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:

A transaction will be given as a tuple (x, y, z). Note that x ≠ y and z > 0.
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.
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 1 public class Solution {
 2     int res = Integer.MAX_VALUE;
 3     public int minTransfers(int[][] transactions) {
 4         HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
 5         for (int[] transaction : transactions) {
 6             map.put(transaction[0], map.getOrDefault(transaction[0], 0)-transaction[2]);
 7             map.put(transaction[1], map.getOrDefault(transaction[1], 0)+transaction[2]);
 8         }
 9         ArrayList<Integer> depts = new ArrayList<Integer>();
10         for (int dept : map.values()) {
11             if (dept != 0) depts.add(dept);
12         }
13         helper(depts, 0, 0);
14         return res;
15     }
16     
17     public void helper(ArrayList<Integer> depts, int start, int count) {
18         while (start<depts.size() && depts.get(start)==0) start++;
19         if (start == depts.size()) {
20             res = Math.min(res, count);
21             return;
22         }
23         for (int i=start+1; i<depts.size(); i++) {
24             if (depts.get(start)<0&&depts.get(i)>0 || depts.get(start)>0&&depts.get(i)<0) {
25                 depts.set(i, depts.get(i)+depts.get(start));
26                 //int store = depts.get(start);
27                 //depts.set(start, 0);
28                 helper(depts, start+1, count+1);
29                 //depts.set(start, store);
30                 depts.set(i, depts.get(i)-depts.get(start));
31             }
32         }
33     }
34 }