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;
}
};