leetcode 53. Maximum Subarray(DP动态规划问题)

问题描述：

  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.

思路：

  本题为最优解问题，可利用动态规划思路求解。从头到尾遍历每一个数组元素，如何前面元素的和为正，则加上本元素的值继续搜索；如何前面元素的和为负，则此元素开始新的和计数。整个过程中要注意更新和的最大值。

代码：

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