---
description: 'Author: @TBC | https://leetcode.com/problems/optimal-account-balancing/'
---

# 0465 - Optimal Account Balancing (Hard)

## Problem Link

https://leetcode.com/problems/optimal-account-balancing/

## Problem Statement

You are given an array of transactions `transactions` where `transactions[i] = [fromi, toi, amounti]` indicates that the person with `ID = fromi` gave `amounti $` to the person with `ID = toi`.

Return _the minimum number of transactions required to settle the debt_.

**Example 1:**

```
Input: transactions = [[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: transactions = [[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.
```

**Constraints:**

* `1 <= transactions.length <= 8`
* `transactions[i].length == 3`
* `0 <= fromi, toi < 12`
* `fromi != toi`
* `1 <= amounti <= 100`

## Approach 1: TBC
