Maximum Subarray

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.

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More practice:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

先直接上代码吧

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

解题思路：刚开始看动态规划相关的题目。也是查看了别人的答案，才大致明白动态规划的解题思路。

每一步，确定一个局部最优解，一个全局最优解。全局最优解相对来说比较好表示：global[i+1]=max(local[i+1],global[i])。局部最优解，是可能存在的解。local[i+1]的表示相对来说比较麻烦一点，local[i+1]=max(local[i]+nums[i],nums[i])。