Given two positive integers X and Y, the task is to find the MSB of X, in the given base Y.
Examples:
Input: X = 55, Y = 3
Output: 2
Explanation:
55 is 2001 in base 3 with first digit as 2.
Input: X = 123, Y = 10
Output: 1
Explanation:
123 is 123 in base 10 with first digit 1.
Approach: Let the task to find 1st digit of X = 1234 in base Y = 10, So to get First digit = 1:
Divide 1234 by 1000
= X / 103
= X / 10Number of Digits in X – 1
= X / 10log(X) / log(10) (which is for base 10)
For any other base, we can replace 10 with Y. Therefore, we can calculate the first digit of a number X in base Y by using the formula:
X / Y(log(X)/log(Y))
Below is the implementation of the above approach:
// C++ Program to find the // first digit of X in base Y #include <bits/stdc++.h> using namespace std;
// Function to find the first // digit of X in base Y void first_digit( int x, int y)
{ // calculating number of digits of
// x in base y
int length = log (x) / log (y) + 1;
// finding first digit of x in base y
int first_digit = x / pow (y, length - 1);
cout << first_digit;
} // Driver code int main()
{ int X = 55, Y = 3;
first_digit(X, Y);
return 0;
} |
// Java Program to find the // first digit of X in base Y import java.util.*;
class GFG{
// Function to find the first // digit of X in base Y static void first_digit( int x, int y)
{ // calculating number of digits of
// x in base y
int length = ( int )(Math.log(x) /
Math.log(y) + 1 );
// finding first digit of x in base y
int first_digit = ( int )(x / Math.pow(y,
length - 1 ));
System.out.println(first_digit);
} // Driver code public static void main(String args[])
{ int X = 55 , Y = 3 ;
first_digit(X, Y);
} } // This code is contributed by AbhiThakur |
# Python3 program to find the # first digit of X in base Y import math
# Function to find the first # digit of X in base Y def first_digit(x, y):
# Calculating number of digits of
# x in base y
length = int (math.log(x) /
math.log(y) + 1 )
# Finding first digit of x in base y
first_digit = x / math. pow (y, length - 1 )
print ( int (first_digit))
# Driver code X = 55
Y = 3
first_digit(X, Y) # This code is contributed by ishayadav181 |
// C# Program to find the // first digit of X in base Y using System;
class GFG{
// Function to find the first // digit of X in base Y static void first_digit( int x, int y)
{ // calculating number of digits of
// x in base y
int length = ( int )(Math.Log(x) /
Math.Log(y) + 1);
// finding first digit of x in base y
int first_digit = ( int )(x / Math.Pow(y,
length - 1));
Console.Write(first_digit);
} // Driver code public static void Main()
{ int X = 55, Y = 3;
first_digit(X, Y);
} } // This code is contributed by Akanksha_Rai |
<script> // Javascript Program to find the // first digit of X in base Y // Function to find the first // digit of X in base Y function first_digit(x, y)
{ // calculating number of digits of
// x in base y
var length = parseInt(Math.log(x) / Math.log(y)) + 1;
// finding first digit of x in base y
var first_digit = parseInt(x / Math.pow(y, length - 1));
document.write( first_digit);
} // Driver code var X = 55, Y = 3;
first_digit(X, Y); </script> |
2
Time Complexity: O(1)
Auxiliary Space: O(1)