else if (compare(node.value, value) < 0) { + dfs(node.right, value, node, 'right'); + } + + parent?.pushUp(); + }; + + dfs(this.root.left, value, this.root, 'left'); + } + + /** + * + * @complexity `O(logn)` + * @description Returns an index to insert value in the sorted set. + * If the value is already present, the insertion point will be before (to the left of) any existing values. + */ + bisectLeft(value: T): number { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): number => { + if (node == null) return 0; + + if (compare(node.value, value) === 0) { + return TreapNode.getSize(node.left); + } else if (compare(node.value, value) > 0) { + return dfs(node.left, value); + } else if (compare(node.value, value) < 0) { + return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; + } + + return 0; + }; + + return dfs(this.root, value) - 1; + } + + /** + * + * @complexity `O(logn)` + * @description Returns an index to insert value in the sorted set. + * If the value is already present, the insertion point will be before (to the right of) any existing values. + */ + bisectRight(value: T): number { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): number => { + if (node == null) return 0; + + if (compare(node.value, value) === 0) { + return TreapNode.getSize(node.left) + node.count; + } else if (compare(node.value, value) > 0) { + return dfs(node.left, value); + } else if (compare(node.value, value) < 0) { + return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; + } + + return 0; + }; + return dfs(this.root, value) - 1; + } + + /** + * + * @complexity `O(logn)` + * @description Returns the index of the first occurrence of a value in the set, or -1 if it is not present. + */ + indexOf(value: T): number { + const compare = this.compareFn; + let isExist = false; + + const dfs = (node: TreapNode | null, value: T): number => { + if (node == null) return 0; + + if (compare(node.value, value) === 0) { + isExist = true; + return TreapNode.getSize(node.left); + } else if (compare(node.value, value) > 0) { + return dfs(node.left, value); + } else if (compare(node.value, value) < 0) { + return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; + } + + return 0; + }; + const res = dfs(this.root, value) - 1; + return isExist ? res : -1; + } + + /** + * + * @complexity `O(logn)` + * @description Returns the index of the last occurrence of a value in the set, or -1 if it is not present. + */ + lastIndexOf(value: T): number { + const compare = this.compareFn; + let isExist = false; + + const dfs = (node: TreapNode | null, value: T): number => { + if (node == null) return 0; + + if (compare(node.value, value) === 0) { + isExist = true; + return TreapNode.getSize(node.left) + node.count - 1; + } else if (compare(node.value, value) > 0) { + return dfs(node.left, value); + } else if (compare(node.value, value) < 0) { + return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; + } + + return 0; + }; + + const res = dfs(this.root, value) - 1; + return isExist ? res : -1; + } + + /** + * + * @complexity `O(logn)` + * @description Returns the item located at the specified index. + * @param index The zero-based index of the desired code unit. A negative index will count back from the last item. + */ + at(index: number): T | undefined { + if (index < 0) index += this.size; + if (index < 0 || index >= this.size) return undefined; + + const dfs = (node: TreapNode | null, rank: number): T | undefined => { + if (node == null) return undefined; + + if (TreapNode.getSize(node.left) >= rank) { + return dfs(node.left, rank); + } else if (TreapNode.getSize(node.left) + node.count >= rank) { + return node.value; + } else { + return dfs(node.right, rank - TreapNode.getSize(node.left) - node.count); + } + }; + + const res = dfs(this.root, index + 2); + return ([this.leftBound, this.rightBound] as any[]).includes(res) ? undefined : res; + } + + /** + * + * @complexity `O(logn)` + * @description Find and return the element less than `val`, return `undefined` if no such element found. + */ + lower(value: T): T | undefined { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): T | undefined => { + if (node == null) return undefined; + if (compare(node.value, value) >= 0) return dfs(node.left, value); + + const tmp = dfs(node.right, value); + if (tmp == null || compare(node.value, tmp) > 0) { + return node.value; + } else { + return tmp; + } + }; + + const res = dfs(this.root, value) as any; + return res === this.leftBound ? undefined : res; + } + + /** + * + * @complexity `O(logn)` + * @description Find and return the element greater than `val`, return `undefined` if no such element found. + */ + higher(value: T): T | undefined { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): T | undefined => { + if (node == null) return undefined; + if (compare(node.value, value) <= 0) return dfs(node.right, value); + + const tmp = dfs(node.left, value); + + if (tmp == null || compare(node.value, tmp) < 0) { + return node.value; + } else { + return tmp; + } + }; + + const res = dfs(this.root, value) as any; + return res === this.rightBound ? undefined : res; + } + + /** + * + * @complexity `O(logn)` + * @description Find and return the element less than or equal to `val`, return `undefined` if no such element found. + */ + floor(value: T): T | undefined { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): T | undefined => { + if (node == null) return undefined; + if (compare(node.value, value) === 0) return node.value; + if (compare(node.value, value) >= 0) return dfs(node.left, value); + + const tmp = dfs(node.right, value); + if (tmp == null || compare(node.value, tmp) > 0) { + return node.value; + } else { + return tmp; + } + }; + + const res = dfs(this.root, value) as any; + return res === this.leftBound ? undefined : res; + } + + /** + * + * @complexity `O(logn)` + * @description Find and return the element greater than or equal to `val`, return `undefined` if no such element found. + */ + ceil(value: T): T | undefined { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): T | undefined => { + if (node == null) return undefined; + if (compare(node.value, value) === 0) return node.value; + if (compare(node.value, value) <= 0) return dfs(node.right, value); + + const tmp = dfs(node.left, value); + + if (tmp == null || compare(node.value, tmp) < 0) { + return node.value; + } else { + return tmp; + } + }; + + const res = dfs(this.root, value) as any; + return res === this.rightBound ? undefined : res; + } + + /** + * @complexity `O(logn)` + * @description + * Returns the last element from set. + * If the set is empty, undefined is returned. + */ + first(): T | undefined { + const iter = this.inOrder(); + iter.next(); + const res = iter.next().value; + return res === this.rightBound ? undefined : res; + } + + /** + * @complexity `O(logn)` + * @description + * Returns the last element from set. + * If the set is empty, undefined is returned . + */ + last(): T | undefined { + const iter = this.reverseInOrder(); + iter.next(); + const res = iter.next().value; + return res === this.leftBound ? undefined : res; + } + + /** + * @complexity `O(logn)` + * @description + * Removes the first element from an set and returns it. + * If the set is empty, undefined is returned and the set is not