【算法作业10】LeetCode 53. Maximum Subarray

53. 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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题解：

挑了道简单的动态规划的题目，然而发现还是不会做。看了一下其他人给的思路才恍然大悟。

这个算法将原问题划分为形如int_local_max[i + 1] = max (int_local_max[i] + nums[i + 1], nums[i + 1])的子问题，其中int_local_max[i]表示以nums[i]结尾的子串。我们只要遍历整个数组，找出最大的int_local_max[i]，就是我们最终要求得的答案。

代码：

class Solution {public:    int maxSubArray(vector<int>& nums) {        if (nums.size() == 0) return 0;        else if (nums.size() == 1) return nums.at(0);                int int_local_max = nums.at(0), int_global_max = nums.at(0);        size_t sz_length  = nums.size();        for (size_t i = 1; i != sz_length; ++i) {            int_local_max  = max(int_local_max + nums.at(i), nums.at(i));            int_global_max = max(int_local_max, int_global_max);        }                return int_global_max;    }};