diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README.md b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README.md index 28c90291cd1d9..b458f00e64007 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README.md +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README.md @@ -57,20 +57,11 @@ **方法一：动态规划** -定义状态 $a$ 表示以当前元素作为正结尾的最大交替子数组和，状态 $b$ 表示以当前元素作为负结尾的最大交替子数组和。初始时 $a = nums[0]$，$b = -\infty$。 +我们定义 $f$ 表示以 $nums[i]$ 结尾的交替子数组的最大和，定义 $g$ 表示以 $-nums[i]$ 结尾的交替子数组的最大和，初始时 $f$ 和 $g$ 均为 $-\infty$。 -遍历数组，对于当前元素 $nums[i]$，有 +接下来，我们遍历数组 $nums$，对于位置 $i$，我们需要维护 $f$ 和 $g$ 的值，即 $f = \max(g, 0) + nums[i]$，而 $g = f - nums[i]$。答案即为所有 $f$ 和 $g$ 中的最大值。 -$$ -\begin{aligned} -a = \max(nums[i], b + nums[i]) \\ -b = a - nums[i] -\end{aligned} -$$ - -求出 $a$ 和 $b$ 后，将 $a$ 和 $b$ 中的最大值与当前最大交替子数组和进行比较，更新最大交替子数组和。 - -时间复杂度 $O(n)$，空间复杂度 $O(1)$。其中 $n$ 为数组长度。 +时间复杂度 $O(n)$，其中 $n$ 是数组 $nums$ 的长度。空间复杂度 $O(1)$。 @@ -81,11 +72,10 @@ $$ ```python class Solution: def maximumAlternatingSubarraySum(self, nums: List[int]) -> int: - ans = nums[0] - a, b = nums[0], -inf - for v in nums[1:]: - a, b = max(v, b + v), a - v - ans = max(ans, a, b) + ans = f = g = -inf + for x in nums: + f, g = max(g, 0) + x, f - x + ans = max(ans, f, g) return ans ``` @@ -96,13 +86,13 @@ class Solution: ```java class Solution { public long maximumAlternatingSubarraySum(int[] nums) { - long ans = nums[0]; - long a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.length; ++i) { - long c = a, d = b; - a = Math.max(nums[i], d + nums[i]); - b = c - nums[i]; - ans = Math.max(ans, Math.max(a, b)); + final long inf = 1L << 60; + long ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + long ff = Math.max(g, 0) + x; + g = f - x; + f = ff; + ans = Math.max(ans, Math.max(f, g)); } return ans; } @@ -112,18 +102,17 @@ class Solution { ### **C++** ```cpp -using ll = long long; - class Solution { public: long long maximumAlternatingSubarraySum(vector& nums) { - ll ans = nums[0]; - ll a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.size(); ++i) { - ll c = a, d = b; - a = max(1ll * nums[i], d + nums[i]); - b = c - nums[i]; - ans = max(ans, max(a, b)); + using ll = long long; + const ll inf = 1LL << 60; + ll ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + ll ff = max(g, 0LL) + x; + g = f - x; + f = ff; + ans = max({ans, f, g}); } return ans; } @@ -134,13 +123,11 @@ public: ```go func maximumAlternatingSubarraySum(nums []int) int64 { - ans := nums[0] - a, b := nums[0], -(1 << 30) - for _, v := range nums[1:] { - c, d := a, b - a = max(v, d+v) - b = c - v - ans = max(ans, max(a, b)) + const inf = 1 << 60 + ans, f, g := -inf, -inf, -inf + for _, x := range nums { + f, g = max(g, 0)+x, f-x + ans = max(ans, max(f, g)) } return int64(ans) } @@ -153,6 +140,19 @@ func max(a, b int) int { } ``` +### **TypeScript** + +```ts +function maximumAlternatingSubarraySum(nums: number[]): number { + let [ans, f, g] = [-Infinity, -Infinity, -Infinity]; + for (const x of nums) { + [f, g] = [Math.max(g, 0) + x, f - x]; + ans = Math.max(ans, f, g); + } + return ans; +} +``` + ### **...** ``` diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README_EN.md b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README_EN.md index c5b06d03573f1..0d5117d3ae591 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README_EN.md +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/README_EN.md @@ -53,6 +53,14 @@ The alternating subarray sum is 1. ## Solutions +**Solution 1: Dynamic Programming** + +We define $f$ as the maximum alternating subarray sum ending with $nums[i]$, and $g$ as the maximum alternating subarray sum ending with $-nums[i]$. Initially, $f$ and $g$ are both $-\infty$. + +Next, we traverse the array $nums$. For each position $i$, we need to maintain the values of $f$ and $g$, which are $f = \max(g, 0) + nums[i]$ and $g = f - nums[i]$, respectively. The answer is the maximum value among all $f$ and $g$. + +The time complexity is $O(n)$, where $n$ is the length of the array $nums$. The space complexity is $O(1)$. + ### **Python3** @@ -60,11 +68,10 @@ The alternating subarray sum is 1. ```python class Solution: def maximumAlternatingSubarraySum(self, nums: List[int]) -> int: - ans = nums[0] - a, b = nums[0], -inf - for v in nums[1:]: - a, b = max(v, b + v), a - v - ans = max(ans, a, b) + ans = f = g = -inf + for x in nums: + f, g = max(g, 0) + x, f - x + ans = max(ans, f, g) return ans ``` @@ -73,13 +80,13 @@ class Solution: ```java class Solution { public long maximumAlternatingSubarraySum(int[] nums) { - long ans = nums[0]; - long a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.length; ++i) { - long c = a, d = b; - a = Math.max(nums[i], d + nums[i]); - b = c - nums[i]; - ans = Math.max(ans, Math.max(a, b)); + final long inf = 1L << 60; + long ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + long ff = Math.max(g, 0) + x; + g = f - x; + f = ff; + ans = Math.max(ans, Math.max(f, g)); } return ans; } @@ -89,18 +96,17 @@ class Solution { ### **C++** ```cpp -using ll = long long; - class Solution { public: long long maximumAlternatingSubarraySum(vector& nums) { - ll ans = nums[0]; - ll a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.size(); ++i) { - ll c = a, d = b; - a = max(1ll * nums[i], d + nums[i]); - b = c - nums[i]; - ans = max(ans, max(a, b)); + using ll = long long; + const ll inf = 1LL << 60; + ll ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + ll ff = max(g, 0LL) + x; + g = f - x; + f = ff; + ans = max({ans, f, g}); } return ans; } @@ -111,13 +117,11 @@ public: ```go func maximumAlternatingSubarraySum(nums []int) int64 { - ans := nums[0] - a, b := nums[0], -(1 << 30) - for _, v := range nums[1:] { - c, d := a, b - a = max(v, d+v) - b = c - v - ans = max(ans, max(a, b)) + const inf = 1 << 60 + ans, f, g := -inf, -inf, -inf + for _, x := range nums { + f, g = max(g, 0)+x, f-x + ans = max(ans, max(f, g)) } return int64(ans) } @@ -130,6 +134,19 @@ func max(a, b int) int { } ``` +### **TypeScript** + +```ts +function maximumAlternatingSubarraySum(nums: number[]): number { + let [ans, f, g] = [-Infinity, -Infinity, -Infinity]; + for (const x of nums) { + [f, g] = [Math.max(g, 0) + x, f - x]; + ans = Math.max(ans, f, g); + } + return ans; +} +``` + ### **...** ``` diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.cpp b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.cpp index df7e18b456d7c..3a807d8890d34 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.cpp +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.cpp @@ -1,16 +1,15 @@ -using ll = long long; - -class Solution { -public: - long long maximumAlternatingSubarraySum(vector& nums) { - ll ans = nums[0]; - ll a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.size(); ++i) { - ll c = a, d = b; - a = max(1ll * nums[i], d + nums[i]); - b = c - nums[i]; - ans = max(ans, max(a, b)); - } - return ans; - } +class Solution { +public: + long long maximumAlternatingSubarraySum(vector& nums) { + using ll = long long; + const ll inf = 1LL << 60; + ll ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + ll ff = max(g, 0LL) + x; + g = f - x; + f = ff; + ans = max({ans, f, g}); + } + return ans; + } }; \ No newline at end of file diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.go b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.go index de6f389de477d..90c9ea9a95f4c 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.go +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.go @@ -1,11 +1,9 @@ func maximumAlternatingSubarraySum(nums []int) int64 { - ans := nums[0] - a, b := nums[0], -(1 << 30) - for _, v := range nums[1:] { - c, d := a, b - a = max(v, d+v) - b = c - v - ans = max(ans, max(a, b)) + const inf = 1 << 60 + ans, f, g := -inf, -inf, -inf + for _, x := range nums { + f, g = max(g, 0)+x, f-x + ans = max(ans, max(f, g)) } return int64(ans) } diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.java b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.java index 78548137fb40e..1f9cac5e9025d 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.java +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.java @@ -1,13 +1,13 @@ -class Solution { - public long maximumAlternatingSubarraySum(int[] nums) { - long ans = nums[0]; - long a = nums[0], b = -(1 << 30); - for (int i = 1; i < nums.length; ++i) { - long c = a, d = b; - a = Math.max(nums[i], d + nums[i]); - b = c - nums[i]; - ans = Math.max(ans, Math.max(a, b)); - } - return ans; - } +class Solution { + public long maximumAlternatingSubarraySum(int[] nums) { + final long inf = 1L << 60; + long ans = -inf, f = -inf, g = -inf; + for (int x : nums) { + long ff = Math.max(g, 0) + x; + g = f - x; + f = ff; + ans = Math.max(ans, Math.max(f, g)); + } + return ans; + } } \ No newline at end of file diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.py b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.py index 3935a8b3c81ce..e9456817e9244 100644 --- a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.py +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.py @@ -1,8 +1,7 @@ -class Solution: - def maximumAlternatingSubarraySum(self, nums: List[int]) -> int: - ans = nums[0] - a, b = nums[0], -inf - for v in nums[1:]: - a, b = max(v, b + v), a - v - ans = max(ans, a, b) - return ans +class Solution: + def maximumAlternatingSubarraySum(self, nums: List[int]) -> int: + ans = f = g = -inf + for x in nums: + f, g = max(g, 0) + x, f - x + ans = max(ans, f, g) + return ans diff --git a/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.ts b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.ts new file mode 100644 index 0000000000000..e08a1b1ef9433 --- /dev/null +++ b/solution/2000-2099/2036.Maximum Alternating Subarray Sum/Solution.ts @@ -0,0 +1,8 @@ +function maximumAlternatingSubarraySum(nums: number[]): number { + let [ans, f, g] = [-Infinity, -Infinity, -Infinity]; + for (const x of nums) { + [f, g] = [Math.max(g, 0) + x, f - x]; + ans = Math.max(ans, f, g); + } + return ans; +}