Simplify debts algorithm in LLD - System Design Exercise

Design: Simplify Debts Algorithm System

Design focuses on the algorithm and system to simplify debts. UI, authentication, and persistent storage are out of scope.

Functional Requirements

FR1: Accept a list of debts between multiple people (who owes whom and how much).

FR2: Calculate the minimum number of transactions required to settle all debts.

FR3: Output the simplified set of transactions that clears all debts.

FR4: Support up to 1000 people and 10,000 debt records.

FR5: Provide results within 1 second for the maximum input size.

Non-Functional Requirements

NFR1: Algorithm must be efficient to handle large inputs.

NFR2: Memory usage should be optimized for up to 1000 people.

NFR3: System should be reliable and produce consistent results.

NFR4: Latency target: p99 < 1 second for processing debts.

Think Before You Design

Questions to Ask

❓ Question 1

❓ Question 2

❓ Question 3

❓ Question 4

❓ Question 5

Key Components

Input parser to read debts data

Debt graph or data structure to represent debts

Algorithm module to simplify debts

Output generator to produce simplified transactions

Design Patterns

Greedy algorithm for debt simplification

Graph representation of debts

Backtracking or DFS for optimization

Use of priority queues or heaps to pick max creditors/debtors

Reference Architecture

  +----------------+       +-------------------+       +-------------------+       +----------------+
  |  Input Parser  | --->  | Debt Graph Builder | --->  | Simplify Algorithm | --->  | Output Generator |
  +----------------+       +-------------------+       +-------------------+       +----------------+

Components

Input Parser

Custom parser in chosen language

Reads and validates input debts data

Debt Graph Builder

In-memory data structures (arrays, hash maps)

Represents debts as net balances per person

Simplify Algorithm

Greedy algorithm with priority queues

Calculates minimal transactions to settle debts

Output Generator

Custom formatter

Formats simplified transactions for output

Request Flow

1. 1. Input Parser receives list of debts (who owes whom and how much).

2. 2. Debt Graph Builder calculates net balance for each person (sum of money lent minus money owed).

3. 3. Simplify Algorithm uses a greedy approach: repeatedly match the person with maximum credit with the person with maximum debt to minimize transactions.

4. 4. Output Generator formats these matches into a list of transactions showing who pays whom and how much.

5. 5. The system returns the simplified transactions as the result.

Database Schema

Not applicable as system is in-memory algorithm focused; no persistent storage required.

Scaling Discussion

Bottlenecks

Handling very large number of people and debts may increase memory usage.

Algorithm complexity can grow if not optimized, causing latency issues.

Single-threaded processing may limit throughput.

Solutions

Use efficient data structures like hash maps for net balances to reduce memory overhead.

Implement greedy algorithm with priority queues to keep complexity near O(N log N).

Parallelize processing if input can be partitioned or use incremental updates for real-time scenarios.

Interview Tips

Time: Spend 10 minutes clarifying requirements and constraints, 20 minutes designing the algorithm and data flow, 10 minutes discussing scaling and optimizations, 5 minutes summarizing.

Explain how net balances simplify the problem from many debts to fewer transactions.

Describe the greedy approach to match max debtor with max creditor.

Discuss time and space complexity and how it meets latency requirements.

Mention possible improvements for very large scale or real-time updates.