https://leetcode.com/problems/maximum-subarray/description/

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.

• 第一個算法用動態規劃。設f[i]表示第j處，以a[i]結尾的子序列的最大和。註意：f[i]並不是前i-1個數中最大的連續子序列之和，而只是包含a[i]的最大連續子序列的和。我們求出f[i]中的最大值，即為所求的最大連續子序列的和。
• 狀態轉移方程：f[i] = max{ a[i], f[i - 1] + a[i] }, target = max { f[i] }。

 1 //
 2 //  main.cpp
 3 //  LeetCode
 4 //
 5 //  Created by Hao on 2017/3/16.
 6 //  Copyright © 2017年 Hao. All rights reserved.
 7 //
 8 
 9 #include <iostream>
10 #include <vector>
11 using namespace std;
12 
13
 
 class Solution {
14 public:
15     int maxSubArray(vector<int>& nums) {
16         // empty array
17         if (nums.empty()) return 0;
18         
19         int result = nums.at(0), f = 0;
20         
21         for (auto i = 0; i < nums.size(); i ++) {
22             // f[i] = max{ a[i], f[i - 1] + a[i] }
 

23             f = max(f + nums.at(i), nums.at(i));
24 
25             // target = max { f[i] }
26             result = max(result, f);
27         }
28         
29         return result;
30     }
31 };
32 
33 int main ()
34 {
35     Solution testSolution;
36     
37     vector< vector<int> > vecTest{ {-2, 5, 3, -6, 4, -8, 6}, {}, {1, 2, 3, 4, 5} };
38     
39     for (auto v : vecTest)
40         cout << testSolution.maxSubArray(v) << endl;
41     
42     return 0;
43 }

LeetCode 53. Maximum Subarray