Program to Division two integers of given base
Last Updated :
25 Aug, 2023
Given three positive integers Base B, Dividend, and Divisor, where Dividend and Divisor are Base-B integers, the task is to find dividend/divisor.
Examples:
Input: Dividend = 513, Divisor = 7, B = 8
Output: 57
Explanation: The value of 513/7 in base 8 is 57.
Input: Dividend = 400, Divisor = 20 B = 8
Output: 20
Approach: To solve the problem follow the below idea:
The given problem can be solved by using basic mathematics division.
Steps that were to follow:
- Convert the dividend and divisor from base B to base 10 using the toDecimal function.
- Initialize decimal = 0 and power = 0
- Repeat the following steps while dividend != 0:
- Extract the last digit of the dividend and store it in the digit
- Add digit * B^power to decimal
- Divide the dividend by 10
- Increment power by 1
- Convert the divisor from base B to base 10 using the same algorithm as above
- Perform the division in base 10 to get the quotient using the operator /: quotient = dividend/divisor
- Convert the quotient from base 10 to base B using the fromDecimal function:
- Initialize num = 0 and power = 0
- Repeat the following steps while quotient != 0:
- Calculate digit = quotient % B
- Add digit * 10^power to num
- Divide quotient by B
- Increment power by 1
- Reverse the digits of the num
- Print the quotient in base B
Below is the code to implement the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int toDecimal(int num, int B)
{
int decimal = 0, power = 0;
while (num != 0) {
int digit = num % 10;
decimal += digit * pow(B, power);
num /= 10;
power++;
}
return decimal;
}
int fromDecimal(int decimal, int B)
{
int num = 0, power = 0;
while (decimal != 0) {
int digit = decimal % B;
num += digit * pow(10, power);
decimal /= B;
power++;
}
return num;
}
int divide(int B, int dividend, int divisor)
{
int dividend_decimal = toDecimal(dividend, B);
int divisor_decimal = toDecimal(divisor, B);
int quotient_decimal
= dividend_decimal / divisor_decimal;
int quotient = fromDecimal(quotient_decimal, B);
return quotient;
}
int main()
{
int B = 8;
int dividend = 513;
int divisor = 7;
int quotient = divide(B, dividend, divisor);
cout << quotient << endl;
return 0;
}
|
Java
import java.lang.Math;
public class Main {
static int toDecimal(int num, int B)
{
int decimal = 0, power = 0;
while (num != 0) {
int digit = num % 10;
decimal += digit * Math.pow(B, power);
num /= 10;
power++;
}
return decimal;
}
static int fromDecimal(int decimal, int B)
{
int num = 0, power = 0;
while (decimal != 0) {
int digit = decimal % B;
num += digit * Math.pow(10, power);
decimal /= B;
power++;
}
return num;
}
static int divide(int B, int dividend, int divisor)
{
int dividend_decimal = toDecimal(dividend, B);
int divisor_decimal = toDecimal(divisor, B);
int quotient_decimal = dividend_decimal / divisor_decimal;
int quotient = fromDecimal(quotient_decimal, B);
return quotient;
}
public static void main(String[] args)
{
int B = 8;
int dividend = 513;
int divisor = 7;
int quotient = divide(B, dividend, divisor);
System.out.println(quotient);
}
}
|
Python
import math
def toDecimal(num, B):
decimal = 0
power = 0
while num != 0:
digit = num % 10
decimal += digit * math.pow(B, power)
num //= 10
power += 1
return int(decimal)
def fromDecimal(decimal, B):
num = 0
power = 0
while decimal != 0:
digit = decimal % B
num += digit * math.pow(10, power)
decimal //= B
power += 1
return int(num)
def divide(B, dividend, divisor):
dividend_decimal = toDecimal(dividend, B)
divisor_decimal = toDecimal(divisor, B)
quotient_decimal = dividend_decimal // divisor_decimal
quotient = fromDecimal(quotient_decimal, B)
return quotient
if __name__ == "__main__":
B = 8
dividend = 513
divisor = 7
quotient = divide(B, dividend, divisor)
print(quotient)
|
C#
using System;
public class MainClass
{
static int ToDecimal(int num, int B)
{
int _decimal = 0, power = 0;
while (num != 0)
{
int digit = num % 10;
_decimal += digit * (int)Math.Pow(B, power);
num /= 10;
power++;
}
return _decimal;
}
static int FromDecimal(int _decimal, int B)
{
int num = 0, power = 0;
while (_decimal != 0)
{
int digit = _decimal % B;
num += digit * (int)Math.Pow(10, power);
_decimal /= B;
power++;
}
return num;
}
static int Divide(int B, int dividend, int divisor)
{
int dividend_decimal = ToDecimal(dividend, B);
int divisor_decimal = ToDecimal(divisor, B);
int quotient_decimal = dividend_decimal / divisor_decimal;
int quotient = FromDecimal(quotient_decimal, B);
return quotient;
}
public static void Main(string[] args)
{
int B = 8;
int dividend = 513;
int divisor = 7;
int quotient = Divide(B, dividend, divisor);
Console.WriteLine(quotient);
}
}
|
Javascript
function toDecimal(num, B) {
let decimal = 0;
let power = 0;
while (num !== 0) {
let digit = num % 10;
decimal += digit * Math.pow(B, power);
num = Math.floor(num / 10);
power++;
}
return decimal;
}
function fromDecimal(decimal, B) {
let num = 0;
let power = 0;
while (decimal !== 0) {
let digit = decimal % B;
num += digit * Math.pow(10, power);
decimal = Math.floor(decimal / B);
power++;
}
return num;
}
function divide(B, dividend, divisor) {
let dividend_decimal = toDecimal(dividend, B);
let divisor_decimal = toDecimal(divisor, B);
let quotient_decimal = Math.floor(dividend_decimal / divisor_decimal);
let quotient = fromDecimal(quotient_decimal, B);
return quotient;
}
let B = 8;
let dividend = 513;
let divisor = 7;
let quotient = divide(B, dividend, divisor);
console.log(quotient);
|
Output:
57
Time Complexity: O(log10N)
Auxiliary Space: O(1)
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