LC 465. Optimal Account Balancing 【lock，hard】

A group of friends went on holiday and sometimes lent each other money. For example, Alice paid for Bill's lunch for $10. Then later Chris gave Alice $5 for a taxi ride. We can model each transaction as a tuple (x, y, z) which means person x gave person y $z. Assuming Alice, Bill, and Chris are person 0, 1, and 2 respectively (0, 1, 2 are the person's ID), the transactions can be represented as [[0, 1, 10], [2, 0, 5]].

Given a list of transactions between a group of people, return the minimum number of transactions required to settle the debt.

Note:

1. A transaction will be given as a tuple (x, y, z). Note that x ≠ y and z > 0.
2. Person's IDs may not be linear, e.g. we could have the persons 0, 1, 2 or we could also have the persons 0, 2, 6.

Example 1:

Input:
[[0,1,10], [2,0,5]]

Output:
2

Explanation:
Person #0 gave person #1 $10.
Person #2 gave person #0 $5.

Two transactions are needed. One way to settle the debt is person #1 pays person #0 and #2 $5 each.

Example 2:

Input:
[[0,1,10], [1,0,1], [1,2,5], [2,0,5]]

Output:
1

Explanation:
Person #0 gave person #1 $10.
Person #1 gave person #0 $1.
Person #1 gave person #2 $5.
Person #2 gave person #0 $5.

Therefore, person #1 only need to give person #0 $4, and all debt is settled.

Runtime 24 ms, faster than 30.39%

这题本来以为是图，结果是数组的题。先建立每一个人的一个账户，然后DFS，DFS的时候从0-n，把第i个账户的钱都转到某一个j，这两个账户的金额是相反的，
因为只有相反的才会有交易。

class Solution {
public:
  int minTransfers(vector<vector<int>>& transactions) {
    map<int,int> m;
    for(auto t: transactions){
      m[t[]] -= t[];
      m[t[]] += t[];
    }
    vector<int> accnt(m.size());
    int cnt = ;
    for(auto a : m){
      if(a.second != ) accnt[cnt++] = a.second;
    }
    return helper(accnt, , cnt, );
  }
  int helper(vector<int>& accnt, int start, int n, int num){
    int ret = INT_MAX;
    while(start < n && accnt[start] == ) start++;
    for(int i=start+; i<n; i++){
      if((accnt[start] <  && accnt[i] > ) || (accnt[start] >  && accnt[i] < )){
        accnt[i] += accnt[start];//加入第i个账户中，这个时候start账户已经没有钱了，可以进行下一个账户清理了
        ret = min(ret, helper(accnt,start+, n, num+));//DFS，保存最小值
        accnt[i] -= accnt[start];
      }
    }
    return ret == INT_MAX ? num : ret;
  }
};