C Programming-Print all combinations of points that can compose - Mathematical Algorithms -You can win three kinds of basketball points, 1 point, 2 points.

You can win three kinds of basketball points, 1 point, 2 points, and 3 points. Given a total score n, print out all the combination to compose n.

Examples:

For n = 1, the program should print following:

1

For n = 2, the program should print following:

1 1

2

For n = 3, the program should print following:

1 1 1

1 2

2 1

3

For n = 4, the program should print following:

1 1 1 1

1 1 2

1 2 1

1 3

2 1 1

2 2

3 1

and so on …

Algorithm:

At first position we can have three numbers 1 or 2 or 3.

First put 1 at first position and recursively call for n-1.

Then put 2 at first position and recursively call for n-2.

Then put 3 at first position and recursively call for n-3.

If n becomes 0 then we have formed a combination that compose n, so print the current combination.

Below is a generalized implementation. In the below implementation, we can change MAX_POINT if there are higher points (more than 3) in the basketball game.

C program

```
#define MAX_POINT 3
#define ARR_SIZE 100
#include<stdio.h>
/* Utility function to print array arr[] */
void printArray(int arr[], int arr_size);
/* The function prints all combinations of numbers 1, 2, ...MAX_POINT
that sum up to n.
i is used in recursion keep track of index in arr[] where next
element is to be added. Initital value of i must be passed as 0 */
void printCompositions(int n, int i)
{
/* array must be static as we want to keep track
of values stored in arr[] using current calls of
printCompositions() in function call stack*/
static int arr[ARR_SIZE];
if (n == 0)
{
printArray(arr, i);
}
else if(n > 0)
{
int k;
for (k = 1; k <= MAX_POINT; k++)
{
arr[i]= k;
printCompositions(n-k, i+1);
}
}
}
/* UTILITY FUNCTIONS */
/* Utility function to print array arr[] */
void printArray(int arr[], int arr_size)
{
int i;
for (i = 0; i < arr_size; i++)
printf("%d ", arr[i]);
printf("\n");
}
/* Driver function to test above functions */
int main()
{
int n = 5;
printf("Differnt compositions formed by 1, 2 and 3 of %d are\n", n);
printCompositions(n, 0);
getchar();
return 0;
}
```