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Implement *, - and / operations using only + arithmetic operator

Last Updated : 23 Mar, 2023
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Given two numbers, perform multiplication, subtraction, and division operations on them, using '+' arithmetic operator only.
 


Operations can be performed as follows: 

Subtraction :-  a - b = a + (-1)*b.
Multiplication :- a * b = a + a + a ... b times.
Division :- a / b =  continuously subtract b from a and 
                  count how many times we can do that.


The above steps look simple, but it is slightly challenging as we can't even use - to subtract. 

C++ 
// CPP code to illustrate *, -, / using only
// '+' arithmetic operator
#include <bits/stdc++.h>
using namespace std;

// Function to flip the sign using only "+"
// operator (It is simple with '*' allowed.
// We need to do a = (-1)*a
int flipSign(int a)
{
    int neg = 0;

    // If sign is + ve turn it -ve
    // and vice-versa
    int tmp = a < 0 ? 1 : -1;
    while (a != 0)
    {
        neg += tmp;
        a += tmp;
    }
    return neg;
}

// Check if a and b are of different signs
bool areDifferentSign(int a, int b)
{
    return ((a<0 && b> 0) || (a > 0 && b < 0));
}

// Function to subtract two numbers
// by negating b and adding them
int sub(int a, int b)
{
    // Negating b
    return a + flipSign(b);
}

// Function to multiply a by b by
// adding a to itself b times
int mul(int a, int b)
{
    // because algo is faster if b<a
    if (a < b)
        return mul(b, a);

    // Adding a to itself b times
    int sum = 0;
    for (int i = abs(b); i > 0; i--)
        sum += a;

    // Check if final sign must be -ve or + ve
    if (b < 0)
        sum = flipSign(sum);

    return sum;
}

// Function to divide a by b by counting how many
// times 'b' can be subtracted from 'a' before
// getting 0
int division(int a, int b)
{
    // Raise exception if b is 0
    if (b == 0)
        throw(b);

    int quotient = 0, dividend;

    // Negating b to subtract from a
    int divisor = flipSign(abs(b));

    // Subtracting divisor from dividend
    for (dividend = abs(a); dividend >= abs(divisor);
                                dividend += divisor)
        quotient++;

    // Check if a and b are of similar symbols or not
    if (areDifferentSign(a, b))
        quotient = flipSign(quotient);
    return quotient;
}

// Driver code
int main()
{
    cout << "Subtraction is " << sub(4, -2) << endl;
    cout << "Product is " << mul(-9, 6) << endl;

    try
    {
        cout << "Division is " << division(8, 2);
    }

    catch (int k)
    {
        cout << " Exception :- Divide by 0";
    }
    return 0;
}
Java 
// Java code to illustrate *, -, / using only 
// '+' arithmetic operator 

class GFG{
    
// Function to flip the sign using only "+" 
// operator (It is simple with '*' allowed. 
// We need to do a = (-1)*a 
static int flipSign(int a) 
{ 
    int neg = 0; 

    // If sign is + ve turn it -ve 
    // and vice-versa 
    int tmp = a < 0 ? 1 : -1; 
    while (a != 0) 
    { 
        neg += tmp; 
        a += tmp; 
    } 
    return neg; 
} 

// Check if a and b are of different signs 
static boolean areDifferentSign(int a, int b) 
{ 
    return ((a < 0 && b > 0) || (a > 0 && b < 0)); 
} 

// Function to subtract two numbers 
// by negating b and adding them 
static int sub(int a, int b) 
{ 
    // Negating b 
    return a + flipSign(b); 
} 

// Function to multiply a by b by 
// adding a to itself b times 
static int mul(int a, int b) 
{ 
    // because algo is faster if b<a 
    if (a < b) 
        return mul(b, a); 

    // Adding a to itself b times 
    int sum = 0; 
    for (int i = Math.abs(b); i > 0; i--) 
        sum += a; 

    // Check if final sign must be -ve or + ve 
    if (b < 0) 
        sum = flipSign(sum); 

    return sum; 
} 

// Function to divide a by b by counting  
// how many times 'b' can be subtracted  
// from 'a' before getting 0 
static int division(int a, int b) 
{ 
    // Raise exception if b is 0 
    if (b == 0) 
        throw new ArithmeticException(); 

    int quotient = 0, dividend; 

    // Negating b to subtract from a 
    int divisor = flipSign(Math.abs(b)); 

    // Subtracting divisor from dividend 
    for (dividend = Math.abs(a); dividend >= Math.abs(divisor); 
         dividend += divisor) 
        quotient++; 

    // Check if a and b are of similar symbols or not 
    if (areDifferentSign(a, b)) 
        quotient = flipSign(quotient); 
    return quotient; 
} 

