feat: add solutions to lc problem: No.1696

No.1696.Jump Game VI
chenxinxue521 · Dec 5, 2022 · 9b12342 · 9b12342
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diff --git a/solution/1600-1699/1696.Jump Game VI/README.md b/solution/1600-1699/1696.Jump Game VI/README.md
@@ -52,22 +52,108 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
+**方法一：动态规划 + 单调队列优化**
+
+我们定义 $f[i]$ 表示到达下标 $i$ 的最大得分，那么 $f[i]$ 的值可以从 $f[j]$ 转移而来，其中 $j$ 满足 $i - k \leq j \leq i - 1$。因此我们可以使用动态规划求解。
+
+状态转移方程为：
+
+$$
+f[i] = \max_{j \in [i - k, i - 1]} f[j] + nums[i]
+$$
+
+我们可以使用单调队列优化状态转移方程，具体做法是维护一个单调递减的队列，队列中存储的是下标 $j$，并且队列中的下标对应的 $f[j]$ 值是单调递减的。在进行状态转移时，我们只需要取出队首的下标 $j$，即可得到 $f[j]$ 的最大值，然后将 $f[i]$ 的值更新为 $f[j] + nums[i]$ 即可。
+
+时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为数组的长度。
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```python
-
+class Solution:
+    def maxResult(self, nums: List[int], k: int) -> int:
+        n = len(nums)
+        f = [0] * n
+        q = deque([0])
+        for i in range(n):
+            if i - q[0] > k:
+                q.popleft()
+            f[i] = nums[i] + f[q[0]]
+            while q and f[q[-1]] <= f[i]:
+                q.pop()
+            q.append(i)
+        return f[-1]
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class Solution {
+    public int maxResult(int[] nums, int k) {
+        int n = nums.length;
+        int[] f = new int[n];
+        Deque<Integer> q = new ArrayDeque<>();
+        q.offer(0);
+        for (int i = 0; i < n; ++i) {
+            if (i - q.peekFirst() > k) {
+                q.pollFirst();
+            }
+            f[i] = nums[i] + f[q.peekFirst()];
+            while (!q.isEmpty() && f[q.peekLast()] <= f[i]) {
+                q.pollLast();
+            }
+            q.offerLast(i);
+        }
+        return f[n - 1];
+    }
+}
+```
+
+### **C++**
+
+```cpp
+class Solution {
+public:
+    int maxResult(vector<int>& nums, int k) {
+        int n = nums.size();
+        int f[n];
+        f[0] = 0;
+        deque<int> q = {0};
+        for (int i = 0; i < n; ++i) {
+            if (i - q.front() > k) q.pop_front();
+            f[i] = nums[i] + f[q.front()];
+            while (!q.empty() && f[q.back()] <= f[i]) q.pop_back();
+            q.push_back(i);
+        }
+        return f[n - 1];
+    }
+};
+```
 
+### **Go**
+
+```go
+func maxResult(nums []int, k int) int {
+	n := len(nums)
+	f := make([]int, n)
+	q := []int{0}
+	for i, v := range nums {
+		if i-q[0] > k {
+			q = q[1:]
+		}
+		f[i] = v + f[q[0]]
+		for len(q) > 0 && f[q[len(q)-1]] <= f[i] {
+			q = q[:len(q)-1]
+		}
+		q = append(q, i)
+	}
+	return f[n-1]
+}
 ```
 
 ### **...**

diff --git a/solution/1600-1699/1696.Jump Game VI/README_EN.md b/solution/1600-1699/1696.Jump Game VI/README_EN.md
@@ -51,13 +51,85 @@
 ### **Python3**
 
 ```python
-
+class Solution:
+    def maxResult(self, nums: List[int], k: int) -> int:
+        n = len(nums)
+        f = [0] * n
+        q = deque([0])
+        for i in range(n):
+            if i - q[0] > k:
+                q.popleft()
+            f[i] = nums[i] + f[q[0]]
+            while q and f[q[-1]] <= f[i]:
+                q.pop()
+            q.append(i)
+        return f[-1]
 ```
 
 ### **Java**
 