modified. + */ + shift(): T | undefined { + const first = this.first(); + if (first === undefined) return undefined; + this.delete(first); + return first; + } + + /** + * @complexity `O(logn)` + * @description + * Removes the last element from an set and returns it. + * If the set is empty, undefined is returned and the set is not modified. + */ + pop(index?: number): T | undefined { + if (index == null) { + const last = this.last(); + if (last === undefined) return undefined; + this.delete(last); + return last; + } + + const toDelete = this.at(index); + if (toDelete == null) return; + this.delete(toDelete); + return toDelete; + } + + /** + * + * @complexity `O(logn)` + * @description + * Returns number of occurrences of value in the sorted set. + */ + count(value: T): number { + const compare = this.compareFn; + const dfs = (node: TreapNode | null, value: T): number => { + if (node == null) return 0; + if (compare(node.value, value) === 0) return node.count; + if (compare(node.value, value) < 0) return dfs(node.right, value); + return dfs(node.left, value); + }; + + return dfs(this.root, value); + } + + *[Symbol.iterator](): Generator { + yield* this.values(); + } + + /** + * @description + * Returns an iterable of keys in the set. + */ + *keys(): Generator { + yield* this.values(); + } + + /** + * @description + * Returns an iterable of values in the set. + */ + *values(): Generator { + const iter = this.inOrder(); + iter.next(); + const steps = this.size; + for (let _ = 0; _ < steps; _++) { + yield iter.next().value; + } + } + + /** + * @description + * Returns a generator for reversed order traversing the set. + */ + *rvalues(): Generator { + const iter = this.reverseInOrder(); + iter.next(); + const steps = this.size; + for (let _ = 0; _ < steps; _++) { + yield iter.next().value; + } + } + + /** + * @description + * Returns an iterable of key, value pairs for every entry in the set. + */ + *entries(): IterableIterator<[number, T]> { + const iter = this.inOrder(); + iter.next(); + const steps = this.size; + for (let i = 0; i < steps; i++) { + yield [i, iter.next().value]; + } + } + + private *inOrder(root: TreapNode | null = this.root): Generator { + if (root == null) return; + yield* this.inOrder(root.left); + const count = root.count; + for (let _ = 0; _ < count; _++) { + yield root.value; + } + yield* this.inOrder(root.right); + } + + private *reverseInOrder(root: TreapNode | null = this.root): Generator { + if (root == null) return; + yield* this.reverseInOrder(root.right); + const count = root.count; + for (let _ = 0; _ < count; _++) { + yield root.value; + } + yield* this.reverseInOrder(root.left); + } +} +``` + + + + + diff --git a/solution/0400-0499/0480.Sliding Window Median/README_EN.md b/solution/0400-0499/0480.Sliding Window Median/README_EN.md index ccb7d96d9ecc3..51aec94e345d2 100644 --- a/solution/0400-0499/0480.Sliding Window Median/README_EN.md +++ b/solution/0400-0499/0480.Sliding Window Median/README_EN.md @@ -36,7 +36,7 @@ tags:
 Input: nums = [1,3,-1,-3,5,3,6,7], k = 3
 Output: [1.00000,-1.00000,-1.00000,3.00000,5.00000,6.00000]
-Explanation: 
+Explanation:
 Window position                Median
 ---------------                -----
 [1  3  -1] -3  5  3  6  7        1
@@ -68,7 +68,29 @@ Window position                Median
 
 
 
-### Solution 1
+### Solution 1: Dual Priority Queues (Min-Heap and Max-Heap) + Lazy Deletion
+
+We can use two priority queues (min-heap and max-heap) to maintain the elements in the current window. One priority queue stores the smaller half of the elements, and the other priority queue stores the larger half of the elements. This way, the median of the current window is either the average of the top elements of the two heaps or one of the top elements.
+
+We design a class $\textit{MedianFinder}$ to maintain the elements in the current window. This class includes the following methods:
+
+-   `add_num(num)`: Adds $\textit{num}$ to the current window.
+-   `find_median()`: Returns the median of the elements in the current window.
+-   `remove_num(num)`: Removes $\textit{num}$ from the current window.
+-   `prune(pq)`: If the top element of the heap is in the lazy deletion dictionary $\textit{delayed}$, it pops the top element from the heap and decrements its lazy deletion count. If the lazy deletion count of the element becomes zero, it removes the element from the lazy deletion dictionary.
+-   `rebalance()`: If the number of elements in the smaller half exceeds the number of elements in the larger half by $2$, it moves the top element of the larger half to the smaller half. If the number of elements in the smaller half is less than the number of elements in the larger half, it moves the top element of the larger half to the smaller half.
+
+In the `add_num(num)` method, we first consider adding $\textit{num}$ to the smaller half. If $\textit{num}$ is greater than the top element of the larger half, we add $\textit{num}$ to the larger half. Then we call the `rebalance()` method to ensure that the size difference between the two priority queues does not exceed $1$.
+
+In the `remove_num(num)` method, we increment the lazy deletion count of $\textit{num}$. Then we compare $\textit{num}$ with the top element of the smaller half. If $\textit{num}$ is less than or equal to the top element of the smaller half, we update the size of the smaller half and call the `prune()` method to ensure that the top element of the smaller half is not in the lazy deletion dictionary. Otherwise, we update the size of the larger half and call the `prune()` method to ensure that the top element of the larger half is not in the lazy deletion dictionary.
+
+In the `find_median()` method, if the current window size is odd, we return the top element of the smaller half; otherwise, we return the average of the top elements of the smaller half and the larger half.
+
+In the `prune(pq)` method, if the top element of the heap is in the lazy deletion dictionary, it pops the top element from the heap and decrements its lazy deletion count. If the lazy deletion count of the element becomes zero, it removes the element from the lazy deletion dictionary.
+
+In the `rebalance()` method, if the number of elements in the smaller half exceeds the number of elements in the larger half by $2$, it moves the top element of the larger half to the smaller half. If the number of elements in the smaller half is less than the number of elements in the larger half, it moves the top element of the larger half to the smaller half.
+
+The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $\textit{nums}$.
 
 
 
@@ -431,4 +453,822 @@ func (h *hp) Pop() any {
 
 
 
+
+
+### Solution 2: Ordered Set
+
+We can use two ordered sets to maintain the elements in the current window. The ordered set $l$ stores the smaller half of the elements in the current window, and the ordered set $r$ stores the larger half of the elements.
+
+We traverse the array $\textit{nums}$. For each element $x$, we add it to the ordered set $r$, then move the smallest element in the ordered set $r$ to the ordered set $l$. If the size of the ordered set $l$ is greater than the size of the ordered set $r$ by more than $1$, we move the largest element in the ordered set $l$ to the ordered set $r$.