// Driver code 
public static void main(String[] args) 
{ 
    System.out.println("Subtraction is " + sub(4, -2)); 
    System.out.println("Product is " + mul(-9, 6)); 

    try
    { 
        System.out.println("Division is " + division(8, 2)); 
    } 

    catch (ArithmeticException e) 
    { 
        System.out.println("Exception :- Divide by 0"); 
    } 
} 
}

// This code is contributed by mits
Python3 
# Python3 code to illustrate *, -, / using 
# only  '+' arithmetic operator 

# Function to flip the sign using only "+" 
# operator (It is simple with '*' allowed. 
# We need to do a = (-1)*a 
def flipSign(a): 

    neg = 0; 

    # If sign is + ve turn it -ve 
    # and vice-versa 
    tmp = 1 if a < 0 else -1; 
    while (a != 0): 
        neg += tmp; 
        a += tmp; 

    return neg; 

# Check if a and b are of different signs 
def areDifferentSign(a, b):
    return ((a < 0 and b > 0) or 
            (a > 0 and b < 0)); 

# Function to subtract two numbers 
# by negating b and adding them 
def sub(a, b): 

    # Negating b 
    return a + flipSign(b); 

# Function to multiply a by b by 
# adding a to itself b times 
def mul(a, b): 

    # because algo is faster if b<a 
    if (a < b): 
        return mul(b, a); 

    # Adding a to itself b times 
    sum = 0; 
    for i in range(abs(b), 0, -1): 
        sum += a; 

    # Check if final sign must 
    # be -ve or + ve 
    if (b < 0): 
        sum = flipSign(sum); 

    return sum; 

# Function to divide a by b by counting 
# how many times 'b' can be subtracted 
# from 'a' before getting 0 
def division(a, b): 

    quotient = 0; 

    # Negating b to subtract from a 
    divisor = flipSign(abs(b)); 

    # Subtracting divisor from dividend 
    for dividend in range(abs(a), 
                          abs(divisor) + divisor, 
                                         divisor): 
        quotient += 1; 

    # Check if a and b are of similar 
    # symbols or not 
    if (areDifferentSign(a, b)): 
        quotient = flipSign(quotient); 
    return quotient; 

# Driver code 
print("Subtraction is", sub(4, -2)); 
print("Product is", mul(-9, 6));
a, b = 8, 2;
if(b):
    print("Division is", division(a, b));
else:
    print("Exception :- Divide by 0"); 

# This code is contributed by mits
C# 
// C# code to illustrate *, -, / using only 
// '+' arithmetic operator 
using System;
class GFG
{
// Function to flip the sign using only "+" 
// operator (It is simple with '*' allowed. 
// We need to do a = (-1)*a 
static int flipSign(int a) 
{ 
    int neg = 0; 

    // If sign is + ve turn it -ve 
    // and vice-versa 
    int tmp = a < 0 ? 1 : -1; 
    while (a != 0) 
    { 
        neg += tmp; 
        a += tmp; 
    } 
    return neg; 
} 

// Check if a and b are of different signs 
static bool areDifferentSign(int a, int b) 
{ 
    return ((a < 0 && b > 0) || (a > 0 && b < 0)); 
} 

// Function to subtract two numbers 
// by negating b and adding them 
static int sub(int a, int b) 
{ 
    // Negating b 
    return a + flipSign(b); 
} 

// Function to multiply a by b by 
// adding a to itself b times 
static int mul(int a, int b) 
{ 
    // because algo is faster if b<a 
    if (a < b) 
        return mul(b, a); 

    // Adding a to itself b times 
    int sum = 0; 
    for (int i = Math.Abs(b); i > 0; i--) 
        sum += a; 

    // Check if final sign must be -ve or + ve 
    if (b < 0) 
        sum = flipSign(sum); 

    return sum; 
} 

// Function to divide a by b by counting how many 
// times 'b' can be subtracted from 'a' before 
// getting 0 
static int division(int a, int b) 
{ 
    // Raise exception if b is 0 
    if (b == 0) 
        throw new ArithmeticException(); 

    int quotient = 0, dividend; 

    // Negating b to subtract from a 
    int divisor = flipSign(Math.Abs(b)); 

    // Subtracting divisor from dividend 
    for (dividend = Math.Abs(a); dividend >= Math.Abs(divisor); 
                                dividend += divisor) 
        quotient++; 

    // Check if a and b are of similar symbols or not 
    if (areDifferentSign(a, b)) 
        quotient = flipSign(quotient); 
    return quotient; 
} 

// Driver code 
public static void Main() 
{ 
    Console.WriteLine("Subtraction is " + sub(4, -2)); 
    Console.WriteLine("Product is " + mul(-9, 6)); 
    try
    { 
        Console.WriteLine("Division is " + division(8, 2)); 
    } 
    catch (Exception) 
    { 
        Console.WriteLine("Exception :- Divide by 0"); 
    } 
} 
}

//This code is contributed by mits
PHP 
<?php
// PHP code to illustrate *, -, / using only 
// '+' arithmetic operator 

