Day 37: Coin Change Problem
Coin Change Problem #
Welcome to Day 37 of our 60 Days of Coding Algorithm Challenge! Today, we’ll explore the Coin Change Problem, a classic dynamic programming problem with applications in various fields, including currency systems and algorithmic trading.
What is the Coin Change Problem? #
The Coin Change Problem is about finding the number of ways to make change for a particular amount of money, given a set of coin denominations. There are two common variations of this problem:
- Finding the total number of ways to make the change.
- Finding the minimum number of coins needed to make the change.
We’ll explore both variations in this lesson.
Variation 1: Number of Ways to Make Change #
Problem Statement #
Given an amount N and a set of coin denominations, find the total number of ways to make change for N.
Naive Recursive Approach #
Let’s start with a naive recursive implementation:
1def coin_change_recursive(coins, amount):
2 def recursive_helper(index, remaining):
3 if remaining == 0:
4 return 1
5 if remaining < 0 or index >= len(coins):
6 return 0
7
8 # …
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