# Print all combinations of points that can compose a given number

• Difficulty Level : Medium
• Last Updated : 13 Jun, 2022

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

1. In the first position, we can have three numbers 1 or 2 or 3.
2. First, put 1 at the first position and recursively call for n-1.
3. Then put 2 at the first position and recursively call for n-2.
4. Then put 3 at the first position and recursively call for n-3.
5. If n becomes 0 then we have formed a combination that composes 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++

 `// C++ program to Print all ` `// combinations of points that ` `// can compose a given number ` `#define MAX_POINT 3 ` `#define ARR_SIZE 100 ` `#include ` `using` `namespace` `std;`   `/* 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. Initial 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++) ` `        ``cout<

## C

 `// C program to Print all ` `// combinations of points that ` `// can compose a given number` `#define MAX_POINT 3` `#define ARR_SIZE 100` `#include`   `/* 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. Initial 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``(``"Different compositions formed by 1, 2 and 3 of %d are\n"``, n);` `    ``printCompositions(n, 0);` `    `  `    ``getchar``();` `    ``return` `0;` `}`

## Java

 `// Java program to Print all ` `// combinations of points that ` `// can compose a given number` `import` `java.io.*;`   `class` `GFG ` `{` `    ``// 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. Initial value of i must be passed as 0 ` `    ``static` `void` `printCompositions(``int` `arr[], ``int` `n, ``int` `i)` `    ``{` `        ``int` `MAX_POINT = ``3``;` `        ``if` `(n == ``0``)` `        ``{` `            ``printArray(arr, i);` `        ``}` `        ``else` `if``(n > ``0``)` `        ``{` `            ``for` `(``int` `k = ``1``; k <= MAX_POINT; k++)` `            ``{` `                ``arr[i]= k;` `                ``printCompositions(arr, n-k, i+``1``);` `            ``}` `        ``}` `    ``}` `    `  `    ``// Utility function to print array arr[] ` `    ``static` `void` `printArray(``int` `arr[], ``int` `m)` `    ``{` `        ``for` `(``int` `i = ``0``; i < m; i++)` `            ``System.out.print(arr[i] + ``" "``);` `        ``System.out.println();` `    ``}` `    `  `    `  `    ``// Driver program` `    ``public` `static` `void` `main (String[] args) ` `    ``{` `        ``int` `n = ``5``;` `        ``int` `size = ``100``;` `        ``int``[] arr = ``new` `int``[size];` `        ``System.out.println(``"Different compositions formed by 1, 2 and 3 of "``+ n + ``" are"``);` `        ``printCompositions(arr, n, ``0``);` `    ``}` `}`   `// Contributed by Pramod Kumar`

## Python3

 `# Python3 program to Print all combinations ` `# of points that can compose a given number` `MAX_POINT ``=` `3``;` `ARR_SIZE ``=` `100``;`   `arr ``=` `[``0``] ``*` `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. Initial value` `# of i must be passed as 0 ` `def` `printCompositions(n, 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*/` `    ``if` `(n ``=``=` `0``):` `        ``printArray(arr, i);` `    ``elif``(n > ``0``):` `        ``for` `k ``in` `range``(``1``,MAX_POINT ``+` `1``):` `            ``arr[i] ``=` `k;` `            ``printCompositions(n ``-` `k, i ``+` `1``);`   `# UTILITY FUNCTIONS */` `# Utility function to print array arr[] */` `def` `printArray(arr, arr_size):` `    ``for` `i ``in` `range``(arr_size):` `        ``print``(arr[i], end ``=` `" "``);` `    ``print``();`   `# Driver Code` `n ``=` `5``;` `print``(``"Different compositions formed "` `+` `         ``"by 1, 2 and 3 of"``, n, ``" are"``);` `printCompositions(n, ``0``);`   `# This code is contributed by mits `

## C#

 `// C# program to Print all` `// combinations of points that` `// can compose a given number` `using` `System;`   `class` `GFG {` `    `  `    ``// 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. ` `    ``// Initial value of i must be passed as 0` `    ``static` `void` `printCompositions(``int``[] arr, ``int` `n, ``int` `i)` `    ``{` `        ``int` `MAX_POINT = 3;` `        ``if` `(n == 0) {` `            ``printArray(arr, i);` `        ``}` `        ``else` `if` `(n > 0) {` `            ``for` `(``int` `k = 1; k <= MAX_POINT; k++) {` `                ``arr[i] = k;` `                ``printCompositions(arr, n - k, i + 1);` `            ``}` `        ``}` `    ``}`   `    ``// Utility function to print array arr[]` `    ``static` `void` `printArray(``int``[] arr, ``int` `m)` `    ``{` `        ``for` `(``int` `i = 0; i < m; i++)` `            ``Console.Write(arr[i] + ``" "``);` `        ``Console.WriteLine();` `    ``}`   `    ``// Driver program` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 5;` `        ``int` `size = 100;` `        ``int``[] arr = ``new` `int``[size];` `        `  `        ``Console.WriteLine(``"Different compositions formed"` `                    ``+ ``" by 1, 2 and 3 of "` `+ n + ``" are"``);` `        ``printCompositions(arr, n, 0);` `    ``}` `}`   `// Contributed by Sam007`

## PHP

 ` 0)` `    ``{` `        ``for` `(``\$k` `= 1; ``\$k` `<= ``\$MAX_POINT``; ``\$k``++)` `        ``{` `            ``\$arr``[``\$i``] = ``\$k``;` `            ``printCompositions(``\$n` `- ``\$k``, ``\$i` `+ 1);` `        ``}` `    ``}` `}`   `/* UTILITY FUNCTIONS */` `/* Utility function to print array arr[] */` `function` `printArray(``\$arr``, ``\$arr_size``)` `{` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$arr_size``; ``\$i``++)` `        ``echo` `\$arr``[``\$i``].``" "``;` `    ``echo` `"\n"``;` `}`   `// Driver Code` `\$n` `= 5;`   `echo` `"Different compositions formed"` `.` `     ``" by 1, 2 and 3 of "``.``\$n``.``" are\n"``;` `printCompositions(``\$n``, 0);`   `// This code is contributed by mits ` `?>`

## Javascript

 ``

Output:

```Different compositions formed by 1, 2 and 3 of 5 are
1 1 1 1 1
1 1 1 2
1 1 2 1
1 1 3
1 2 1 1
1 2 2
1 3 1
2 1 1 1
2 1 2
2 2 1
2 3
3 1 1
3 2 ```

Time Complexity:O(n)

Space Complexity:O(n)

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

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