// Function to flip the sign using only "+" 
// operator (It is simple with '*' allowed. 
// We need to do a = (-1)*a 
function flipSign($a) 
{ 
    $neg = 0; 

    // If sign is + ve turn it -ve 
    // and vice-versa 
    $tmp = $a < 0 ? 1 : -1; 
    while ($a != 0) 
    { 
        $neg += $tmp; 
        $a += $tmp; 
    } 
    return $neg; 
} 

// Check if a and b are of different signs 
function areDifferentSign($a, $b) 
{ 
    return (($a < 0 && $b > 0) || 
            ($a > 0 && $b < 0)); 
} 

// Function to subtract two numbers 
// by negating b and adding them 
function sub($a, $b) 
{ 
    // Negating b 
    return $a + flipSign($b); 
} 

// Function to multiply a by b by 
// adding a to itself b times 
function mul($a, $b) 
{ 
    // because algo is faster if b<a 
    if ($a < $b) 
        return mul($b, $a); 

    // Adding a to itself b times 
    $sum = 0; 
    for ($i = abs($b); $i > 0; $i--) 
        $sum += $a; 

    // Check if final sign must be 
    // -ve or + ve 
    if ($b < 0) 
        $sum = flipSign($sum); 

    return $sum; 
} 

// Function to divide a by b by counting 
// how many times 'b' can be subtracted 
// from 'a' before getting 0 
function division($a, $b) 
{
    $quotient = 0; 

    // Negating b to subtract from a 
    $divisor = flipSign(abs($b)); 

    // Subtracting divisor from dividend 
    for ($dividend = abs($a);
         $dividend >= abs($divisor); 
         $dividend += $divisor) 
        $quotient++; 

    // Check if a and b are of similar
    // symbols or not 
    if (areDifferentSign($a, $b)) 
        $quotient = flipSign($quotient); 
    return $quotient; 
} 

// Driver code 
print("Subtraction is " . sub(4, -2) . "\n"); 
print("Product is " . mul(-9, 6) . "\n");
list($a, $b) = array(8, 2);
if($b)
    print("Division is " . division($a, $b));
else
    print("Exception :- Divide by 0"); 

// This code is contributed by mits
?>
JavaScript 
<script>

// JavaScript code to illustrate *, -, / using only 
// '+' arithmetic operator    

// Function to flip the sign using only "+" 
// operator (It is simple with '*' allowed. 
// We need to do a = (-1)*a 
function flipSign(a) 
{ 
    var neg = 0; 

    // If sign is + ve turn it -ve 
    // and vice-versa 
    var tmp = a < 0 ? 1 : -1; 
    while (a != 0) 
    { 
        neg += tmp; 
        a += tmp; 
    } 
    return neg; 
} 

// Check if a and b are of different signs 
function areDifferentSign(a , b) 
{ 
    return ((a < 0 && b > 0) || (a > 0 && b < 0)); 
} 

// Function to subtract two numbers 
// by negating b and adding them 
function sub(a , b) 
{ 
    // Negating b 
    return a + flipSign(b); 
} 

// Function to multiply a by b by 
// adding a to itself b times 
function mul(a , b) 
{ 
    // because algo is faster if b<a 
    if (a < b) 
        return mul(b, a); 

    // Adding a to itself b times 
    var sum = 0; 
    for (i = Math.abs(b); i > 0; i--) 
        sum += a; 

    // Check if final sign must be -ve or + ve 
    if (b < 0) 
        sum = flipSign(sum); 

    return sum; 
} 

// Function to divide a by b by counting  
// how many times 'b' can be subtracted  
// from 'a' before getting 0 
function division(a , b) 
{ 
    // Raise exception if b is 0 
    if (b == 0) 
        throw new ArithmeticException(); 

    var quotient = 0, dividend; 

    // Negating b to subtract from a 
    var divisor = flipSign(Math.abs(b)); 

    // Subtracting divisor from dividend 
    for (dividend = Math.abs(a); 
    dividend >= Math.abs(divisor); 
         dividend += divisor) 
        quotient++; 

    // Check if a and b are of similar symbols or not 
    if (areDifferentSign(a, b)) 
        quotient = flipSign(quotient); 
    return quotient; 
} 

// Driver code 
 

document.write("Subtraction is " + sub(4, -2)); 
document.write("<br>Product is " + mul(-9, 6)); 

try
{ 
    document.write("<br>Division is " + division(8, 2)); 
} 

catch (e) 
{ 
    document.write("Exception :- Divide by 0"); 
} 


// This code is contributed by Amit Katiyar 

</script>

Output:  

Subtraction is 6
Product is -54
Division is 4

Time Complexity: O(max(|a|, |b|)), Where flipSign() function is O(|a|), sub() function is O(|b|), mul() function is O(max(|a|, |b|)) and division() function is O(|a/b|), Thus Overall, the time complexity of the code is O(max(|a|, |b|)).

Space Complexity: O(1), as it does not use any additional data structures.


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