[LeetCode 解题报告]053. Maximum Subarray

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.

考察：最大连续字段和

Method 1. 

class Solution {
public:
    int maxSubArray(vector& nums) {
        int res = INT_MIN, curSum = 0;
        for (int i = 0; i < nums.size(); i ++) {
            curSum = max(nums[i], curSum+nums[i]);
            res = max(res, curSum);
        }
        return res;
    }
};

Method 2.  

class Solution {
public:
    int maxSubArray(vector& nums) {
        if (nums.empty())
            return 0;
        return helper(nums, 0, nums.size()-1);
        
    }
    
    int helper(vector& nums, int left, int right) {
        if (left >= right)
            return nums[left];
        
        int mid = (left + right) / 2;
        int lmax = helper(nums, left, mid-1);
        int rmax = helper(nums, mid+1, right);
        
        int mmax = nums[mid], t = mmax;
        for (int i = mid-1; i >= left; i --) {
            t += nums[i];
            mmax = max(mmax, t);
        }
        
        t = mmax;
        for (int i = mid+1; i <= right; i ++) {
            t += nums[i];
            mmax = max(mmax, t);
        }
        
        return max(mmax, max(lmax, rmax));
    }
};