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.
// 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;
}
// CPP code to illustrate *, -, / using only// '+' arithmetic operatorusing namespace std;// Function to flip the sign using only "+"// operator (It is simple with '*' allowed.// We need to do a = (-1)*aint 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 signsbool areDifferentSign(int a, int b){ return ((a<0 && b> 0) || (a > 0 && b < 0));}// Function to subtract two numbers// by negating b and adding themint sub(int a, int b){ // Negating b return a + flipSign(b);}// Function to multiply a by b by// adding a to itself b timesint 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 0int 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 codeint 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 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 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# 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 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
?>
<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.
Related Articles :
- Add two numbers without using arithmetic operators
- Subtract two numbers without using arithmetic operators
- Multiply two integers without using multiplication, division and bitwise operators, and no loops
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