 ```java
+class Solution {
+    public int maxResult(int[] nums, int k) {
+        int n = nums.length;
+        int[] f = new int[n];
+        Deque<Integer> q = new ArrayDeque<>();
+        q.offer(0);
+        for (int i = 0; i < n; ++i) {
+            if (i - q.peekFirst() > k) {
+                q.pollFirst();
+            }
+            f[i] = nums[i] + f[q.peekFirst()];
+            while (!q.isEmpty() && f[q.peekLast()] <= f[i]) {
+                q.pollLast();
+            }
+            q.offerLast(i);
+        }
+        return f[n - 1];
+    }
+}
+```
+
+### **C++**
+
+```cpp
+class Solution {
+public:
+    int maxResult(vector<int>& nums, int k) {
+        int n = nums.size();
+        int f[n];
+        f[0] = 0;
+        deque<int> q = {0};
+        for (int i = 0; i < n; ++i) {
+            if (i - q.front() > k) q.pop_front();
+            f[i] = nums[i] + f[q.front()];
+            while (!q.empty() && f[q.back()] <= f[i]) q.pop_back();
+            q.push_back(i);
+        }
+        return f[n - 1];
+    }
+};
+```
 
+### **Go**
+
+```go
+func maxResult(nums []int, k int) int {
+	n := len(nums)
+	f := make([]int, n)
+	q := []int{0}
+	for i, v := range nums {
+		if i-q[0] > k {
+			q = q[1:]
+		}
+		f[i] = v + f[q[0]]
+		for len(q) > 0 && f[q[len(q)-1]] <= f[i] {
+			q = q[:len(q)-1]
+		}
+		q = append(q, i)
+	}
+	return f[n-1]
+}
 ```
 
 ### **...**

diff --git a/solution/1600-1699/1696.Jump Game VI/Solution.cpp b/solution/1600-1699/1696.Jump Game VI/Solution.cpp
@@ -0,0 +1,16 @@
+class Solution {
+public:
+    int maxResult(vector<int>& nums, int k) {
+        int n = nums.size();
+        int f[n];
+        f[0] = 0;
+        deque<int> q = {0};
+        for (int i = 0; i < n; ++i) {
+            if (i - q.front() > k) q.pop_front();
+            f[i] = nums[i] + f[q.front()];
+            while (!q.empty() && f[q.back()] <= f[i]) q.pop_back();
+            q.push_back(i);
+        }
+        return f[n - 1];
+    }
+};
diff --git a/solution/1600-1699/1696.Jump Game VI/Solution.go b/solution/1600-1699/1696.Jump Game VI/Solution.go
@@ -0,0 +1,16 @@
+func maxResult(nums []int, k int) int {
+	n := len(nums)
+	f := make([]int, n)
+	q := []int{0}
+	for i, v := range nums {
+		if i-q[0] > k {
+			q = q[1:]
+		}
+		f[i] = v + f[q[0]]
+		for len(q) > 0 && f[q[len(q)-1]] <= f[i] {
+			q = q[:len(q)-1]
+		}
+		q = append(q, i)
+	}
+	return f[n-1]
+}
diff --git a/solution/1600-1699/1696.Jump Game VI/Solution.java b/solution/1600-1699/1696.Jump Game VI/Solution.java
@@ -0,0 +1,19 @@
+class Solution {
+    public int maxResult(int[] nums, int k) {
+        int n = nums.length;
+        int[] f = new int[n];
+        Deque<Integer> q = new ArrayDeque<>();
+        q.offer(0);
+        for (int i = 0; i < n; ++i) {
+            if (i - q.peekFirst() > k) {
+                q.pollFirst();
+            }
+            f[i] = nums[i] + f[q.peekFirst()];
+            while (!q.isEmpty() && f[q.peekLast()] <= f[i]) {
+                q.pollLast();
+            }
+            q.offerLast(i);
+        }
+        return f[n - 1];
+    }
+}
diff --git a/solution/1600-1699/1696.Jump Game VI/Solution.py b/solution/1600-1699/1696.Jump Game VI/Solution.py
@@ -0,0 +1,13 @@
+class Solution:
+    def maxResult(self, nums: List[int], k: int) -> int:
+        n = len(nums)
+        f = [0] * n
+        q = deque([0])
+        for i in range(n):
+            if i - q[0] > k:
+                q.popleft()
+            f[i] = nums[i] + f[q[0]]
+            while q and f[q[-1]] <= f[i]:
+                q.pop()
+            q.append(i)
+        return f[-1]