feat: add solutions to lc problem: No.0315

No.0315.Count of Smaller Numbers After Self

Author: yanglbme

solution/0300-0399/0315.Count of Smaller Numbers After Self/README.md

@@ -49,7 +49,7 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
-树状数组。
+**方法一：树状数组**
 
 树状数组，也称作“二叉索引树”（Binary Indexed Tree）或 Fenwick 树。 它可以高效地实现如下两个操作：
 
@@ -64,12 +64,16 @@
 
 解决方案是直接遍历数组，每个位置先求出 `query(a[i])`，然后再修改树状数组 `update(a[i], 1)` 即可。当数的范围比较大时，需要进行离散化，即先进行去重并排序，然后对每个数字进行编号。
 
+**方法二：线段树**
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+树状数组：
+
 ```python
 class BinaryIndexedTree:
     def __init__(self, n):
@@ -106,10 +110,73 @@ class Solution:
         return ans[::-1]
 ```
 
+线段树：
+
+```python
+class Node:
+    def __init__(self):
+        self.l = 0
+        self.r = 0
+        self.v = 0
+
+class SegmentTree:
+    def __init__(self, n):
+        self.tr = [Node() for _ in range(4 * n)]
+        self.build(1, 1, n)
+        
+    def build(self, u, l, r):
+        self.tr[u].l = l
+        self.tr[u].r = r
+        if l == r:
+            return
+        mid = (l + r) >> 1
+        self.build(u << 1, l, mid)
+        self.build(u << 1 | 1, mid + 1, r)
+
+    def modify(self, u, x, v):
+        if self.tr[u].l == x and self.tr[u].r == x:
+            self.tr[u].v += v
+            return
+        mid = (self.tr[u].l + self.tr[u].r) >> 1
+        if x <= mid:
+            self.modify(u << 1, x, v)
+        else:
+            self.modify(u << 1 | 1, x, v)
+        self.pushup(u)
+    
+    def pushup(self, u):
+        self.tr[u].v = self.tr[u << 1].v + self.tr[u << 1 | 1].v
+
+    def query(self, u, l, r):
+        if self.tr[u].l >= l and self.tr[u].r <= r:
+            return self.tr[u].v
+        mid = (self.tr[u].l + self.tr[u].r) >> 1
+        v = 0
+        if l <= mid:
+            v += self.query(u << 1, l, r)
+        if r > mid:
+            v += self.query(u << 1 | 1, l, r)
+        return v
+
+class Solution:
+    def countSmaller(self, nums: List[int]) -> List[int]:
+        s = sorted(set(nums))
+        m = {v: i for i, v in enumerate(s, 1)}
+        tree = SegmentTree(len(s))
+        ans = []
+        for v in nums[::-1]:
+            x = m[v]
+            ans.append(tree.query(1, 1, x - 1))
+            tree.modify(1, x, 1)
+        return ans[::-1]
+```
+
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+树状数组：
+
 ```java
 class Solution {
     public List<Integer> countSmaller(int[] nums) {
@@ -166,8 +233,100 @@ class BinaryIndexedTree {
 }
 ```
 
