Introduction to Coin Change Problem

The coin change problem is a classic algorithmic problem that involves finding the minimum number of coins needed to make a certain amount of change. Given a set of coin denominations and an amount, the goal is to determine the fewest number of coins needed to make the amount using the given denominations.

This problem is often encountered in real-life scenarios such as making change at a cash register or vending machine. It is also a common problem in programming interviews as it requires a solid understanding of dynamic programming.

Dynamic programming is an optimization technique that solves complex problems by breaking them down into smaller overlapping subproblems. By solving these subproblems and storing their solutions, we can avoid redundant computations and greatly improve performance.

In the context of the coin change problem, dynamic programming allows us to efficiently explore all possible combinations of coins and find the one with the minimum number of coins.

A common approach to solving the coin change problem is by using a recursive solution. However, this approach can be inefficient and lead to overlapping subproblems. That's where dynamic programming comes in to save the day!

In the upcoming sections of this tutorial, we will explore various solutions to the coin change problem using dynamic programming. We will start with a recursive solution and gradually optimize it using dynamic programming techniques.

So buckle up, and let's dive into the fascinating world of the coin change problem!