# C Program Coin Change

• Last Updated : 14 May, 2021

Given a value N, if we want to make change for N cents, and we have infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn\’t matter.
For example, for N = 4 and S = {1,2,3}, there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}. So output should be 4. For N = 10 and S = {2, 5, 3, 6}, there are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}. So the output should be 5.

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## C

 `// C program for coin change problem.``#include` `int` `count( ``int` `S[], ``int` `m, ``int` `n )``{``    ``int` `i, j, x, y;` `    ``// We need n+1 rows as the table is constructed``    ``// in bottom up manner using the base case 0``    ``// value case (n = 0)``    ``int` `table[n+1][m];``   ` `    ``// Fill the entries for 0 value case (n = 0)``    ``for` `(i=0; i= 0)? table[i - S[j]][j]: 0;` `            ``// Count of solutions excluding S[j]``            ``y = (j >= 1)? table[i][j-1]: 0;` `            ``// total count``            ``table[i][j] = x + y;``        ``}``    ``}``    ``return` `table[n][m-1];``}` `// Driver program to test above function``int` `main()``{``    ``int` `arr[] = {1, 2, 3};``    ``int` `m = ``sizeof``(arr)/``sizeof``(arr);``    ``int` `n = 4;``    ``printf``(``" %d "``, count(arr, m, n));``    ``return` `0;``}`

Output:

`4`

Time Complexity: O(mn)
Following is a simplified version of method 2. The auxiliary space required here is O(n) only.

## C

 `int` `count( ``int` `S[], ``int` `m, ``int` `n )``{``    ``// table[i] will be storing the number of solutions for``    ``// value i. We need n+1 rows as the table is constructed``    ``// in bottom up manner using the base case (n = 0)``    ``int` `table[n+1];` `    ``// Initialize all table values as 0``    ``memset``(table, 0, ``sizeof``(table));` `    ``// Base case (If given value is 0)``    ``table = 1;` `    ``// Pick all coins one by one and update the table[] values``    ``// after the index greater than or equal to the value of the``    ``// picked coin``    ``for``(``int` `i=0; i

Please refer complete article on Dynamic Programming | Set 7 (Coin Change) for more details!

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