+线段树：
+
+```java
+class Solution {
+    public List<Integer> countSmaller(int[] nums) {
+        Set<Integer> s = new HashSet<>();
+        for (int v : nums) {
+            s.add(v);
+        }
+        List<Integer> alls = new ArrayList<>(s);
+        alls.sort(Comparator.comparingInt(a -> a));
+        int n = alls.size();
+        Map<Integer, Integer> m = new HashMap<>(n);
+        for (int i = 0; i < n; ++i) {
+            m.put(alls.get(i), i + 1);
+        }
+        SegmentTree tree = new SegmentTree(n);
+        LinkedList<Integer> ans = new LinkedList<>();
+        for (int i = nums.length - 1; i >= 0; --i) {
+            int x = m.get(nums[i]);
+            tree.modify(1, x, 1);
+            ans.addFirst(tree.query(1, 1, x - 1));
+        }
+        return ans;
+    }
+}
+
+class Node {
+    int l;
+    int r;
+    int v;
+}
+
+class SegmentTree {
+    private Node[] tr;
+
+    public SegmentTree(int n) {
+        tr = new Node[4 * n];
+        for (int i = 0; i < tr.length; ++i) {
+            tr[i] = new Node();
+        }
+        build(1, 1, n);
+    }
+
+    public void build(int u, int l, int r) {
+        tr[u].l = l;
+        tr[u].r = r;
+        if (l == r) {
+            return;
+        }
+        int mid = (l + r) >> 1;
+        build(u << 1, l, mid);
+        build(u << 1 | 1, mid + 1, r);
+    }
+
+    public void modify(int u, int x, int v) {
+        if (tr[u].l == x && tr[u].r == x) {
+            tr[u].v += v;
+            return;
+        }
+        int mid = (tr[u].l + tr[u].r) >> 1;
+        if (x <= mid) {
+            modify(u << 1, x, v);
+        } else {
+            modify(u << 1 | 1, x, v);
+        }
+        pushup(u);
+    }
+
+    public void pushup(int u) {
+        tr[u].v = tr[u << 1].v + tr[u << 1 | 1].v;
+    }
+
+    public int query(int u, int l, int r) {
+        if (tr[u].l >= l && tr[u].r <= r) {
+            return tr[u].v;
+        }
+        int mid = (tr[u].l + tr[u].r) >> 1;
+        int v = 0;
+        if (l <= mid) {
+            v += query(u << 1, l, r);
+        }
+        if (r > mid) {
+            v += query(u << 1 | 1, l, r);
+        }
+        return v;
+    }
+}
+```
+
 ### **C++**
 
+树状数组：
+
 ```cpp
 class BinaryIndexedTree {
 public:
@@ -221,6 +380,83 @@ public:
 };
 ```
 
+线段树：
+
+```cpp
+class Node {
+public:
+    int l;
+    int r;
+    int v;
+};
+
+class SegmentTree {
+public:
+    vector<Node*> tr;
+
+    SegmentTree(int n) {
+        tr.resize(4 * n);
+        for (int i = 0; i < tr.size(); ++i) tr[i] = new Node();
+        build(1, 1, n);
+    }
+
+    void build(int u, int l, int r) {
+        tr[u]->l = l;
+        tr[u]->r = r;
+        if (l == r) return;
+        int mid = (l + r) >> 1;
+        build(u << 1, l, mid);
+        build(u << 1 | 1, mid + 1, r);
+    }
+
+    void modify(int u, int x, int v) {
+        if (tr[u]->l == x && tr[u]->r == x)
+        {
+            tr[u]->v += v;
+            return;
+        }
+        int mid = (tr[u]->l + tr[u]->r) >> 1;
+        if (x <= mid) modify(u << 1, x, v);
+        else modify(u << 1 | 1, x, v);
+        pushup(u);
+    }
+
+    void pushup(int u) {
+        tr[u]->v = tr[u << 1]->v + tr[u << 1 | 1]->v;
+    }
+
+    int query(int u, int l, int r) {
+        if (tr[u]->l >= l && tr[u]->r <= r) return tr[u]->v;
+        int mid = (tr[u]->l + tr[u]->r) >> 1;
+        int v = 0;
+        if (l <= mid) v += query(u << 1, l, r);
+        if (r > mid) v += query(u << 1 | 1, l, r);
+        return v;
+    }
+};
+
+class Solution {
+public:
+    vector<int> countSmaller(vector<int>& nums) {
+        unordered_set<int> s(nums.begin(), nums.end());
+        vector<int> alls(s.begin(), s.end());
+        sort(alls.begin(), alls.end());
+        unordered_map<int, int> m;
+        int n = alls.size();
+        for (int i = 0; i < n; ++i) m[alls[i]] = i + 1;
+        SegmentTree* tree = new SegmentTree(n);
+        vector<int> ans(nums.size());
+        for (int i = nums.size() - 1; i >= 0; --i)
+        {
+            int x = m[nums[i]];
+            tree->modify(1, x, 1);
+            ans[i] = tree->query(1, 1, x - 1);
+        }
+        return ans;
+    }
+};
+```
+
 ### **Go**
 
 ```go