leetcode(53):Maximum Subarray

题目

Maximum Subarray
Easy
Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.
Follow up:

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

思路

Dynamic Programming

这个算法又称为Kadane算法，它是又美国卡耐基梅隆大学的教授Kadane发明的一种用于求解最大连续子序列和问题的最优算法。对于一个长度为n的数组A而言，从A[0] 到 A[j] 是一个子数组（j<n），那么以A[j]结尾的子数组之最大和，要么是 A[j]，要么是 max(A[i]~A[j-1])+A[j] ，其中0 ≤ i ≤ j-1。这就是该算法设计的出发点。
下面我直接给出基于该算法实现的程序代码：
leetcode(53):Maximum Subarray

代码


	class Solution {
	public:
		int maxSubArray(vector<int>& nums) {
			if (nums.size() < 2)
				return nums[0];
			int maxNum = nums[0];
            int sum = maxNum;
				for (int i = 1; i<nums.size(); i++) {
					maxNum = max(maxNum + nums[i], nums[i]);
                    if(maxNum>sum)
                        sum =maxNum;
				}
				return sum;
		}
	};