feat: add solutions to lc problem: No.3013 (doocs#2248)

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

Author: Nothing-avil

solution/3000-3099/3013.Divide an Array Into Subarrays With Minimum Cost II/README.md

@@ -63,19 +63,330 @@
 <!-- tabs:start -->
 
 ```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
+	}
+}
 ```
 
 <!-- tabs:end -->