Program to Subtract two integers of given base
Last Updated :
02 Dec, 2023
Given three positive integers X, Y, and B, where X and Y are Base-B integers, the task is to find the value of X - Y such that X >= Y.
Examples:
Input: X = 1212, Y = 256, B = 8
Output: 0734
Explanation: The value of 1212 - 256 in base 8 is 734.
Input: X = 546, Y = 248, B = 9
Output: 287
Approach: The given problem can be solved by using basic mathematics subtraction. Follow the steps below to solve the given problem:
- Initialize two variables say power = 1, carry = 0, to keep track of current power and carry generated while subtracting respectively.
- Initialize a variable, say finalVal = 0, to store the resultant value of X - Y.
- Iterate a loop until X > 0 and perform the following steps:
- Store last digits from the current value of X and Y in two variables, say n1 = X % 10 and n2 = Y % 10 respectively.
- Remove last digits from X and Y by updating X = X / 10 and Y = Y / 10.
- Initialize temp = n1 - n2 + carry.
- If temp < 0, then add base B to N, that is N = N + B and set carry = -1, which will act as a borrow. Otherwise, set carry = 0.
- Add current temp * power to finalVal, that is finalVal = finalVal + temp * power and set power = power * 10.
- After completing the above steps, print the value of finalVal as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find X - Y in base B
int getDifference(int B, int X, int Y)
{
// To store final answer
int finalVal = 0;
// To store carry generated
int carry = 0;
// To keep track of power
int power = 1;
while (X > 0) {
// Store last digits of current
// value of X and Y in n1 and
// n2 respectively
int n1 = X % 10;
int n2 = Y % 10;
// Remove last digits from
// X and Y
X = X / 10;
Y = Y / 10;
int temp = n1 - n2 + carry;
if (temp < 0) {
// Carry = -1 will act
// as borrow
carry = -1;
temp += B;
}
else {
carry = 0;
}
// Add in final result
finalVal += temp * power;
power = power * 10;
}
// Return final result
return finalVal;
}
// Driver Code
int main()
{
int X = 1212;
int Y = 256;
int B = 8;
cout << (getDifference(B, X, Y));
return 0;
}
// This code is contributed by rakeshsahni
// Java program for the above approach
import java.io.*;
class GFG {
// Function to find X - Y in base B
public static int getDifference(
int B, int X, int Y)
{
// To store final answer
int finalVal = 0;
// To store carry generated
int carry = 0;
// To keep track of power
int power = 1;
while (X > 0) {
// Store last digits of current
// value of X and Y in n1 and
// n2 respectively
int n1 = X % 10;
int n2 = Y % 10;
// Remove last digits from
// X and Y
X = X / 10;
Y = Y / 10;
int temp = n1 - n2 + carry;
if (temp < 0) {
// Carry = -1 will act
// as borrow
carry = -1;
temp += B;
}
else {
carry = 0;
}
// Add in final result
finalVal += temp * power;
power = power * 10;
}
// Return final result
return finalVal;
}
// Driver Code
public static void main(String[] args)
{
int X = 1212;
int Y = 256;
int B = 8;
System.out.println(
getDifference(B, X, Y));
}
}
# Python3 program for the above approach
# Function to find X - Y in base B
def getDifference(B, X, Y) :
# To store final answer
finalVal = 0;
# To store carry generated
carry = 0;
# To keep track of power
power = 1;
while (X > 0) :
# Store last digits of current
# value of X and Y in n1 and
# n2 respectively
n1 = X % 10;
n2 = Y % 10;
# Remove last digits from
# X and Y
X = X // 10;
Y = Y // 10;
temp = n1 - n2 + carry;
if (temp < 0) :
# Carry = -1 will act
# as borrow
carry = -1;
temp += B;
else :
carry = 0;
# Add in final result
finalVal += temp * power;
power = power * 10;
# Return final result
return finalVal;
# Driver Code
if __name__ == "__main__" :
X = 1212;
Y = 256;
B = 8;
print(getDifference(B, X, Y));
# This code is contributed by AnkThon
// C# program for the above approach
using System;
public class GFG
{
// Function to find X - Y in base B
public static int getDifference(int B, int X, int Y)
{
// To store final answer
int finalVal = 0;
// To store carry generated
int carry = 0;
// To keep track of power
int power = 1;
while (X > 0) {
// Store last digits of current
// value of X and Y in n1 and
// n2 respectively
int n1 = X % 10;
int n2 = Y % 10;
// Remove last digits from
// X and Y
X = X / 10;
Y = Y / 10;
int temp = n1 - n2 + carry;
if (temp < 0) {
// Carry = -1 will act
// as borrow
carry = -1;
temp += B;
}
else {
carry = 0;
}
// Add in final result
finalVal += temp * power;
power = power * 10;
}
// Return final result
return finalVal;
}
// Driver Code
public static void Main(string[] args)
{
int X = 1212;
int Y = 256;
int B = 8;
Console.WriteLine(getDifference(B, X, Y));
}
}
// This code is contributed by AnkThon
<script>
// Javascript program for the above approach
// Function to find X - Y in base B
function getDifference(B, X, Y) {
// To store final answer
let finalVal = 0;
// To store carry generated
let carry = 0;
// To keep track of power
let power = 1;
while (X > 0) {
// Store last digits of current
// value of X and Y in n1 and
// n2 respectively
let n1 = X % 10;
let n2 = Y % 10;
// Remove last digits from
// X and Y
X = Math.floor(X / 10);
Y = Math.floor(Y / 10);
let temp = n1 - n2 + carry;
if (temp < 0) {
// Carry = -1 will act
// as borrow
carry = -1;
temp += B;
} else {
carry = 0;
}
// Add in final result
finalVal += temp * power;
power = power * 10;
}
// Return final result
return finalVal;
}
// Driver Code
let X = 1212;
let Y = 256;
let B = 8;
document.write(getDifference(B, X, Y));
// This code is contributed by gfgking
</script>
Time Complexity: O(log10N)
Auxiliary Space: O(1)
However, we can optimize the solution by performing the following steps:
- First, convert the given numbers X and Y into decimal form.