+
+If the total number of elements in the current window is $k$ and the size is odd, the maximum value in the ordered set $l$ is the median. If the size of the current window is even, the average of the maximum value in the ordered set $l$ and the minimum value in the ordered set $r$ is the median. Then, we remove the leftmost element of the window and continue traversing the array.
+
+The time complexity is $O(n \log k)$, and the space complexity is $O(k)$. Here, $n$ is the length of the array $\textit{nums}$.
+
+
+
+#### Python3
+
+```python
+from sortedcontainers import SortedList
+
+
+class Solution:
+    def medianSlidingWindow(self, nums: List[int], k: int) -> List[float]:
+        l = SortedList()
+        r = SortedList()
+        ans = []
+        for i, x in enumerate(nums):
+            r.add(x)
+            l.add(r.pop(0))
+            while len(l) - len(r) > 1:
+                r.add(l.pop())
+            j = i - k + 1
+            if j >= 0:
+                ans.append(l[-1] if k & 1 else (l[-1] + r[0]) / 2)
+                if nums[j] in l:
+                    l.remove(nums[j])
+                else:
+                    r.remove(nums[j])
+        return ans
+```
+
+#### Java
+
+```java
+class Solution {
+    public double[] medianSlidingWindow(int[] nums, int k) {
+        TreeMap l = new TreeMap<>();
+        TreeMap r = new TreeMap<>();
+        int n = nums.length;
+        double[] ans = new double[n - k + 1];
+        int lSize = 0, rSize = 0;
+        for (int i = 0; i < n; ++i) {
+            r.merge(nums[i], 1, Integer::sum);
+            int x = r.firstKey();
+            if (r.merge(x, -1, Integer::sum) == 0) {
+                r.remove(x);
+            }
+            l.merge(x, 1, Integer::sum);
+            ++lSize;
+            while (lSize - rSize > 1) {
+                x = l.lastKey();
+                if (l.merge(x, -1, Integer::sum) == 0) {
+                    l.remove(x);
+                }
+                r.merge(x, 1, Integer::sum);
+                --lSize;
+                ++rSize;
+            }
+            int j = i - k + 1;
+            if (j >= 0) {
+                ans[j] = k % 2 == 1 ? l.lastKey() : ((double) l.lastKey() + r.firstKey()) / 2;
+                if (l.containsKey(nums[j])) {
+                    if (l.merge(nums[j], -1, Integer::sum) == 0) {
+                        l.remove(nums[j]);
+                    }
+                    --lSize;
+                } else {
+                    if (r.merge(nums[j], -1, Integer::sum) == 0) {
+                        r.remove(nums[j]);
+                    }
+                    --rSize;
+                }
+            }
+        }
+        return ans;
+    }
+}
+```
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    vector medianSlidingWindow(vector& nums, int k) {
+        multiset l, r;
+        int n = nums.size();
+        vector ans;
+        for (int i = 0; i < n; ++i) {
+            r.insert(nums[i]);
+            l.insert(*r.begin());
+            r.erase(r.begin());
+            while (l.size() - r.size() > 1) {
+                r.insert(*l.rbegin());
+                l.erase(prev(l.end()));
+            }
+            int j = i - k + 1;
+            if (j >= 0) {
+                ans.push_back(k % 2 ? *l.rbegin() : ((double) *l.rbegin() + *r.begin()) / 2);
+                auto it = l.find(nums[j]);
+                if (it != l.end()) {
+                    l.erase(it);
+                } else {
+                    r.erase(r.find(nums[j]));
+                }
+            }
+        }
+        return ans;
+    }
+};
+```
+
+#### Go
+
+```go
+func medianSlidingWindow(nums []int, k int) (ans []float64) {
+	l := redblacktree.New[int, int]()
+	r := redblacktree.New[int, int]()
+	merge := func(st *redblacktree.Tree[int, int], x, v int) {
+		c, _ := st.Get(x)
+		if c+v == 0 {
+			st.Remove(x)
+		} else {
+			st.Put(x, c+v)
+		}
+	}
+	lSize, rSize := 0, 0
+	for i, x := range nums {
+		merge(r, x, 1)
+		x = r.Left().Key
+		merge(r, x, -1)
+		merge(l, x, 1)
+		lSize++
+		for lSize-rSize > 1 {
+			x = l.Right().Key
+			merge(l, x, -1)
+			merge(r, x, 1)
+			lSize--
+			rSize++
+		}
+		if j := i - k + 1; j >= 0 {
+			if k%2 == 1 {
+				ans = append(ans, float64(l.Right().Key))
+			} else {
+				ans = append(ans, float64(l.Right().Key+r.Left().Key)/2)
+			}
+			if x = nums[j]; x <= l.Right().Key {
+				merge(l, x, -1)
+				lSize--
+			} else {
+				merge(r, x, -1)
+				rSize--
+			}
+		}
+	}
+	return
+}
+```
+
+#### TypeScript
+
+```ts
+function medianSlidingWindow(nums: number[], k: number): number[] {
+    const l = new TreapMultiSet((a, b) => a - b);
+    const r = new TreapMultiSet((a, b) => a - b);
+    const n = nums.length;
+    const ans: number[] = [];
+    for (let i = 0; i < n; ++i) {
+        r.add(nums[i]);
+        l.add(r.shift()!);
+        while (l.size - r.size > 1) {
+            r.add(l.pop()!);
+        }
+        const j = i - k + 1;
+        if (j >= 0) {
+            ans[j] = k % 2 ? l.last()! : (l.last()! + r.first()!) / 2;
+            if (nums[j] <= l.last()!) {
+                l.delete(nums[j]);
+            } else {
+                r.delete(nums[j]);
+            }
+        }
+    }
+    return ans;
+}
+
+type CompareFunction = (
+    a: T,
+    b: T,
+) => R extends 'number' ? number : boolean;
+
+interface ITreapMultiSet extends Iterable {
+    add: (...value: T[]) => this;
+    has: (value: T) => boolean;
+    delete: (value: T) => void;
+
+    bisectLeft: (value: T) => number;
+    bisectRight: (value: T) => number;
+
+    indexOf: (value: T) => number;
+    lastIndexOf: (value: T) => number;
+
+    at: (index: number) => T | undefined;
+    first: () => T | undefined;
+    last: () => T | undefined;
+
+    lower: (value: T) => T | undefined;
+    higher: (value: T) => T | undefined;
+    floor: (value: T) => T | undefined;
+    ceil: (value: T) => T | undefined;
+
+    shift: () => T | undefined;
+    pop: (index?: number) => T | undefined;
+
+    count: (value: T) => number;
+
+    keys: () => IterableIterator;
+    values: () => IterableIterator;
+    rvalues: () => IterableIterator;
+    entries: () => IterableIterator<[number, T]>;
+
+    readonly size: number;
+}
+
+class TreapNode {
+    value: T;
+    count: number;
+    size: number;
+    priority: number;
+    left: TreapNode | null;
+    right: TreapNode | null;
+
+    constructor(value: T) {
+        this.value = value;
+        this.count = 1;
+        this.size = 1;
+        this.priority = Math.random();
+        this.left = null;
+        this.right = null;
+    }
+
+    static getSize(node: TreapNode | null): number {
+        return node?.size ?? 0;
+    }
+
+    static getFac(node: TreapNode | null): number {
+        return node?.priority ?? 0;
+    }
+
+    pushUp(): void {
+        let tmp = this.count;
+        tmp += TreapNode.getSize(this.left);
+        tmp += TreapNode.getSize(this.right);
+        this.size = tmp;
+    }
+
+    rotateRight(): TreapNode {
+        // eslint-disable-next-line @typescript-eslint/no-this-alias
