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No.3013.Divide an Array Into Subarrays With Minimum Cost II #2248

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Original file line number Diff line number Diff line change
Expand Up @@ -63,19 +63,330 @@
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```python
from sortedcontainers import SortedList


class Solution:
def minimumCost(self, nums: List[int], k: int, dist: int) -> int:
n = len(nums)

sl = SortedList()
y = nums[0]
ans = float("inf")
i = 1
running_sum = 0

for j in range(1, n):
pos = bisect.bisect_left(sl, nums[j])
sl.add(nums[j])

if pos < k - 1:
running_sum += nums[j]
if len(sl) > k - 1:
running_sum -= sl[k - 1]

while j - i > dist:
removed_pos = sl.index(nums[i])
removed_element = nums[i]
sl.remove(removed_element)

if removed_pos < k - 1:
running_sum -= removed_element
if len(sl) >= k - 1:
running_sum += sl[k - 2]
i += 1

if j - i + 1 >= k - 1:
ans = min(ans, running_sum)

return ans + y
```

```java

class Solution {
public long minimumCost(int[] nums, int k, int dist) {
long result = Long.MAX_VALUE, sum = 0L;
int n = nums.length;
TreeSet<Integer> set1
= new TreeSet<>((a, b) -> nums[a] == nums[b] ? a - b : nums[a] - nums[b]);
TreeSet<Integer> set2
= new TreeSet<>((a, b) -> nums[a] == nums[b] ? a - b : nums[a] - nums[b]);
for (int i = 1; i < n; i++) {
set1.add(i);
sum += nums[i];
if (set1.size() >= k) {
int x = set1.pollLast();
sum -= nums[x];
set2.add(x);
}
if (i - dist > 0) {
result = Math.min(result, sum);
int temp = i - dist;
if (set1.contains(temp)) {
set1.remove(temp);
sum -= nums[temp];
if (set2.size() > 0) {
int y = set2.pollFirst();
sum += nums[y];
set1.add(y);
}
} else {
set2.remove(i - dist);
}
}
}
return result + nums[0];
}
}
```

```cpp
class Solution {
public:
long long minimumCost(vector<int>& nums, int k, int dist) {
multiset<int> sml, big;
int sz = dist + 1;
long long sum = 0, ans = 0;
for (int i = 1; i <= sz; i++) {
sml.insert(nums[i]);
sum += nums[i];
}
while (sml.size() > k - 1) {
big.insert(*sml.rbegin());
sum -= *sml.rbegin();
sml.erase(sml.find(*sml.rbegin()));
}
ans = sum;
for (int i = sz + 1; i < nums.size(); i++) {
sum += nums[i];
sml.insert(nums[i]);
if (big.find(nums[i - sz]) != big.end()) {
big.erase(big.find(nums[i - sz]));
} else {
sum -= nums[i - sz];
sml.erase(sml.find(nums[i - sz]));
}

while (sml.size() > k - 1) {
sum -= *sml.rbegin();
big.insert(*sml.rbegin());
sml.erase(sml.find(*sml.rbegin()));
}
while (sml.size() < k - 1) {
sum += *big.begin();
sml.insert(*big.begin());
big.erase(big.begin());
}
while (!sml.empty() && !big.empty() && *sml.rbegin() > *big.begin()) {
sum -= *sml.rbegin() - *big.begin();
sml.insert(*big.begin());
big.insert(*sml.rbegin());
sml.erase(sml.find(*sml.rbegin()));
big.erase(big.begin());
}
ans = min(ans, sum);
}
int p = 0;
return nums[0] + ans;
}
};
```

