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:
- In the first position, we can have three numbers 1 or 2 or 3.
- First, put 1 at the first position and recursively call for n-1.
- Then put 2 at the first position and recursively call for n-2.
- Then put 3 at the first position and recursively call for n-3.
- 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 <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. 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<<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 |
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. 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
<?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. Initial 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 ?> |
Javascript
<script> // Javascript program to print all // combinations of points that // can compose a given number // Function prints all combinations of numbers // 1, 2, ...MAX_POlet 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 function printCompositions(arr, n, i)
{ let MAX_POINT = 3;
if (n == 0)
{
printArray(arr, i);
}
else if (n > 0)
{
for (let k = 1; k <= MAX_POINT; k++)
{
arr[i] = k;
printCompositions(arr, n - k, i + 1);
}
}
} // Utility function to print array arr[] function printArray(arr, m)
{ for (let i = 0; i < m; i++)
document.write(arr[i] + " " );
document.write( "<br/>" );
} // Driver code let n = 5; let size = 100; let arr = new Array(size).fill(0);
document.write( "Different compositions formed " +
"by 1, 2 and 3 of " + n + " are" + "<br/>" );
printCompositions(arr, n, 0); // This code is contributed by avijitmondal1998 </script> |
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(3n)
Auxiliary Space: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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