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++
// 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 Yvoid 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 codeint main(){ int X = 55, Y = 3; first_digit(X, Y); return 0;} |
Java
// Java Program to find the// first digit of X in base Yimport java.util.*;class GFG{// Function to find the first// digit of X in base Ystatic 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 codepublic static void main(String args[]){ int X = 55, Y = 3; first_digit(X, Y);}}// This code is contributed by AbhiThakur |
Python3
# 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 = 55Y = 3first_digit(X, Y)# This code is contributed by ishayadav181 |
C#
// C# Program to find the// first digit of X in base Yusing System;class GFG{// Function to find the first// digit of X in base Ystatic 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 codepublic static void Main(){ int X = 55, Y = 3; first_digit(X, Y);}}// This code is contributed by Akanksha_Rai |
Javascript
<script>// Javascript Program to find the// first digit of X in base Y// Function to find the first// digit of X in base Yfunction 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 codevar X = 55, Y = 3;first_digit(X, Y);</script> |
Output:
2
Time Complexity: O(1)
Auxiliary Space: O(1)
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