Print all combinations of points that can compose a given number
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++
// C++ program to Print all // combinations of points that // can compose a given number #define MAX_POINT 3 #define ARR_SIZE 100 #include <bits/stdc++.h> 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. 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++) cout<<arr[i]<< " " ; cout<<endl; } /* Driver code */ int main() { int n = 5; cout<< "Different compositions formed by 1, 2 and 3 of " <<n<< " are\n" ; printCompositions(n, 0); return 0; } // This code is contributed by rathbhupendra |
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C
// C program to Print all // combinations of points that // can compose a given number #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 ( "Different compositions formed by 1, 2 and 3 of %d are\n" , n); printCompositions(n, 0); getchar (); return 0; } |
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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. Initital 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 |
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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. Initital 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 |
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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. // Initital 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 |
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PHP
<?php // PHP program to Print all // combinations of points that // can compose a given number $MAX_POINT = 3; $ARR_SIZE = 100; $arr = array ( $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 */ function printCompositions( $n , $i ) { global $arr , $MAX_POINT , $ARR_SIZE ; /* 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 ); } else if ( $n > 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 ?> |
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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
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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