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

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.

This article is contributed by Sakshi Tiwari. If you like GeeksforGeeks (We know you do!) and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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