🪙 Coin Change Problem – Algorithms Comparison

This repository presents a small algorithm study of the classic Coin Change problem, implemented in Python 🐍.

Problem statement:
Given a set of coin denominations and a target amount, determine the
minimum number of coins needed to make that amount.
If it is not possible to form the amount using the given coins, return -1.

The goal of this repo is to compare two different approaches to solving this problem:

• 🧪 Naive recursive solution – algorithm1.py
• ⚙️ Optimized dynamic-programming solution – algorithm2.py

The code is kept clean and minimal so that the focus stays on the core idea of each algorithm.

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📁 Repository Contents

• algorithm1.py – naive recursive solution
• algorithm2.py – optimized dynamic-programming solution
• Coin_Change_Algorithms_Report.pdf – full detailed report, including:
  • formal problem definition and examples
  • pseudocode for both algorithms
  • time and space complexity analysis
  • experimental results, tables, and graphs 📊
  • discussion and conclusions

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📄 Full Details

This README only gives a high-level overview.
For all explanations, proofs, measurements, and graphs,
please refer to the PDF report:
Coin_Change_Algorithms_Report.pdf ✅