Given a number N and base b if N in base b representation starts with 1 print Yes else print No
Examples :
Input : n = 6, b = 4 Output : Yes 6 can be written asin base 4so answer is Yes as it starts with 1Input : n = 24, b = 2Output : Yes24 can be written as
in base 2so answer is Yes as it starts with 1Input : n = 24, b = 7Output : No24 can be written as
in base 7so answer is No as it starts with 3
in base 4so answer is Yes as it starts with 1Input : n = 24, b = 2Output : Yes24 can be written as 
in base 2so answer is Yes as it starts with 1Input : n = 24, b = 7Output : No24 can be written as 
in base 7so answer is No as it starts with 3 
When a number N is represented in base ‘b’ it gets converted to m+1 length sequence 
[Tex]b_{m-1} [/Tex]…..
which implies *
+ 
*
…..+*
= N
The smallest number in base b and starting with ‘1’ i.e. 100..00 and m+1 digits in base is
and largest number is 2*-1.So N should lie in this range. <= N <= 2*-1
Now another thing to notice is that m cannot exceed floor(
(N)) because when we represent any number in base-2 it gets converted into a sequence of only 1s and 0s so the length of this sequence will always be greater than any other base representation and its length will be equal to floor((N))+1.
So to check for a given base ‘b’ if N starts with 1 or not we will traverse from m = 1 to m = floor((N)) and check if for any m N lies in the range <= N <= 2*-1 or not and accordingly print “Yes” or “No”.
C++
// C++ program to check if number starts with // one in base b representation #include <bits/stdc++.h> using namespace std; // Returns true if n starts with 1 in // base b representation bool CheckIfstartsWithOne(int n, int b) { // highest m can be log2(n) int m = log2(n); for (int i = 1; i <= m; i++) { // if b^m <= N <= 2*b^m - 1, // return true if (n >= pow(b, i) && n <= 2 * pow(b, i) - 1) return true; } return false; } // printing yes or no void printYesORno(int n, int b) { if (CheckIfstartsWithOne(n, b) == true) cout << "Yes" << endl; else if (CheckIfstartsWithOne(n, b) == false) cout << "No" << endl; } // driver function int main() { printYesORno(6, 4); printYesORno(24, 2); printYesORno(24, 7); printYesORno(24, 15); } |
Java
// Java program to check if number starts with // one in base b representation class GFG { // Returns true if n starts with 1 in // base b representation static boolean CheckIfstartsWithOne(int n, int b) { // highest m can be log2(n) int m = (int)(Math.log10(n) / Math.log10(2)); for (int i = 1; i <= m; i++) { // if b^m <= N <= 2*b^m - 1, // return true if (n >= (int)Math.pow(b, i) && n <= 2 * (int)Math.pow(b, i) - 1) return true; } return false; } // Driver method public static void main(String args[]) { System.out.println( CheckIfstartsWithOne(6, 4) ? "Yes" : "No"); System.out.println( CheckIfstartsWithOne(24, 2) ? "Yes" : "No"); System.out.println( CheckIfstartsWithOne(24, 7) ? "Yes" : "No"); System.out.println( CheckIfstartsWithOne(24, 15) ? "Yes" : "No"); } } |
Python3
# Python3 program to check # if number starts with one # in base b representation import math # Returns true if n # starts with 1 in # base b representation def CheckIfstartsWithOne(n, b): # highest m can be log2(n) m = (int)(math.log2(n)); for i in range (1, m + 1): # if b^m <= N <= 2*b^m - 1, #return true x = (int)(math.pow(b, i)); if n >= x and n <= 2 * x - 1: return 1; return 0; # printing yes or no def printYesORno(n, b): if CheckIfstartsWithOne(n, b) == 1: print("Yes"); if CheckIfstartsWithOne(n, b) == 0: print("No"); # Driver Code printYesORno(6, 4); printYesORno(24, 2); printYesORno(24, 7); printYesORno(24, 15); # This code is contributed by mits. |
C#
// C# program to check if number starts with // one in base b representation using System; class GFG{ // Returns true if n starts with 1 in // base b representation static bool CheckIfstartsWithOne(int n, int b) { // highest m can be log2(n) int m = (int)(Math.Log10(n) / Math.Log10(2)); for(int i = 1; i <= m; i++) { // if b^m <= N <= 2*b^m - 1, // return true if (n >= (int)Math.Pow(b, i) && n <= 2 * (int)Math.Pow(b, i) - 1) return true; } return false; } // Driver code public static void Main(String []args) { Console.WriteLine( CheckIfstartsWithOne(6, 4) ? "Yes" : "No"); Console.WriteLine( CheckIfstartsWithOne(24, 2) ? "Yes" : "No"); Console.WriteLine( CheckIfstartsWithOne(24, 7) ? "Yes" : "No"); Console.WriteLine( CheckIfstartsWithOne(24, 15) ? "Yes" : "No"); } } // This code is contributed by Princi Singh |
PHP
<?php // PHP program to check if // number starts with one // in base b representation // Returns true if n starts // with 1 in base b representation function CheckIfstartsWithOne($n, $b) { // highest m can be log2(n) $m = log($n, 2); for ($i = 1; $i <= $m; $i++) { // if b^m <= N <= 2*b^m - 1, // return true if ($n >= pow($b, $i) && $n <= 2 * pow($b, $i) - 1) return true; } return false; } // printing yes or no function printYesORno($n, $b) { if (CheckIfstartsWithOne($n, $b) == true) echo "Yes" ,"\n"; else if (CheckIfstartsWithOne($n, $b) == false) echo "No" ,"\n"; } // Driver Code printYesORno(6, 4); printYesORno(24, 2); printYesORno(24, 7); printYesORno(24, 15); // This code is contributed by ajit ?> |
Javascript
<script> // Javascript program to check if number starts // with one in base b representation // Returns true if n starts with // 1 in base b representation function CheckIfstartsWithOne(n, b) { // highest m can be log2(n) let m = parseInt(Math.log10(n) / Math.log10(2), 10); for (let i = 1; i <= m; i++) { // if b^m <= N <= 2*b^m - 1, // return true if (n >= Math.pow(b, i) && n <= 2 * Math.pow(b, i) - 1) return true; } return false; } document.write(CheckIfstartsWithOne(6, 4) ? "Yes" + "</br>" : "No" + "</br>"); document.write(CheckIfstartsWithOne(24, 2) ? "Yes" + "</br>" : "No" + "</br>"); document.write(CheckIfstartsWithOne(24, 7) ? "Yes" + "</br>" : "No" + "</br>"); document.write(CheckIfstartsWithOne(24, 15) ? "Yes" : "No"); </script> |
Output :
Yes Yes No Yes
Time Complexity: O(m), where m is calculated as log2(n)
Auxiliary Space: O(1), as no extra space is required
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