Print all the possible arithmetic expressions for a given number

Last Updated : 02 Jan, 2023

Given an integer N, the task is to print all the possible arithmetic expressions using all numbers from 1 to N and with binary operator +, –, * and /.
Examples:

Input: n = 2
Output:
1+2, 1-2, 1/2, 1*2
Input: n = 3
Output:
1+2+3, 1+2-3, 1+2/3, 1+2*3, 1-2+3, 1-2-3, 1-2/3, 1-2*3
1/2+3, 1/2-3, 1/2/3, 1/2*3, 1*2+3, 1*2-3, 1*2/3, 1*2*3

Approach:

We will create a character array of length = n + n - 1, because for an expression with n operands to be valid we will need n-1 operators.
Iterate the array and put numbers at even position whereas symbols at the odd position and call the function recursively.
If number of characters becomes equal to the length of array, print the array.

Below is the implementation of the above approach:

CPP

// C++ program to print all the 
// expressions for the input value 

#include<iostream>
#include<bits/stdc++.h>
using namespace std;

// Function to print all the
// expressions using the number
void PrintRecursive(char *str,int arr[],
                 int i, int n,char *res,
                 int j, int len,int ln)
{
    // Termination condition
    if(j==len)
    {
        res[j]='\0';
        cout<<res<<endl;
        return;
    }
    // Even position will contain 
    // the numbers
    if(j%2==0)
    {
        res[j]='0'+arr[i];
        
        // Recursive call
         PrintRecursive(str,arr,i+1,n,res,
                        j+1,len,ln);
    }
    else
    {
        // Add a symbol from string in 
        // odd position.
        for(int k=0;k<ln;k++)
        {
            res[j]=str[k];
            PrintRecursive(str,arr,i,n,res,
                           j+1,len,ln);
        }
    }
}

void PrintExpressions(int n)
{
    // Character array containing 
    // expressions 
    char str[4]={'+','-','/','*'};
   
    str[4]='\0';
    
    int ln=strlen(str);
    
    int a[n];
    for(int i=0;i<n;i++)
    {
        a[i] = i + 1;
    }
    char res[( 2 * n ) - 1];
    
    PrintRecursive(str,a,0,n,res,0,
                   2*n-1,ln);
    return;
}

//Driver code
int main()
{
    int n = 2;
    
    PrintExpressions(n);
     
    return 0;
}

Java

/*package whatever //do not write package name here */
import java.util.*;

class GFG {

  // Function to print all the
  // expressions using the number
  static void PrintRecursive(char []str,int arr[], int i,
                             int n,char []res, int j, 
                             int len,int ln)
  {
    // Termination condition
    if(j == len)
    {
      System.out.println(res);
      return;
    }
    // Even position will contain 
    // the numbers
    if(j%2==0)
    {
      res[j]=(char)('0'+arr[i]);

      // Recursive call
      PrintRecursive(str,arr,i+1,n,res,j+1,len,ln);
    }
    else
    {
      // Add a symbol from string in 
      // odd position.
      for(int k=0;k<ln;k++)
      {
        res[j]=str[k];
        PrintRecursive(str,arr,i,n,res,j+1,len,ln);
      }
    }
  }

  static void PrintExpressions(int n)
  {
    // Character array containing 
    // expressions 
    char str[] = {'+','-','/','*'};

    int ln=str.length;

    int a[] = new int[n];
    for(int i=0;i<n;i++)
    {
      a[i] = i + 1;
    }
    char res[] = new char[( 2 * n ) - 1];

    PrintRecursive(str,a,0,n,res,0,2*n-1,ln);
  }


  public static void main (String[] args)
  {
    int n = 2;
    PrintExpressions(n);
  }
}

// This code is contributed by aadityaburujwale.

