53. Maximum Subarray

Description

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [-2,1,-3,4,-1,2,1,-5,4],
the contiguous subarray [4,-1,2,1] has the largest sum = 6.

Solution

DP

dp[i]表示以i为结尾的连续子串的最大和，子状态转移方程是

• if dp[i] <= 0, dp[i + 1] = a[i + 1];
• else dp[i + 1] = dp[i] + a[i + 1];

public class Solution {
    public int maxSubArray(int[] nums) {
        int max = Integer.MIN_VALUE;
        int sum = 0;
        
        for (int i = 0; i < nums.length; ++i) {
            if (sum < 0) sum = 0;
            sum += nums[i];
            if (sum > max) max = sum;
        }
        
        return max;
    }
}