Content
Given an integer array nums, find the subarray with the largest sum, and return its sum.
Example 1:
Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The subarray [4,-1,2,1] has the largest sum 6.
Example 2:
Input: nums = [1]
Output: 1
Explanation: The subarray [1] has the largest sum 1.
Example 3:
Input: nums = [5,4,-1,7,8]
Output: 23
Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.
Constraints:
1 <= nums.length <= 105
-104 <= nums[i] <= 104
Follow up: If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.
Solution
1. 动态规划
Java
class Solution {
public int maxSubArray(int[] nums) {
// 1 <= nums.length <= 10⁵
// -10⁴ <= nums[i] <= 10⁴
int n = nums.length;
// dp[i]表示以下标i结尾的求和最大的子数组的求和的值
int[] dp = new int[n];
dp[0] = nums[0];
int max = dp[0];
for (int i = 1; i < n; i++) {
if (dp[i - 1] > 0) {
dp[i] = dp[i - 1] + nums[i];
} else {
dp[i] = nums[i];
}
max = Math.max(max, dp[i]);
}
return max;
}
}
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