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Subtract 1 without arithmetic operators

  • Difficulty Level : Easy
  • Last Updated : 26 May, 2021

Write a program to subtract one from a given number. The use of operators like ‘+’, ‘-‘, ‘*’, ‘/’, ‘++’, ‘–‘ …etc are not allowed. 

Examples: 

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Input:  12
Output: 11

Input:  6
Output: 5

Method 1 
To subtract 1 from a number x (say 0011001000), flip all the bits after the rightmost 1 bit (we get 0011001111). Finally, flip the rightmost 1 bit also (we get 0011000111) to get the answer.

C++




// C++ code to subtract
// one from a given number
#include <iostream>
using namespace std;
 
int subtractOne(int x)
{
    int m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!(x & m))
    {
        x = x ^ m;
        m <<= 1;
    }
 
    // Flip the rightmost 1 bit
    x = x ^ m;
    return x;
}
 
// Driver code
int main()
{
    cout << subtractOne(13) << endl;
    return 0;
}
 
// This code is contributed by noob2000

C




// C code to subtract
// one from a given number
#include <stdio.h>
 
int subtractOne(int x)
{
    int m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!(x & m)) {
        x = x ^ m;
        m <<= 1;
    }
 
    // flip the rightmost 1 bit
    x = x ^ m;
    return x;
}
 
/* Driver program to test above functions*/
int main()
{
    printf("%d", subtractOne(13));
    return 0;
}

Java




// Java code to subtract
// one from a given number
import java.io.*;
 
class GFG
{
static int subtractOne(int x)
{
    int m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!((x & m) > 0))
    {
        x = x ^ m;
        m <<= 1;
    }
 
    // flip the rightmost
    // 1 bit
    x = x ^ m;
    return x;
}
 
// Driver Code
public static void main (String[] args)
{
    System.out.println(subtractOne(13));
}
}
 
// This code is contributed
// by anuj_67.

Python3




# Python 3 code to subtract one from
# a given number
def subtractOne(x):
    m = 1
 
    # Flip all the set bits
    # until we find a 1
    while ((x & m) == False):
        x = x ^ m
        m = m << 1
     
    # flip the rightmost 1 bit
    x = x ^ m
    return x
 
# Driver Code
if __name__ == '__main__':
    print(subtractOne(13))
     
# This code is contributed by
# Surendra_Gangwar

C#




// C# code to subtract
// one from a given number
using System;
 
class GFG
{
static int subtractOne(int x)
{
    int m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!((x & m) > 0))
    {
        x = x ^ m;
        m <<= 1;
    }
 
    // flip the rightmost
    // 1 bit
    x = x ^ m;
    return x;
}
 
// Driver Code
public static void Main ()
{
    Console.WriteLine(subtractOne(13));
}
}
 
// This code is contributed
// by anuj_67.

PHP




<?php
// PHP code to subtract
// one from a given number
 
function subtractOne($x)
{
    $m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!($x & $m))
    {
        $x = $x ^ $m;
        $m <<= 1;
    }
 
    // flip the
    // rightmost 1 bit
    $x = $x ^ $m;
    return $x;
}
 
// Driver Code
    echo subtractOne(13);
     
// This code is contributed
// by anuj_67.
?>

Javascript




<script>
 
// JavaScript code to subtract
// one from a given number
 
function subtractOne(x)
{
    let m = 1;
 
    // Flip all the set bits
    // until we find a 1
    while (!(x & m)) {
        x = x ^ m;
        m <<= 1;
    }
 
    // flip the rightmost 1 bit
    x = x ^ m;
    return x;
}
 
/* Driver program to test above functions*/
 
    document.write(subtractOne(13));
 
 
// This code is contributed by Surbhi Tyagi.
 
</script>
Output: 
12

 

Method 2 (If + is allowed) 
We know that the negative number is represented in 2’s complement form on most of the architectures. We have the following lemma hold for 2’s complement representation of signed numbers.
Say, x is numerical value of a number, then
~x = -(x+1) [ ~ is for bitwise complement ]
Adding 2x on both the sides, 
2x + ~x = x – 1
To obtain 2x, left shift x once. 

C++




#include <stdio.h>
 
int subtractOne(int x)
{
    return ((x << 1) + (~x));
}
 
/* Driver program to test above functions*/
int main()
{
    printf("%d", subtractOne(13));
    return 0;
}

Java




class GFG
{
 
    static int subtractOne(int x)
    {
        return ((x << 1) + (~x));
    }
 
    /* Driver code*/
    public static void main(String[] args)
    {
        System.out.printf("%d", subtractOne(13));
    }
}
 
// This code has been contributed by 29AjayKumar

Python3




def subtractOne(x):
 
    return ((x << 1) + (~x));
 
# Driver code
print(subtractOne(13));
 
# This code is contributed by mits

C#




using System;
     
class GFG
{
 
    static int subtractOne(int x)
    {
        return ((x << 1) + (~x));
    }
 
    /* Driver code*/
    public static void Main(String[] args)
    {
        Console.Write("{0}", subtractOne(13));
    }
}
 
// This code contributed by Rajput-Ji

PHP




<?php
function subtractOne($x)
{
    return (($x << 1) + (~$x));
}
 
/* Driver code*/
 
print(subtractOne(13));
 
// This code has been contributed by mits
?>

Javascript




<script>
 
function subtractOne(x)
{
    return ((x << 1) + (~x));
}
 
/* Driver program to test above functions*/
 
    document.write((subtractOne(13)));
 
// This is code is contributed by Mayank Tyagi
 
</script>
Output: 
12

 




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