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LeetCode 465: Optimal Account Balancing Solution

Master LeetCode problem 465 (Optimal Account Balancing), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

Problem Explanation

Explanation:

To solve this problem, we can use a recursive backtracking approach with some optimizations. We start by converting the transactions into a map where the key is the person's id and the value is their net balance. We then iterate through the map and generate all possible pairs of debts and credits. For each pair, we try to settle the debt by recursively exploring all possible combinations. We keep track of the minimum number of transactions required to settle all debts.

Algorithm:

  1. Create a map to store the net balance of each person.
  2. Generate all unique pairs of debts and credits from the map.
  3. For each pair, try to settle the debt and recursively explore all possible combinations.
  4. Keep track of the minimum number of transactions required to settle all debts.

Time Complexity: O(2^N * N), where N is the number of people. Space Complexity: O(N)

:

Solution Code

class Solution {
    public int minTransfers(int[][] transactions) {
        Map<Integer, Integer> balances = new HashMap<>();
        
        for (int[] transaction : transactions) {
            balances.put(transaction[0], balances.getOrDefault(transaction[0], 0) - transaction[2]);
            balances.put(transaction[1], balances.getOrDefault(transaction[1], 0) + transaction[2]);
        }
        
        List<Integer> debts = new ArrayList<>();
        for (int balance : balances.values()) {
            if (balance != 0) {
                debts.add(balance);
            }
        }
        
        return settleDebts(debts, 0);
    }
    
    private int settleDebts(List<Integer> debts, int start) {
        while (start < debts.size() && debts.get(start) == 0) {
            start++;
        }
        
        if (start == debts.size()) {
            return 0;
        }
        
        int minTransactions = Integer.MAX_VALUE;
        for (int i = start + 1; i < debts.size(); i++) {
            if (debts.get(start) * debts.get(i) < 0) {
                debts.set(i, debts.get(i) + debts.get(start));
                minTransactions = Math.min(minTransactions, 1 + settleDebts(debts, start + 1));
                debts.set(i, debts.get(i) - debts.get(start));
            }
        }
        
        return minTransactions;
    }
}

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