- Then, find the difference between X and Y.
- Finally, convert the decimal difference back into the given base.
Here's the implementation of the above approach:
C++
//C++ progarm for above approach
#include <iostream>
#include <cmath>
using namespace std;
// Function to convert a number in given base
// to decimal form
int toDecimal(int num, int base) {
int res = 0, power = 1;
while (num > 0) {
int digit = num % 10;
res += digit * power;
power *= base;
num /= 10;
}
return res;
}
// Function to convert a decimal number
// to given base form
int toBase(int num, int base) {
int res = 0, power = 1;
while (num > 0) {
int digit = num % base;
res += digit * power;
power *= 10;
num /= base;
}
return res;
}
// Function to find X - Y in base B
int getDifference(int B, int X, int Y)
{
// Convert X and Y to decimal form
int X_dec = toDecimal(X, B);
int Y_dec = toDecimal(Y, B);
// Find the difference in decimal form
int diff_dec = X_dec - Y_dec;
// Convert the difference to base B form
int diff = toBase(diff_dec, B);
// Return the difference
return diff;
}
// Driver Code
int main()
{
int X = 1212;
int Y = 256;
int B = 8;
cout << getDifference(B, X, Y);
return 0;
}
//Java code for above approach
import java.lang.Math;
public class Main {
// Function to convert a number in given base
// to decimal form
static int toDecimal(int num, int base) {
int res = 0, power = 1;
while (num > 0) {
int digit = num % 10;
res += digit * power;
power *= base;
num /= 10;
}
return res;
}
// Function to convert a decimal number
// to given base form
static int toBase(int num, int base) {
int res = 0, power = 1;
while (num > 0) {
int digit = num % base;
res += digit * power;
power *= 10;
num /= base;
}
return res;
}
// Function to find X - Y in base B
static int getDifference(int B, int X, int Y) {
// Convert X and Y to decimal form
int X_dec = toDecimal(X, B);
int Y_dec = toDecimal(Y, B);
// Find the difference in decimal form
int diff_dec = X_dec - Y_dec;
// Convert the difference to base B form
int diff = toBase(diff_dec, B);
// Return the difference
return diff;
}
// Driver Code
public static void main(String[] args) {
int X = 1212;
int Y = 256;
int B = 8;
System.out.println(getDifference(B, X, Y));
}
}
# Python code
# Function to convert a number in the given base to decimal form
def to_decimal(num, base):
res, power = 0, 1
while num > 0:
digit = num % 10
res += digit * power
power *= base
num //= 10
return res
# Function to convert a decimal number to the given base form
def to_base(num, base):
res, power = 0, 1
while num > 0:
digit = num % base
res += digit * power
power *= 10
num //= base
return res
# Function to find X - Y in base B
def get_difference(B, X, Y):
# Convert X and Y to decimal form
X_dec = to_decimal(X, B)
Y_dec = to_decimal(Y, B)
# Find the difference in decimal form
diff_dec = X_dec - Y_dec
# Convert the difference to base B form
diff = to_base(diff_dec, B)
return diff
# Driver Code
if __name__ == "__main__":
X = 1212
Y = 256
B = 8
print(get_difference(B, X, Y))
using System;
class Program
{
// Function to convert a number in given base
// to decimal form
static int ToDecimal(int num, int baseValue)
{
int res = 0, power = 1;
while (num > 0)
{
int digit = num % 10;
res += digit * power;
power *= baseValue;
num /= 10;
}
return res;
}
// Function to convert a decimal number
// to given base form
static int ToBase(int num, int baseValue)
{
int res = 0, power = 1;
while (num > 0)
{
int digit = num % baseValue;
res += digit * power;
power *= 10;
num /= baseValue;
}
return res;
}
// Function to find X - Y in base B
static int GetDifference(int B, int X, int Y)
{
// Convert X and Y to decimal form
int X_dec = ToDecimal(X, B);
int Y_dec = ToDecimal(Y, B);
// Find the difference in decimal form
int diff_dec = X_dec - Y_dec;
// Convert the difference to base B form
int diff = ToBase(diff_dec, B);
// Return the difference
return diff;
}
// Driver Code
static void Main()
{
int X = 1212;
int Y = 256;
int B = 8;
Console.WriteLine(GetDifference(B, X, Y));
}
}
// Function to convert a number in given base to decimal form
function toDecimal(num, base) {
let res = 0, power = 1;
while (num > 0) {
const digit = num % 10;
res += digit * power;
power *= base;
num = Math.floor(num / 10);
}
return res;
}
// Function to convert a decimal number to given base form
function toBase(num, base) {
let res = 0, power = 1;
while (num > 0) {
const digit = num % base;
res += digit * power;
power *= 10;
num = Math.floor(num / base);
}
return res;
}
// Function to find X - Y in base B
function getDifference(B, X, Y) {
// Convert X and Y to decimal form
const X_dec = toDecimal(X, B);
const Y_dec = toDecimal(Y, B);
// Find the difference in decimal form
const diff_dec = X_dec - Y_dec;
// Convert the difference to base B form
const diff = toBase(diff_dec, B);
// Return the difference
return diff;
}
// Driver Code
const X = 1212;
const Y = 256;
const B = 8;
console.log(getDifference(B, X, Y));
Output:
734
Time Complexity: O(log^2 N)
Auxiliary Space: O(log N)
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