+        let node: TreapNode = this;
+        const left = node.left;
+        node.left = left?.right ?? null;
+        left && (left.right = node);
+        left && (node = left);
+        node.right?.pushUp();
+        node.pushUp();
+        return node;
+    }
+
+    rotateLeft(): TreapNode {
+        // eslint-disable-next-line @typescript-eslint/no-this-alias
+        let node: TreapNode = this;
+        const right = node.right;
+        node.right = right?.left ?? null;
+        right && (right.left = node);
+        right && (node = right);
+        node.left?.pushUp();
+        node.pushUp();
+        return node;
+    }
+}
+
+class TreapMultiSet implements ITreapMultiSet {
+    private readonly root: TreapNode;
+    private readonly compareFn: CompareFunction;
+    private readonly leftBound: T;
+    private readonly rightBound: T;
+
+    constructor(compareFn?: CompareFunction);
+    constructor(compareFn: CompareFunction, leftBound: T, rightBound: T);
+    constructor(
+        compareFn: CompareFunction = (a: any, b: any) => a - b,
+        leftBound: any = -Infinity,
+        rightBound: any = Infinity,
+    ) {
+        this.root = new TreapNode(rightBound);
+        this.root.priority = Infinity;
+        this.root.left = new TreapNode(leftBound);
+        this.root.left.priority = -Infinity;
+        this.root.pushUp();
+
+        this.leftBound = leftBound;
+        this.rightBound = rightBound;
+        this.compareFn = compareFn;
+    }
+
+    get size(): number {
+        return this.root.size - 2;
+    }
+
+    get height(): number {
+        const getHeight = (node: TreapNode | null): number => {
+            if (node == null) return 0;
+            return 1 + Math.max(getHeight(node.left), getHeight(node.right));
+        };
+
+        return getHeight(this.root);
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns true if value is a member.
+     */
+    has(value: T): boolean {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): boolean => {
+            if (node == null) return false;
+            if (compare(node.value, value) === 0) return true;
+            if (compare(node.value, value) < 0) return dfs(node.right, value);
+            return dfs(node.left, value);
+        };
+
+        return dfs(this.root, value);
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Add value to sorted set.
+     */
+    add(...values: T[]): this {
+        const compare = this.compareFn;
+        const dfs = (
+            node: TreapNode | null,
+            value: T,
+            parent: TreapNode,
+            direction: 'left' | 'right',
+        ): void => {
+            if (node == null) return;
+            if (compare(node.value, value) === 0) {
+                node.count++;
+                node.pushUp();
+            } else if (compare(node.value, value) > 0) {
+                if (node.left) {
+                    dfs(node.left, value, node, 'left');
+                } else {
+                    node.left = new TreapNode(value);
+                    node.pushUp();
+                }
+
+                if (TreapNode.getFac(node.left) > node.priority) {
+                    parent[direction] = node.rotateRight();
+                }
+            } else if (compare(node.value, value) < 0) {
+                if (node.right) {
+                    dfs(node.right, value, node, 'right');
+                } else {
+                    node.right = new TreapNode(value);
+                    node.pushUp();
+                }
+
+                if (TreapNode.getFac(node.right) > node.priority) {
+                    parent[direction] = node.rotateLeft();
+                }
+            }
+            parent.pushUp();
+        };
+
+        values.forEach(value => dfs(this.root.left, value, this.root, 'left'));
+        return this;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Remove value from sorted set if it is a member.
+     * If value is not a member, do nothing.
+     */
+    delete(value: T): void {
+        const compare = this.compareFn;
+        const dfs = (
+            node: TreapNode | null,
+            value: T,
+            parent: TreapNode,
+            direction: 'left' | 'right',
+        ): void => {
+            if (node == null) return;
+
+            if (compare(node.value, value) === 0) {
+                if (node.count > 1) {
+                    node.count--;
+                    node?.pushUp();
+                } else if (node.left == null && node.right == null) {
+                    parent[direction] = null;
+                } else {
+                    // 旋到根节点
+                    if (
+                        node.right == null ||
+                        TreapNode.getFac(node.left) > TreapNode.getFac(node.right)
+                    ) {
+                        parent[direction] = node.rotateRight();
+                        dfs(parent[direction]?.right ?? null, value, parent[direction]!, 'right');
+                    } else {
+                        parent[direction] = node.rotateLeft();
+                        dfs(parent[direction]?.left ?? null, value, parent[direction]!, 'left');
+                    }
+                }
+            } else if (compare(node.value, value) > 0) {
+                dfs(node.left, value, node, 'left');
+            } else if (compare(node.value, value) < 0) {
+                dfs(node.right, value, node, 'right');
+            }
+
+            parent?.pushUp();
+        };
+
+        dfs(this.root.left, value, this.root, 'left');
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns an index to insert value in the sorted set.
+     * If the value is already present, the insertion point will be before (to the left of) any existing values.
+     */
+    bisectLeft(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                return TreapNode.getSize(node.left);
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+
+        return dfs(this.root, value) - 1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns an index to insert value in the sorted set.
+     * If the value is already present, the insertion point will be before (to the right of) any existing values.
+     */
+    bisectRight(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                return TreapNode.getSize(node.left) + node.count;
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+        return dfs(this.root, value) - 1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the index of the first occurrence of a value in the set, or -1 if it is not present.
+     */
+    indexOf(value: T): number {
+        const compare = this.compareFn;
+        let isExist = false;
+
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                isExist = true;
+                return TreapNode.getSize(node.left);
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+        const res = dfs(this.root, value) - 1;
+        return isExist ? res : -1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the index of the last occurrence of a value in the set, or -1 if it is not present.
