maximum-subarray

【题目描述】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.
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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.

【解题思路】可使用动态规划来解决。时间复杂度为O(n)。假设已知0, …, k的最大和sum[k]以后，则0, …, k+1的最大和sum[k+1]分为以下两种情况：
1）若sum[k]>=0，则sum[k+1]=sum[k]+A[k+1]。
2）若sum[k]<0，另起一个SubArray，令sum[k+1]=A[k+1]。
在计算过程中，使用一个变量maxsum用于存储sum的最大值，一旦出现更大的sum值则更新之，最后返回该变量即可。

【考查内容】数组，动态规划

class Solution {
public:
    int maxSubArray(int A[], int n) {
        if (n <= 0) 
            return 0;
        int sum = 0;
        int maxsum = INT_MIN;
        for (int i = 0; i < n; i++){
            sum += A[i];
            if (sum > maxsum)
                maxsum = sum;
            if (sum < 0) 
                sum = 0;
        }
        return maxsum;  
    }
};