```go
func minimumCost(nums []int, k int, dist int) int64 {
res := nums[0] + slices.Min(windowTopKSum(nums[1:], dist+1, k-1, true))
return int64(res)
}

func windowTopKSum(nums []int, windowSize, k int, min bool) []int {
n := len(nums)
ts := NewTopKSum(k, min)
res := []int{}
for right := 0; right < n; right++ {
ts.Add(nums[right])
if right >= windowSize {
ts.Discard(nums[right-windowSize])
}
if right >= windowSize-1 {
res = append(res, ts.Query())
}
}
return res
}

type TopKSum struct {
sum int
k int
in *Heap
out *Heap
dIn *Heap
dOut *Heap
counter map[int]int
}

func NewTopKSum(k int, min bool) *TopKSum {
var less func(a, b int) bool
if min {
less = func(a, b int) bool { return a < b }
} else {
less = func(a, b int) bool { return a > b }
}
return &TopKSum{
k: k,
in: NewHeap(less),
out: NewHeap(less),
dIn: NewHeap(less),
dOut: NewHeap(less),
counter: map[int]int{},
}
}

func (t *TopKSum) Query() int {
return t.sum
}

func (t *TopKSum) Add(x int) {
t.counter[x]++
t.in.Push(-x)
t.sum += x
t.modify()
}

func (t *TopKSum) Discard(x int) bool {
if t.counter[x] == 0 {
return false
}
t.counter[x]--
if t.in.Len() > 0 && -t.in.Top() == x {
t.sum -= x
t.in.Pop()
} else if t.in.Len() > 0 && -t.in.Top() > x {
t.sum -= x
t.dIn.Push(-x)
} else {
t.dOut.Push(x)
}
t.modify()
return true
}

func (t *TopKSum) SetK(k int) {
t.k = k
t.modify()
}

func (t *TopKSum) GetK() int {
return t.k
}

func (t *TopKSum) Len() int {
return t.in.Len() + t.out.Len() - t.dIn.Len() - t.dOut.Len()
}

func (t *TopKSum) Has(x int) bool {
return t.counter[x] > 0
}

func (t *TopKSum) modify() {
for t.out.Len() > 0 && (t.in.Len()-t.dIn.Len() < t.k) {
p := t.out.Pop()
if t.dOut.Len() > 0 && p == t.dOut.Top() {
t.dOut.Pop()
} else {
t.sum += p
t.in.Push(-p)
}
}

for t.in.Len()-t.dIn.Len() > t.k {
p := -t.in.Pop()
if t.dIn.Len() > 0 && p == -t.dIn.Top() {
t.dIn.Pop()
} else {
t.sum -= p
t.out.Push(p)
}
}

for t.dIn.Len() > 0 && t.in.Top() == t.dIn.Top() {
t.in.Pop()
t.dIn.Pop()
}
}

type H = int

func NewHeap(less func(a, b H) bool, nums ...H) *Heap {
nums = append(nums[:0:0], nums...)
heap := &Heap{less: less, data: nums}
heap.heapify()
return heap
}

type Heap struct {
data []H
less func(a, b H) bool
}

func (h *Heap) Push(value H) {
h.data = append(h.data, value)
h.pushUp(h.Len() - 1)
}

func (h *Heap) Pop() (value H) {
if h.Len() == 0 {
panic("heap is empty")
}

value = h.data[0]
h.data[0] = h.data[h.Len()-1]
h.data = h.data[:h.Len()-1]
h.pushDown(0)
return
}

func (h *Heap) Top() (value H) {
value = h.data[0]
return
}

func (h *Heap) Len() int { return len(h.data) }

func (h *Heap) heapify() {
n := h.Len()
for i := (n >> 1) - 1; i > -1; i-- {
h.pushDown(i)
}
}

func (h *Heap) pushUp(root int) {
for parent := (root - 1) >> 1; parent >= 0 && h.less(h.data[root], h.data[parent]); parent = (root - 1) >> 1 {
h.data[root], h.data[parent] = h.data[parent], h.data[root]
root = parent
}
}

func (h *Heap) pushDown(root int) {
n := h.Len()
for left := (root<<1 + 1); left < n; left = (root<<1 + 1) {
right := left + 1
minIndex := root

if h.less(h.data[left], h.data[minIndex]) {
minIndex = left
}

if right < n && h.less(h.data[right], h.data[minIndex]) {
minIndex = right
}

if minIndex == root {
return
}
h.data[root], h.data[minIndex] = h.data[minIndex], h.data[root]
root = minIndex
}
}
```

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