# Coin change dynamic programming

Coin change problem is the last algorithm we are going to discuss in this section of dynamic programming. In the coin change problem, we are basically. The Coin Changing problem exhibits opti- mal substructure in the following manner. Consider any optimal solution to making change for n cents using coins of. The Coin Change Problem is considered by many to be essential to understanding the paradigm of programming known as Dynamic Programming. In other words, dynamic problem is a method of programming that is used to simplify a problem into smaller pieces.

### Coin change dynamic programming -

The following is an example of one of the many variations of the coin change problem. Using this modified algorithm reduces the number of recursive calls we need to make for the four coin, 63 cent problem to calls! With this, we have successfully understood the solution of coin change problem using dynamic programming approach. Now, we have to make an amount by using these coins such that a minimum number of coins are used. We must set the first element at index 0 of the ways array to 1. According to the coin change problem, we are given a set of coins of various denominations. Okay so we understand what we have to do, but how is a program going to determine how many ways the list of coins can output N? Considering the above example, when we reach denomination 4 and index 7 in our**coin change dynamic programming,**we check that excluding the value of 4, we coin change dynamic programming 3 to reach 7. In this instance our greedy method fails to find the optimal solution for 63 cents in change. In greedy algorithms, the goal is usually local optimization. Using coin having value 1, we need 1 coin.