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.

#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; }

Asked by Aloe

Please write comments if you find any bug in above code/algorithm, or find other ways to solve the same problem.