+     */
+    lastIndexOf(value: T): number {
+        const compare = this.compareFn;
+        let isExist = false;
+
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                isExist = true;
+                return TreapNode.getSize(node.left) + node.count - 1;
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+
+        const res = dfs(this.root, value) - 1;
+        return isExist ? res : -1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the item located at the specified index.
+     * @param index The zero-based index of the desired code unit. A negative index will count back from the last item.
+     */
+    at(index: number): T | undefined {
+        if (index < 0) index += this.size;
+        if (index < 0 || index >= this.size) return undefined;
+
+        const dfs = (node: TreapNode | null, rank: number): T | undefined => {
+            if (node == null) return undefined;
+
+            if (TreapNode.getSize(node.left) >= rank) {
+                return dfs(node.left, rank);
+            } else if (TreapNode.getSize(node.left) + node.count >= rank) {
+                return node.value;
+            } else {
+                return dfs(node.right, rank - TreapNode.getSize(node.left) - node.count);
+            }
+        };
+
+        const res = dfs(this.root, index + 2);
+        return ([this.leftBound, this.rightBound] as any[]).includes(res) ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element less than `val`, return `undefined` if no such element found.
+     */
+    lower(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) >= 0) return dfs(node.left, value);
+
+            const tmp = dfs(node.right, value);
+            if (tmp == null || compare(node.value, tmp) > 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element greater than `val`, return `undefined` if no such element found.
+     */
+    higher(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) <= 0) return dfs(node.right, value);
+
+            const tmp = dfs(node.left, value);
+
+            if (tmp == null || compare(node.value, tmp) < 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element less than or equal to `val`, return `undefined` if no such element found.
+     */
+    floor(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) === 0) return node.value;
+            if (compare(node.value, value) >= 0) return dfs(node.left, value);
+
+            const tmp = dfs(node.right, value);
+            if (tmp == null || compare(node.value, tmp) > 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element greater than or equal to `val`, return `undefined` if no such element found.
+     */
+    ceil(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) === 0) return node.value;
+            if (compare(node.value, value) <= 0) return dfs(node.right, value);
+
+            const tmp = dfs(node.left, value);
+
+            if (tmp == null || compare(node.value, tmp) < 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Returns the last element from set.
+     * If the set is empty, undefined is returned.
+     */
+    first(): T | undefined {
+        const iter = this.inOrder();
+        iter.next();
+        const res = iter.next().value;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Returns the last element from set.
+     * If the set is empty, undefined is returned .
+     */
+    last(): T | undefined {
+        const iter = this.reverseInOrder();
+        iter.next();
+        const res = iter.next().value;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Removes the first element from an set and returns it.
+     * If the set is empty, undefined is returned and the set is not modified.
+     */
+    shift(): T | undefined {
+        const first = this.first();
+        if (first === undefined) return undefined;
+        this.delete(first);
+        return first;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Removes the last element from an set and returns it.
+     * If the set is empty, undefined is returned and the set is not modified.
+     */
+    pop(index?: number): T | undefined {
+        if (index == null) {
+            const last = this.last();
+            if (last === undefined) return undefined;
+            this.delete(last);
+            return last;
+        }
+
+        const toDelete = this.at(index);
+        if (toDelete == null) return;
+        this.delete(toDelete);
+        return toDelete;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description
+     * Returns number of occurrences of value in the sorted set.
+     */
+    count(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+            if (compare(node.value, value) === 0) return node.count;
+            if (compare(node.value, value) < 0) return dfs(node.right, value);
+            return dfs(node.left, value);
+        };
+
+        return dfs(this.root, value);
+    }
+
+    *[Symbol.iterator](): Generator {
+        yield* this.values();
+    }
+
+    /**
+     * @description
+     * Returns an iterable of keys in the set.
+     */
+    *keys(): Generator {
+        yield* this.values();
+    }
+
+    /**
+     * @description
+     * Returns an iterable of values in the set.
+     */
+    *values(): Generator {
+        const iter = this.inOrder();
+        iter.next();
+        const steps = this.size;
+        for (let _ = 0; _ < steps; _++) {
+            yield iter.next().value;
+        }
+    }
+
+    /**
+     * @description
+     * Returns a generator for reversed order traversing the set.
+     */
+    *rvalues(): Generator {
+        const iter = this.reverseInOrder();
+        iter.next();
+        const steps = this.size;
+        for (let _ = 0; _ < steps; _++) {
+            yield iter.next().value;
+        }
+    }
+
+    /**
+     * @description
+     * Returns an iterable of key, value pairs for every entry in the set.
+     */
+    *entries(): IterableIterator<[number, T]> {
+        const iter = this.inOrder();
+        iter.next();
+        const steps = this.size;
+        for (let i = 0; i < steps; i++) {
+            yield [i, iter.next().value];
+        }
+    }
+
+    private *inOrder(root: TreapNode | null = this.root): Generator {
+        if (root == null) return;
+        yield* this.inOrder(root.left);
+        const count = root.count;
+        for (let _ = 0; _ < count; _++) {
+            yield root.value;
+        }
+        yield* this.inOrder(root.right);
+    }
+
+    private *reverseInOrder(root: TreapNode | null = this.root): Generator {
+        if (root == null) return;
+        yield* this.reverseInOrder(root.right);
+        const count = root.count;
+        for (let _ = 0; _ < count; _++) {
+            yield root.value;
+        }
+        yield* this.reverseInOrder(root.left);
+    }
+}
+```
+
+
+
+
+
 
diff --git a/solution/0400-0499/0480.Sliding Window Median/Solution2.cpp b/solution/0400-0499/0480.Sliding Window Median/Solution2.cpp
new file mode 100644
index 0000000000000..19309934af9d3
--- /dev/null
+++ b/solution/0400-0499/0480.Sliding Window Median/Solution2.cpp	
