# Coin change problem and solution in Java

Here, we are going to solve a problem of called Coin change problem using java programming. This problem can be solved by using dynamic programming. By Anamika Gupta Last updated : March 23, 2024

## The Coin Change Problem

You are working at the cash counter at a fun-fair, and you have different types of coins available to you in infinite quantities. The value of each coin is already given. Can you determine the number of ways of making change for a particular number of units using the given types of coins?

## Example of Coin Change Problem

If you have 3 types of coins, and the value of each type is given as 1,2,3 respectively, you can make change for 4 units in four ways:

```{1,1,1,1}
{1,1,2}
{1,3}
{2,2}

Distribute as total sum is 4.

f(4)=1+f(3)
f(4)=2+f(2)
f(4)=3+f(1)
f(3)=1+f(2) and so on
```

## Solution of Coin Change Problem in Java

```import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {
static long[][] memo;
static long count(int i, long coin[], int j) {
if (i == 0)
return 1;
if (i < 0)
return 0;
if (j <= 0)
return 0;
if (memo[i][j] != -1)
return memo[i][j];
memo[i][j] = count(i, coin, j - 1) + count(i - (int) coin[j - 1], coin, j);
//memo[i][j]=memo[i][j-1]+memo[i-value(c[j-1])][j]
//where  0<=j<=m hence j-1 is used.
//for example if c[]=1,2,3 and n=4 then
//memo[4][3]=memo[4][2]+memo[4- value(c[2]])][3]
//i.e. memo[4][3]=memo[4][2]+memo[1][3]
return memo[i][j];
}

public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int n = in.nextInt();
int m = in.nextInt();
long c[] = new long[m];

memo = new long[n + 1][m + 1];

for (int i = 0; i <= n; i++)
for (int j = 0; j <= m; j++)
memo[i][j] = -1;
for (int c_i = 0; c_i < m; c_i++) {
c[c_i] = in.nextLong();
}
long ways = count(n, c, m);
// Print the number of ways of making change for 'n'
//units using coins having the values given by 'c'
System.out.println(ways);
}
}
```