feat(leecode): 53.最大子数组和

docs/10.LeeCode/53.最大子数组和.md

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+---
+title: 53.最大子数组和
+date: 2024-03-24
+lang: 'zh-CN'
+sidebar: 'auto'
+categories:
+  - LeeCode
+tags:
+location: HangZhou
+---
+
+# Heading
+
+[[toc]]
+
+[53.最大子数组和](https://leetcode.cn/problems/maximum-subarray/description/)
+
+Tags: algorithms bloomberg linkedin microsoft array divide-and-conquer dynamic-programming
+
+Langs: c cpp csharp dart elixir erlang golang java javascript kotlin php python python3 racket ruby rust scala swift typescript
+
+- algorithms
+- Medium (55.22%)
+- Likes: 6594
+- Dislikes: -
+- Total Accepted: 1.7M
+- Total Submissions: 3M
+- Testcase Example: '[-2,1,-3,4,-1,2,1,-5,4]'
+
+<p>给你一个整数数组 <code>nums</code> ，请你找出一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。</p>
+
+<p><strong><span data-keyword="subarray-nonempty">子数组 </span></strong>是数组中的一个连续部分。</p>
+
+<p>&nbsp;</p>
+
+<p><strong>示例 1：</strong></p>
+
+<pre>
+<strong>输入：</strong>nums = [-2,1,-3,4,-1,2,1,-5,4]
+<strong>输出：</strong>6
+<strong>解释：</strong>连续子数组&nbsp;[4,-1,2,1] 的和最大，为&nbsp;6 。
+</pre>
+
+<p><strong>示例 2：</strong></p>
+
+<pre>
+<strong>输入：</strong>nums = [1]
+<strong>输出：</strong>1
+</pre>
+
+<p><strong>示例 3：</strong></p>
+
+<pre>
+<strong>输入：</strong>nums = [5,4,-1,7,8]
+<strong>输出：</strong>23
+</pre>
+
+<p>&nbsp;</p>
+
+<p><strong>提示：</strong></p>
+
+<ul>
+	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
+</ul>
+
+<p>&nbsp;</p>
+
+<p><strong>进阶：</strong>如果你已经实现复杂度为 <code>O(n)</code> 的解法，尝试使用更为精妙的 <strong>分治法</strong> 求解。</p>
+
+<<< @/src/LeeCode/53.最大子数组和.js
+<<< @/src/LeeCode/53.最大子数组和1.js

src/LeeCode/53.最大子数组和.js

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+/*
+ * @lc app=leetcode.cn id=53 lang=javascript
+ *
+ * [53] 最大子数组和
+ * 动态规划
+ */
+
+// @lc code=start
+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+var maxSubArray = function (nums) {
+  if (nums.length < 1) {
+    return 0
+  }
+
+  // f(n) = max(f(n-1)+nums(n),nums(n));
+  let max = nums[0]
+  const dp = [nums[0]]
+  for (let i = 1; i < nums.length; i++) {
+    if (dp[i - 1] + nums[i] > nums[i]) {
+      dp[i] = dp[i - 1] + nums[i]
+    } else {
+      dp[i] = nums[i]
+    }
+    if (dp[i] > max) {
+      max = dp[i]
+    }
+  }
+  return max
+}
+// @lc code=end

src/LeeCode/53.最大子数组和1.js

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+/*
+ * @lc app=leetcode.cn id=53 lang=javascript
+ *
+ * [53] 最大子数组和
+ * 贪心
+ */
+
+// @lc code=start
+/**
+ * @param {number[]} nums
+ * @return {number}
+ */
+var maxSubArray = function (nums) {
+  if (nums.length < 1) {
+    return 0
+  }
+
+  let maxSum = nums[0]
+  let currentSum = nums[0]
+  for (let i = 1; i < nums.length; i++) {
+    currentSum = Math.max(currentSum + nums[i], nums[i])
+    maxSum = Math.max(currentSum, maxSum)
+  }
+  return maxSum
+}
+// @lc code=end