#include<stdio.h>
// Returns the count of ways we can sum S[0...m-1] coins to get sum nint count( int S[], int m, int n )
{
// If n is 0 then there is 1 solution (do not include any coin) if (n == 0)
return 1;
// If n is less than 0 then no solution exists if (n < 0)
return 0;
// If there are no coins and n is greater than 0, then no solution exist if (m <=0 && n >= 1)
return 0;
// count is sum of solutions (i) including S[m-1] (ii) excluding S[m-1] return count( S, m - 1, n ) + count( S, m, n-S[m-1] );
}
/
/ Driver program to test above functionint main()
{
int i, j;
int arr[] = {1, 3, 5};
int m = sizeof(arr)/sizeof(arr[0]);
printf("%d ", count(arr, m, 5));
getchar();
return 0;
}
It should be noted that the above function computes the same
subproblems again and again. See the following recursion tree for S =
{1, 2, 3} and n = 5.
The function C({1}, 3) is called two times. If we draw the complete
tree, then we can see that there are many subproblems being called more
than once.
C() --> count()
C({1,2,3}, 5)
/ \
/ \
C({1,2,3}, 2) C({1,2}, 5)
/ \ / \
/ \ / \
C({1,2,3}, -1) C({1,2}, 2) C({1,2}, 3) C({1}, 5)
/ \ / \ / \
/ \ / \ / \
C({1,2},0) C({1},2) C({1,2},1) C({1},3) C({1}, 4) C({}, 5)
/ \ / \ / \ / \
/ \ / \ / \ / \
. . . . . . C({1}, 3) C({}, 4)
/ \
/ \