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.

Practice

1. What is the main goal of the Simplify debts algorithm in group expense management?

easy

A. To calculate individual spending only

B. To increase the number of transactions

C. To reduce multiple debts into fewer payments

D. To create more complex debt chains

Solution

1. Step 1: Understand the purpose of the algorithm

   The algorithm aims to make settling debts easier by reducing the number of payments needed.

2. Step 2: Identify the effect on transactions

   It simplifies the process by minimizing transactions, not increasing them.

3. Final Answer:

   To reduce multiple debts into fewer payments -> Option C

4. Quick Check:

   Simplify debts = fewer payments [OK]

Hint: Focus on reducing payments, not increasing them [OK]

Common Mistakes:

• Thinking it increases transactions
• Confusing with individual spending calculation
• Assuming it complicates debt chains

2. Which of the following is the correct way to represent a person's net balance in a debts simplification system?

easy

A. A zero value means the person neither owes nor is owed money

B. A negative value means the person is owed money

C. Net balance is always zero for all participants

D. A positive value means the person owes money

Solution

1. Step 1: Understand net balance meaning

   Positive net balance means the person should receive money; negative means they owe money.

2. Step 2: Interpret zero net balance

   If net balance is zero, the person neither owes nor is owed money.

3. Final Answer:

   A zero value means the person neither owes nor is owed money -> Option A

4. Quick Check:

   Zero net balance = no debt [OK]

Hint: Zero net balance means no money owed or owed to you [OK]

Common Mistakes:

• Mixing positive and negative meanings
• Assuming net balance is always zero
• Confusing who owes and who is owed

3. Given the net balances: Alice: +50, Bob: -30, Charlie: -20, what is the minimum number of transactions to settle debts using the simplify debts algorithm?

medium

A. 2 transactions

B. 3 transactions

C. 1 transaction

D. 4 transactions

Solution

1. Step 1: Analyze net balances

   Alice is owed 50, Bob owes 30, Charlie owes 20.

2. Step 2: Match debtors with creditor

   Bob pays Alice 30, Charlie pays Alice 20, totaling 2 transactions.

3. Final Answer:

   2 transactions -> Option A

4. Quick Check:

   Sum debts to creditor = 2 transactions [OK]

Hint: Match debtors to creditors directly to minimize transactions [OK]

Common Mistakes:

• Counting each debt separately without simplification
• Assuming one transaction can cover all debts
• Misallocating amounts between participants

4. In the following code snippet for simplifying debts, what is the error?

net_balances = {"A": 40, "B": -40}
for person, balance in net_balances.items():
    if balance > 0:
        print(f"{person} owes money")
    else:
        print(f"{person} is owed money")

medium

A. The loop should use net_balances.keys() instead of items()

B. The condition for owing money is reversed

C. The print statements are missing parentheses

D. The dictionary keys should be integers, not strings

Solution

1. Step 1: Check condition logic

   Positive balance means the person is owed money, not owes money.

2. Step 2: Verify print statements

   Print syntax is correct; keys as strings are valid in Python.

3. Final Answer:

   The condition for owing money is reversed -> Option B

4. Quick Check:

   Positive balance = owed money, not owes [OK]

Hint: Positive balance means you get money, not owe it [OK]

Common Mistakes:

• Confusing who owes and who is owed
• Incorrect loop usage assumptions
• Syntax errors that don't exist here

5. You have a group with net balances: Dave: +70, Emma: -50, Frank: -20. How would you apply the simplify debts algorithm to minimize transactions and what are the transactions?

hard

A. Emma pays Frank 20, Frank pays Dave 50 (2 transactions)

B. Dave pays Emma 50, Dave pays Frank 20 (2 transactions)

C. Emma pays Dave 70, Frank pays Emma 0 (2 transactions)

D. Emma pays Dave 50, Frank pays Dave 20 (2 transactions)

Solution

1. Step 1: Identify creditors and debtors

   Dave is owed 70, Emma owes 50, Frank owes 20.

2. Step 2: Match debtors to creditor to minimize transactions

   Emma pays Dave 50, Frank pays Dave 20, totaling 2 transactions.

3. Final Answer:

   Emma pays Dave 50, Frank pays Dave 20 (2 transactions) -> Option D

4. Quick Check:

   Debtors pay creditor directly = 2 transactions [OK]

Hint: Debtors pay creditor amounts equal to their debts [OK]

Common Mistakes:

• Reversing payer and receiver roles
• Assigning incorrect amounts
• Adding unnecessary transactions