Given a positive integer n. The problem is to check whether only the first and last bits are set in the binary representation of n.
Examples:
Input : 9 Output : Yes (9)10 = (1001)2, only the first and last bits are set. Input : 15 Output : No (15)10 = (1111)2, except first and last there are other bits also which are set.
Approach: Following are the steps:
- If n == 1, return “Yes”.
- Else check whether n-1 is a power of 2. Refer this post.
C++
// C++ to check whether the number has only // first and last bits set#include <bits/stdc++.h>using namespace std;// function to check whether 'n'// is a power of 2 or notbool powerOfTwo(unsigned int n){ return (!(n & n-1));}// function to check whether the number has only // first and last bits setbool onlyFirstAndLastAreSet(unsigned int n){ if (n == 1) return true; if (n == 2) return false; return powerOfTwo(n-1); }// Driver program to test aboveint main(){ unsigned int n = 9; if (onlyFirstAndLastAreSet(n)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java program to check whether the // number has only first and last // bits setimport java.util.*;class GFG{ // function to check whether 'n' // is a power of 2 or not static boolean powerOfTwo(int n) { return ((n & n - 1) == 0); } // function to check whether the number has // only first and last bits set static boolean onlyFirstAndLastAreSet(int n) { if (n == 1) return true; return powerOfTwo(n-1); } // Driver program to test above public static void main (String[] args) { int n = Integer.parseUnsignedInt("9"); if (onlyFirstAndLastAreSet(n)) System.out.println("Yes"); else System.out.println("No"); }} /* This code is contributed by Mr. Somesh Awasthi */ |
Python3
# Python3 program to check whether number # has only first and last bits set# function to check whether 'n'# is a power of 2 or notdef powerOfTwo (n): return (not(n & n-1))# function to check whether number # has only first and last bits setdef onlyFirstAndLastAreSet (n): if (n == 1): return True return powerOfTwo (n-1)# Driver program to test aboven = 9if (onlyFirstAndLastAreSet (n)): print('Yes')else: print('No')# This code is contributed by Shariq Raza |
C#
// C# program to check whether the// number has only first and last// bits setusing System;class GFG { // function to check whether 'n' // is a power of 2 or not static bool powerOfTwo(uint n) { return ((n & n - 1) == 0); } // function to check whether the number has // only first and last bits set static bool onlyFirstAndLastAreSet(uint n) { if (n == 1) return true; return powerOfTwo(n - 1); } // Driver program to test above public static void Main() { uint n = (uint)9; if (onlyFirstAndLastAreSet(n)) Console.WriteLine("Yes"); else Console.WriteLine("No"); }}// This code is contributed by Sam007 |
PHP
<?php// PHP to check whether the number // has only first and last bits set // function to check whether 'n' // is a power of 2 or not function powerOfTwo($n) { return (!($n & $n - 1)); } // function to check whether // the number has only first// and last bits set function onlyFirstAndLastAreSet($n) { if ($n == 1) return true; if ($n == 2) return false; return powerOfTwo($n - 1); } // Driver Code$n = 9; if (onlyFirstAndLastAreSet($n)) echo "Yes"; else echo "No"; // This code is contributed// by Sach_Code?> |
Javascript
<script>// Javascript to check whether the number has only // first and last bits set // function to check whether 'n' // is a power of 2 or not function powerOfTwo(n) { return (!(n & n-1)); } // function to check whether the number has only // first and last bits set function onlyFirstAndLastAreSet(n) { if (n == 1) return true; if (n == 2) return false; return powerOfTwo(n-1); } // Driver program to test above var n = 9; if (onlyFirstAndLastAreSet(n)) document.write("Yes"); else document.write("No"); </script> |
Output:
Yes
Time Complexity – O(1)
Space Complexity – O(1)
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