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75 lines
1.6 KiB
Markdown
Executable File
75 lines
1.6 KiB
Markdown
Executable File
# [53. Maximum Subarray](https://leetcode.com/problems/maximum-subarray/)
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## 题目
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Given an integer array `nums`, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
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**Example**:
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Input: [-2,1,-3,4,-1,2,1,-5,4],
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Output: 6
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Explanation: [4,-1,2,1] has the largest sum = 6.
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**Follow up**:
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If you have figured out the O(*n*) solution, try coding another solution using the divide and conquer approach, which is more subtle.
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## 题目大意
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给定一个整数数组 nums ，找到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。
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## 解题思路
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- 这一题可以用 DP 求解也可以不用 DP。
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- 题目要求输出数组中某个区间内数字之和最大的那个值。`dp[i]` 表示 `[0,i]` 区间内各个子区间和的最大值，状态转移方程是 `dp[i] = nums[i] + dp[i-1] (dp[i-1] > 0)`，`dp[i] = nums[i] (dp[i-1] ≤ 0)`。
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## 代码
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```go
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package leetcode
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// 解法一 DP
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func maxSubArray(nums []int) int {
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if len(nums) == 0 {
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return 0
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}
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if len(nums) == 1 {
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return nums[0]
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}
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dp, res := make([]int, len(nums)), nums[0]
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dp[0] = nums[0]
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for i := 1; i < len(nums); i++ {
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if dp[i-1] > 0 {
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dp[i] = nums[i] + dp[i-1]
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} else {
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dp[i] = nums[i]
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}
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res = max(res, dp[i])
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}
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return res
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}
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// 解法二 模拟
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func maxSubArray1(nums []int) int {
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if len(nums) == 1 {
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return nums[0]
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}
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maxSum, res, p := nums[0], 0, 0
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for p < len(nums) {
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res += nums[p]
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if res > maxSum {
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maxSum = res
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}
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if res < 0 {
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res = 0
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}
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p++
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}
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return maxSum
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}
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``` |