DP-Maximum Subarray

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：

定义f(i)为array[0...i]的最大子数组。

状态转移方程：

f(i) = i;   　　　　　　f(i - 1) <= 0

f(i) = f(i-1) + i;  　　f(i - 1) > 0

解决：

class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int maxSum = nums[0];
        for (int i = 1; i < (nums.size()); i++)
        {
            if (nums[i-1] <= 0)
                nums[i] = nums[i];
            else
                nums[i] = nums[i-1] + nums[i];
            maxSum = max(maxSum, nums[i]);
        }
        
        
        return maxSum;
    }
};