@@ -0,0 +1,28 @@
+class Solution {
+public:
+    vector medianSlidingWindow(vector& nums, int k) {
+        multiset l, r;
+        int n = nums.size();
+        vector ans;
+        for (int i = 0; i < n; ++i) {
+            r.insert(nums[i]);
+            l.insert(*r.begin());
+            r.erase(r.begin());
+            while (l.size() - r.size() > 1) {
+                r.insert(*l.rbegin());
+                l.erase(prev(l.end()));
+            }
+            int j = i - k + 1;
+            if (j >= 0) {
+                ans.push_back(k % 2 ? *l.rbegin() : ((double) *l.rbegin() + *r.begin()) / 2);
+                auto it = l.find(nums[j]);
+                if (it != l.end()) {
+                    l.erase(it);
+                } else {
+                    r.erase(r.find(nums[j]));
+                }
+            }
+        }
+        return ans;
+    }
+};
diff --git a/solution/0400-0499/0480.Sliding Window Median/Solution2.go b/solution/0400-0499/0480.Sliding Window Median/Solution2.go
new file mode 100644
index 0000000000000..86160c2ca5e60
--- /dev/null
+++ b/solution/0400-0499/0480.Sliding Window Median/Solution2.go	
@@ -0,0 +1,42 @@
+func medianSlidingWindow(nums []int, k int) (ans []float64) {
+	l := redblacktree.New[int, int]()
+	r := redblacktree.New[int, int]()
+	merge := func(st *redblacktree.Tree[int, int], x, v int) {
+		c, _ := st.Get(x)
+		if c+v == 0 {
+			st.Remove(x)
+		} else {
+			st.Put(x, c+v)
+		}
+	}
+	lSize, rSize := 0, 0
+	for i, x := range nums {
+		merge(r, x, 1)
+		x = r.Left().Key
+		merge(r, x, -1)
+		merge(l, x, 1)
+		lSize++
+		for lSize-rSize > 1 {
+			x = l.Right().Key
+			merge(l, x, -1)
+			merge(r, x, 1)
+			lSize--
+			rSize++
+		}
+		if j := i - k + 1; j >= 0 {
+			if k%2 == 1 {
+				ans = append(ans, float64(l.Right().Key))
+			} else {
+				ans = append(ans, float64(l.Right().Key+r.Left().Key)/2)
+			}
+			if x = nums[j]; x <= l.Right().Key {
+				merge(l, x, -1)
+				lSize--
+			} else {
+				merge(r, x, -1)
+				rSize--
+			}
+		}
+	}
+	return
+}
diff --git a/solution/0400-0499/0480.Sliding Window Median/Solution2.java b/solution/0400-0499/0480.Sliding Window Median/Solution2.java
new file mode 100644
index 0000000000000..b83b70ae2f0ff
--- /dev/null
+++ b/solution/0400-0499/0480.Sliding Window Median/Solution2.java	
@@ -0,0 +1,43 @@
+class Solution {
+    public double[] medianSlidingWindow(int[] nums, int k) {
+        TreeMap l = new TreeMap<>();
+        TreeMap r = new TreeMap<>();
+        int n = nums.length;
+        double[] ans = new double[n - k + 1];
+        int lSize = 0, rSize = 0;
+        for (int i = 0; i < n; ++i) {
+            r.merge(nums[i], 1, Integer::sum);
+            int x = r.firstKey();
+            if (r.merge(x, -1, Integer::sum) == 0) {
+                r.remove(x);
+            }
+            l.merge(x, 1, Integer::sum);
+            ++lSize;
+            while (lSize - rSize > 1) {
+                x = l.lastKey();
+                if (l.merge(x, -1, Integer::sum) == 0) {
+                    l.remove(x);
+                }
+                r.merge(x, 1, Integer::sum);
+                --lSize;
+                ++rSize;
+            }
+            int j = i - k + 1;
+            if (j >= 0) {
+                ans[j] = k % 2 == 1 ? l.lastKey() : ((double) l.lastKey() + r.firstKey()) / 2;
+                if (l.containsKey(nums[j])) {
+                    if (l.merge(nums[j], -1, Integer::sum) == 0) {
+                        l.remove(nums[j]);
+                    }
+                    --lSize;
+                } else {
+                    if (r.merge(nums[j], -1, Integer::sum) == 0) {
+                        r.remove(nums[j]);
+                    }
+                    --rSize;
+                }
+            }
+        }
+        return ans;
+    }
+}
diff --git a/solution/0400-0499/0480.Sliding Window Median/Solution2.py b/solution/0400-0499/0480.Sliding Window Median/Solution2.py
new file mode 100644
index 0000000000000..389ee94665db9
--- /dev/null
+++ b/solution/0400-0499/0480.Sliding Window Median/Solution2.py	
@@ -0,0 +1,21 @@
+from sortedcontainers import SortedList
+
+
+class Solution:
+    def medianSlidingWindow(self, nums: List[int], k: int) -> List[float]:
+        l = SortedList()
+        r = SortedList()
+        ans = []
+        for i, x in enumerate(nums):
+            r.add(x)
+            l.add(r.pop(0))
+            while len(l) - len(r) > 1:
+                r.add(l.pop())
+            j = i - k + 1
+            if j >= 0:
+                ans.append(l[-1] if k & 1 else (l[-1] + r[0]) / 2)
+                if nums[j] in l:
+                    l.remove(nums[j])
+                else:
+                    r.remove(nums[j])
+        return ans
diff --git a/solution/0400-0499/0480.Sliding Window Median/Solution2.ts b/solution/0400-0499/0480.Sliding Window Median/Solution2.ts
new file mode 100644
index 0000000000000..8e84276a3c185
--- /dev/null
+++ b/solution/0400-0499/0480.Sliding Window Median/Solution2.ts	
@@ -0,0 +1,641 @@
+function medianSlidingWindow(nums: number[], k: number): number[] {
+    const l = new TreapMultiSet((a, b) => a - b);
+    const r = new TreapMultiSet((a, b) => a - b);
+    const n = nums.length;
+    const ans: number[] = [];
+    for (let i = 0; i < n; ++i) {
+        r.add(nums[i]);
+        l.add(r.shift()!);
+        while (l.size - r.size > 1) {
+            r.add(l.pop()!);
+        }
+        const j = i - k + 1;
+        if (j >= 0) {
+            ans[j] = k % 2 ? l.last()! : (l.last()! + r.first()!) / 2;
+            if (nums[j] <= l.last()!) {
+                l.delete(nums[j]);
+            } else {
+                r.delete(nums[j]);
+            }
+        }
+    }
+    return ans;
+}
+
+type CompareFunction = (
+    a: T,
+    b: T,
+) => R extends 'number' ? number : boolean;
+
+interface ITreapMultiSet extends Iterable {
+    add: (...value: T[]) => this;
+    has: (value: T) => boolean;
+    delete: (value: T) => void;
+
+    bisectLeft: (value: T) => number;
+    bisectRight: (value: T) => number;
+
+    indexOf: (value: T) => number;
+    lastIndexOf: (value: T) => number;
+
+    at: (index: number) => T | undefined;
+    first: () => T | undefined;
+    last: () => T | undefined;
+
+    lower: (value: T) => T | undefined;
+    higher: (value: T) => T | undefined;
+    floor: (value: T) => T | undefined;
+    ceil: (value: T) => T | undefined;
+
+    shift: () => T | undefined;
+    pop: (index?: number) => T | undefined;
+
+    count: (value: T) => number;
+
+    keys: () => IterableIterator;
+    values: () => IterableIterator;
+    rvalues: () => IterableIterator;
+    entries: () => IterableIterator<[number, T]>;
+
+    readonly size: number;
+}
+
+class TreapNode {
+    value: T;
+    count: number;
+    size: number;
+    priority: number;
+    left: TreapNode | null;
+    right: TreapNode | null;
+
+    constructor(value: T) {
+        this.value = value;
+        this.count = 1;
+        this.size = 1;
+        this.priority = Math.random();
+        this.left = null;