Python3

# Python3 program to print all the 
# expressions for the input value 

# Function to print all the
# expressions using the number
def PrintRecursive(str, arr, i, n, res, j, len, ln):
    
    # Termination condition
    if(j==len):
        print(res)
        return

    # Even position will contain 
    # the numbers
    if(j%2==0):
        res[j] = arr[i]
        
        # Recursive call
        PrintRecursive(str,arr,i+1,n,res,j+1,len,ln)
    else:
        # Add a symbol from string in 
        # odd position.
        for k in range(0,ln):
            res[j] = str[k]
            PrintRecursive(str,arr,i,n,res,j+1,len,ln)

def PrintExpressions(n):
    # Character array containing 
    # expressions 
    str = [ '+','-','/','*' ]
    
    ln = len(str)
    
    a = []
    for i in range(0,n):
        a.append(0)
        a[i] = i + 1
    res = []
    for i in range(0,(2 * n)-1):
        res.append('')
    
    PrintRecursive(str, a, 0, n, res, 0, 2*n-1, ln)
    return


# Driver code
n = 2
PrintExpressions(n)

# This code is contributed by akashish__

using System;
using System.Collections.Generic;

public class GFG {

  // Function to print all the
  // expressions using the number
  public static void PrintRecursive(char[] str, int[] arr,
                                    int i, int n,
                                    char[] res, int j,
                                    int len, int ln)
  {
    // Termination condition
    if (j == len) {
      Console.WriteLine(res);
      return;
    }
    // Even position will contain
    // the numbers
    if (j % 2 == 0) {
      string temp = arr[i].ToString();
      res[j] = temp[0];
      // Recursive call
      PrintRecursive(str, arr, i + 1, n, res, j + 1,
                     len, ln);
    }
    else {
      // Add a symbol from string in
      // odd position.
      for (int k = 0; k < ln; k++) {
        res[j] = str[k];
        PrintRecursive(str, arr, i, n, res, j + 1,
                       len, ln);
      }
    }
  }

  public static void PrintExpressions(int n)
  {
    // Character array containing
    // expressions
    char[] str = new char[4] { '+', '-', '/', '*' };

    int ln = str.Length;

    int[] a = new int[n];

    for (int i = 0; i < n; i++) {
      a[i] = i + 1;
    }
    char[] res = new char[(2 * n) - 1];

    PrintRecursive(str, a, 0, n, res, 0, 2 * n - 1, ln);
    return;
  }

  static public void Main()
  {

    int n = 2;

    PrintExpressions(n);
  }
}

// This code is contributed by akashish__

JavaScript

// JS program to print all the 
// expressions for the input value 

// Function to print all the
// expressions using the number
function PrintRecursive(str, arr, i, n, res, j, len, ln)
{
    // Termination condition
    if(j==len)
    {
        res[j];
        console.log(res);
        return;
    }
    // Even position will contain 
    // the numbers
    if(j%2==0)
    {
        res[j] = arr[i].toString();
        
        // Recursive call
         PrintRecursive(str,arr,i+1,n,res,j+1,len,ln);
    }
    else
    {
        // Add a symbol from string in 
        // odd position.
        for(let k = 0; k < ln; k++)
        {
            res[j] = str[k];
            PrintRecursive(str,arr,i,n,res,j+1,len,ln);
        }
    }
}

function PrintExpressions(n)
{
    // Character array containing 
    // expressions 
    let str = [ '+','-','/','*' ];
    
    let ln=str.length;
    
    let a = [];
    for(let i = 0; i < n; i++)
    {
        a.push(0);
        a[i] = i + 1;
    }
    let res = [];
    for(let i = 0; i < ( 2 * n ) - 1; i++)
    {
        res.push('');
    }
    
    PrintRecursive(str, a, 0, n, res, 0, 2*n-1, ln);
    return;
}

// Driver code
let n = 2;

PrintExpressions(n);

// This code is contributed by akashish__

Output:

1+2
1-2
1/2
1*2

Print all the possible arithmetic expressions for a given number

manavgoswami001

Improve

Article Tags :

Practice Tags :

Strings

Print all the possible arithmetic expressions for a given number

Similar Reads

Thank You!

What kind of Experience do you want to share?