Simplify debts algorithm in LLD - Architecture Diagram

System Overview - Simplify debts algorithm

This system helps a group of people settle debts among themselves with the fewest transactions possible. It calculates who owes whom and how much, then suggests simplified payments to clear all debts efficiently.

Architecture Diagram

User
  |
  v
Load Balancer
  |
  v
API Gateway
  |
  v
Debt Simplification Service
  |
  +------------------+
  |                  |
  v                  v
Database           Cache

Components

User

client

Initiates debt data input and requests simplified debt results

Load Balancer

load_balancer

Distributes incoming user requests evenly to API Gateway instances

API Gateway

api_gateway

Handles authentication, routing, and request validation before forwarding to service

Debt Simplification Service

service

Processes debts data, runs the simplify debts algorithm, and returns optimized transactions

Database

database

Stores user debts data and transaction history

Cache

cache

Stores recent simplified debt results for quick retrieval to reduce computation

Request Flow - 9 Hops

User → Load Balancer

Load Balancer → API Gateway

API Gateway → Cache

Cache → API Gateway

API Gateway → Debt Simplification Service

Debt Simplification Service → Database

Debt Simplification Service → Cache

Debt Simplification Service → API Gateway

API Gateway → User

Failure Scenario

Component Fails:Database

Impact:New debts cannot be saved or updated; service cannot fetch latest debts data, causing stale or failed responses

Mitigation:Use database replication for failover; serve cached results if available; notify users of degraded service

Architecture Quiz - 3 Questions

Which component first checks if the simplified debts result is already available to avoid recomputation?

A Load Balancer

B Database

C Cache

D Debt Simplification Service

Design Principle

This architecture uses caching to reduce repeated computation and database load, a load balancer to distribute user requests, and a dedicated service to run the simplify debts algorithm. It ensures scalability and responsiveness by separating concerns and using fast cache lookups before expensive computations.

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