+        this.right = null;
+    }
+
+    static getSize(node: TreapNode | null): number {
+        return node?.size ?? 0;
+    }
+
+    static getFac(node: TreapNode | null): number {
+        return node?.priority ?? 0;
+    }
+
+    pushUp(): void {
+        let tmp = this.count;
+        tmp += TreapNode.getSize(this.left);
+        tmp += TreapNode.getSize(this.right);
+        this.size = tmp;
+    }
+
+    rotateRight(): TreapNode {
+        // eslint-disable-next-line @typescript-eslint/no-this-alias
+        let node: TreapNode = this;
+        const left = node.left;
+        node.left = left?.right ?? null;
+        left && (left.right = node);
+        left && (node = left);
+        node.right?.pushUp();
+        node.pushUp();
+        return node;
+    }
+
+    rotateLeft(): TreapNode {
+        // eslint-disable-next-line @typescript-eslint/no-this-alias
+        let node: TreapNode = this;
+        const right = node.right;
+        node.right = right?.left ?? null;
+        right && (right.left = node);
+        right && (node = right);
+        node.left?.pushUp();
+        node.pushUp();
+        return node;
+    }
+}
+
+class TreapMultiSet implements ITreapMultiSet {
+    private readonly root: TreapNode;
+    private readonly compareFn: CompareFunction;
+    private readonly leftBound: T;
+    private readonly rightBound: T;
+
+    constructor(compareFn?: CompareFunction);
+    constructor(compareFn: CompareFunction, leftBound: T, rightBound: T);
+    constructor(
+        compareFn: CompareFunction = (a: any, b: any) => a - b,
+        leftBound: any = -Infinity,
+        rightBound: any = Infinity,
+    ) {
+        this.root = new TreapNode(rightBound);
+        this.root.priority = Infinity;
+        this.root.left = new TreapNode(leftBound);
+        this.root.left.priority = -Infinity;
+        this.root.pushUp();
+
+        this.leftBound = leftBound;
+        this.rightBound = rightBound;
+        this.compareFn = compareFn;
+    }
+
+    get size(): number {
+        return this.root.size - 2;
+    }
+
+    get height(): number {
+        const getHeight = (node: TreapNode | null): number => {
+            if (node == null) return 0;
+            return 1 + Math.max(getHeight(node.left), getHeight(node.right));
+        };
+
+        return getHeight(this.root);
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns true if value is a member.
+     */
+    has(value: T): boolean {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): boolean => {
+            if (node == null) return false;
+            if (compare(node.value, value) === 0) return true;
+            if (compare(node.value, value) < 0) return dfs(node.right, value);
+            return dfs(node.left, value);
+        };
+
+        return dfs(this.root, value);
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Add value to sorted set.
+     */
+    add(...values: T[]): this {
+        const compare = this.compareFn;
+        const dfs = (
+            node: TreapNode | null,
+            value: T,
+            parent: TreapNode,
+            direction: 'left' | 'right',
+        ): void => {
+            if (node == null) return;
+            if (compare(node.value, value) === 0) {
+                node.count++;
+                node.pushUp();
+            } else if (compare(node.value, value) > 0) {
+                if (node.left) {
+                    dfs(node.left, value, node, 'left');
+                } else {
+                    node.left = new TreapNode(value);
+                    node.pushUp();
+                }
+
+                if (TreapNode.getFac(node.left) > node.priority) {
+                    parent[direction] = node.rotateRight();
+                }
+            } else if (compare(node.value, value) < 0) {
+                if (node.right) {
+                    dfs(node.right, value, node, 'right');
+                } else {
+                    node.right = new TreapNode(value);
+                    node.pushUp();
+                }
+
+                if (TreapNode.getFac(node.right) > node.priority) {
+                    parent[direction] = node.rotateLeft();
+                }
+            }
+            parent.pushUp();
+        };
+
+        values.forEach(value => dfs(this.root.left, value, this.root, 'left'));
+        return this;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Remove value from sorted set if it is a member.
+     * If value is not a member, do nothing.
+     */
+    delete(value: T): void {
+        const compare = this.compareFn;
+        const dfs = (
+            node: TreapNode | null,
+            value: T,
+            parent: TreapNode,
+            direction: 'left' | 'right',
+        ): void => {
+            if (node == null) return;
+
+            if (compare(node.value, value) === 0) {
+                if (node.count > 1) {
+                    node.count--;
+                    node?.pushUp();
+                } else if (node.left == null && node.right == null) {
+                    parent[direction] = null;
+                } else {
+                    // 旋到根节点
+                    if (
+                        node.right == null ||
+                        TreapNode.getFac(node.left) > TreapNode.getFac(node.right)
+                    ) {
+                        parent[direction] = node.rotateRight();
+                        dfs(parent[direction]?.right ?? null, value, parent[direction]!, 'right');
+                    } else {
+                        parent[direction] = node.rotateLeft();
+                        dfs(parent[direction]?.left ?? null, value, parent[direction]!, 'left');
+                    }
+                }
+            } else if (compare(node.value, value) > 0) {
+                dfs(node.left, value, node, 'left');
+            } else if (compare(node.value, value) < 0) {
+                dfs(node.right, value, node, 'right');
+            }
+
+            parent?.pushUp();
+        };
+
+        dfs(this.root.left, value, this.root, 'left');
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns an index to insert value in the sorted set.
+     * If the value is already present, the insertion point will be before (to the left of) any existing values.
+     */
+    bisectLeft(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                return TreapNode.getSize(node.left);
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+
+        return dfs(this.root, value) - 1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns an index to insert value in the sorted set.
+     * If the value is already present, the insertion point will be before (to the right of) any existing values.
+     */
+    bisectRight(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                return TreapNode.getSize(node.left) + node.count;
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+        return dfs(this.root, value) - 1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the index of the first occurrence of a value in the set, or -1 if it is not present.
