0053. Maximum Subarray

# 53. Maximum Subarray#

## 题目 #

Given an integer array `nums`, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

``````Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.
``````

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

## 解题思路 #

• 这一题可以用 DP 求解也可以不用 DP。
• 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)`

## 代码 #

``````
package leetcode

// 解法一 DP
func maxSubArray(nums []int) int {
if len(nums) == 0 {
return 0
}
if len(nums) == 1 {
return nums[0]
}
dp, res := make([]int, len(nums)), nums[0]
dp[0] = nums[0]
for i := 1; i < len(nums); i++ {
if dp[i-1] > 0 {
dp[i] = nums[i] + dp[i-1]
} else {
dp[i] = nums[i]
}
res = max(res, dp[i])
}
return res
}

// 解法二 模拟
func maxSubArray1(nums []int) int {
if len(nums) == 1 {
return nums[0]
}
maxSum, res, p := nums[0], 0, 0
for p < len(nums) {
res += nums[p]
if res > maxSum {
maxSum = res
}
if res < 0 {
res = 0
}
p++
}
return maxSum
}

``````

Sep 6, 2020