Maximum Subarray leetcode

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.

对于sum[i] 最大的情况有两种 一种是和前边其他的数一起组成最大 一中是单独自己组成最大 所以每次sum[i] 要判定哪个大就取哪个作为sum[i] 的值

state:sum[i]表示 largest sum

initial sum[0] = nums[0]

function: sum[i] = Math.max(sum[i-1] + nums[i], nums[i])     max = math.max(max, sum[i])

return max
时间复杂度为O(n)

public class Solution {
    public int maxSubArray(int[] nums) {
        if (nums.length == 0) {
            return 0;
        }
        int len = nums.length;
        int[] sum = new int[len];
        int max = nums[0];
        sum[0] = nums[0];
        for (int i = 1; i < len; i++) {
            sum[i] = Math.max(sum[i - 1] + nums[i], nums[i]);
            max = Math.max(max, sum[i]);
        }
        return max;
    }
}