+     */
+    indexOf(value: T): number {
+        const compare = this.compareFn;
+        let isExist = false;
+
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                isExist = true;
+                return TreapNode.getSize(node.left);
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+        const res = dfs(this.root, value) - 1;
+        return isExist ? res : -1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the index of the last occurrence of a value in the set, or -1 if it is not present.
+     */
+    lastIndexOf(value: T): number {
+        const compare = this.compareFn;
+        let isExist = false;
+
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+
+            if (compare(node.value, value) === 0) {
+                isExist = true;
+                return TreapNode.getSize(node.left) + node.count - 1;
+            } else if (compare(node.value, value) > 0) {
+                return dfs(node.left, value);
+            } else if (compare(node.value, value) < 0) {
+                return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count;
+            }
+
+            return 0;
+        };
+
+        const res = dfs(this.root, value) - 1;
+        return isExist ? res : -1;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Returns the item located at the specified index.
+     * @param index The zero-based index of the desired code unit. A negative index will count back from the last item.
+     */
+    at(index: number): T | undefined {
+        if (index < 0) index += this.size;
+        if (index < 0 || index >= this.size) return undefined;
+
+        const dfs = (node: TreapNode | null, rank: number): T | undefined => {
+            if (node == null) return undefined;
+
+            if (TreapNode.getSize(node.left) >= rank) {
+                return dfs(node.left, rank);
+            } else if (TreapNode.getSize(node.left) + node.count >= rank) {
+                return node.value;
+            } else {
+                return dfs(node.right, rank - TreapNode.getSize(node.left) - node.count);
+            }
+        };
+
+        const res = dfs(this.root, index + 2);
+        return ([this.leftBound, this.rightBound] as any[]).includes(res) ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element less than `val`, return `undefined` if no such element found.
+     */
+    lower(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) >= 0) return dfs(node.left, value);
+
+            const tmp = dfs(node.right, value);
+            if (tmp == null || compare(node.value, tmp) > 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element greater than `val`, return `undefined` if no such element found.
+     */
+    higher(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) <= 0) return dfs(node.right, value);
+
+            const tmp = dfs(node.left, value);
+
+            if (tmp == null || compare(node.value, tmp) < 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element less than or equal to `val`, return `undefined` if no such element found.
+     */
+    floor(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) === 0) return node.value;
+            if (compare(node.value, value) >= 0) return dfs(node.left, value);
+
+            const tmp = dfs(node.right, value);
+            if (tmp == null || compare(node.value, tmp) > 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description Find and return the element greater than or equal to `val`, return `undefined` if no such element found.
+     */
+    ceil(value: T): T | undefined {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): T | undefined => {
+            if (node == null) return undefined;
+            if (compare(node.value, value) === 0) return node.value;
+            if (compare(node.value, value) <= 0) return dfs(node.right, value);
+
+            const tmp = dfs(node.left, value);
+
+            if (tmp == null || compare(node.value, tmp) < 0) {
+                return node.value;
+            } else {
+                return tmp;
+            }
+        };
+
+        const res = dfs(this.root, value) as any;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Returns the last element from set.
+     * If the set is empty, undefined is returned.
+     */
+    first(): T | undefined {
+        const iter = this.inOrder();
+        iter.next();
+        const res = iter.next().value;
+        return res === this.rightBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Returns the last element from set.
+     * If the set is empty, undefined is returned .
+     */
+    last(): T | undefined {
+        const iter = this.reverseInOrder();
+        iter.next();
+        const res = iter.next().value;
+        return res === this.leftBound ? undefined : res;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Removes the first element from an set and returns it.
+     * If the set is empty, undefined is returned and the set is not modified.
+     */
+    shift(): T | undefined {
+        const first = this.first();
+        if (first === undefined) return undefined;
+        this.delete(first);
+        return first;
+    }
+
+    /**
+     * @complexity `O(logn)`
+     * @description
+     * Removes the last element from an set and returns it.
+     * If the set is empty, undefined is returned and the set is not modified.
+     */
+    pop(index?: number): T | undefined {
+        if (index == null) {
+            const last = this.last();
+            if (last === undefined) return undefined;
+            this.delete(last);
+            return last;
+        }
+
+        const toDelete = this.at(index);
+        if (toDelete == null) return;
+        this.delete(toDelete);
+        return toDelete;
+    }
+
+    /**
+     *
+     * @complexity `O(logn)`
+     * @description
+     * Returns number of occurrences of value in the sorted set.
+     */
+    count(value: T): number {
+        const compare = this.compareFn;
+        const dfs = (node: TreapNode | null, value: T): number => {
+            if (node == null) return 0;
+            if (compare(node.value, value) === 0) return node.count;
+            if (compare(node.value, value) < 0) return dfs(node.right, value);
+            return dfs(node.left, value);
+        };
+
+        return dfs(this.root, value);
+    }
+
+    *[Symbol.iterator](): Generator {
+        yield* this.values();
+    }
+
+    /**
+     * @description
+     * Returns an iterable of keys in the set.
+     */
+    *keys(): Generator {
+        yield* this.values();
+    }
+
+    /**
+     * @description
+     * Returns an iterable of values in the set.
+     */
+    *values(): Generator {
+        const iter = this.inOrder();
+        iter.next();
+        const steps = this.size;
+        for (let _ = 0; _ < steps; _++) {
+            yield iter.next().value;
+        }
+    }
+
+    /**
+     * @description
+     * Returns a generator for reversed order traversing the set.
+     */
+    *rvalues(): Generator {
+        const iter = this.reverseInOrder();
+        iter.next();
+        const steps = this.size;
+        for (let _ = 0; _ < steps; _++) {
+            yield iter.next().value;
+        }
+    }
+
+    /**
+     * @description
+     * Returns an iterable of key, value pairs for every entry in the set.
+     */
+    *entries(): IterableIterator<[number, T]> {
+        const iter = this.inOrder();
+        iter.next();
+        const steps = this.size;
+        for (let i = 0; i < steps; i++) {
+            yield [i, iter.next().value];
+        }
+    }
+
+    private *inOrder(root: TreapNode | null = this.root): Generator {
+        if (root == null) return;
+        yield* this.inOrder(root.left);
+        const count = root.count;
+        for (let _ = 0; _ < count; _++) {
+            yield root.value;
+        }
+        yield* this.inOrder(root.right);
+    }
+
+    private *reverseInOrder(root: TreapNode | null = this.root): Generator {
+        if (root == null) return;
+        yield* this.reverseInOrder(root.right);
+        const count = root.count;
+        for (let _ = 0; _ < count; _++) {
+            yield root.value;
+        }
+        yield* this.reverseInOrder(root.left);
+    }
+}