53. Maximum Subarray

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#最大连续子序列 #动态规划 #Maximum Subarray #连续子序列

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本文深入探讨了寻找最大子数组和的经典算法问题，通过动态规划方法高效解决该问题，提供了一个简洁的C++实现案例。

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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.

方法一：动态规划

class Solution {
public:
    int maxSubArray(vector<int>& nums) {        
        if(nums.empty())
           return 0;

        int sum =nums[0];
        int maxSum = nums[0];
        for(int i = 1; i<nums.size();i++)
        {
            if(sum < 0)
              sum = nums[i];
            else
              sum+=nums[i];

            if(maxSum < sum)
              maxSum = sum;     
        }  
        return maxSum;
    }
};