Highest power of 2 less than or equal to given Integer
Given an integer N, the task is to find the highest power of 2 that is smaller than or equal to N.
Examples:
Input: N = 9
Output: 8
Explanation:
Highest power of 2 less than 9 is 8.Input: N = -20
Output: -32
Explanation:
Highest power of 2 less than -20 is -32.Input: N = -84
Output: -128
Approach: The idea is to use logarithm to solve the above problem. For any given number N, it can be either positive or negative. The following task can be performed for each case:
- If the input is positive: floor(log2(N)) can be calculated.
- If the input is negative: ceil(log2(N)) can be calculated and a -ve sign can be added to the value.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach #include <bits/stdc++.h> using namespace std; // Function to return the lowest power // of 2 close to given positive number int powOfPositive( int n) { // Floor function is used to determine // the value close to the number int pos = floor (log2(n)); return pow (2, pos); } // Function to return the lowest power // of 2 close to given negative number int powOfNegative( int n) { // Ceil function is used for negative numbers // as -1 > -4. It would be opposite // to positive numbers where 1 < 4 int pos = ceil (log2(n)); return (-1 * pow (2, pos)); } // Function to find the highest power of 2 void highestPowerOf2( int n) { // To check if the given number // is positive or negative if (n > 0) { cout << powOfPositive(n); } else { // If the number is negative, // then the ceil of the positive number // is calculated and // negative sign is added n = -n; cout << powOfNegative(n); } } // Driver code int main() { int n = -24; highestPowerOf2(n); return 0; } |
Java
// Java implementation of the above approach class GFG { // Function to return the lowest power // of 2 close to given positive number static int powOfPositive( int n) { // Floor function is used to determine // the value close to the number int pos = ( int )Math.floor((Math.log(n)/Math.log( 2 ))); return ( int )Math.pow( 2 , pos); } // Function to return the lowest power // of 2 close to given negative number static int powOfNegative( int n) { // Ceil function is used for negative numbers // as -1 > -4. It would be opposite // to positive numbers where 1 < 4 int pos = ( int )Math.ceil((Math.log(n)/Math.log( 2 ))); return ( int )(- 1 * Math.pow( 2 , pos)); } // Function to find the highest power of 2 static void highestPowerOf2( int n) { // To check if the given number // is positive or negative if (n > 0 ) { System.out.println(powOfPositive(n)); } else { // If the number is negative, // then the ceil of the positive number // is calculated and // negative sign is added n = -n; System.out.println(powOfNegative(n)); } } // Driver code public static void main (String[] args) { int n = - 24 ; highestPowerOf2(n); } } // This code is contributed by AnkitRai01 |
C#
// C# implementation of the above approach using System; class GFG { // Function to return the lowest power // of 2 close to given positive number static int powOfPositive( int n) { // Floor function is used to determine // the value close to the number int pos = ( int )Math.Floor((Math.Log(n)/Math.Log(2))); return ( int )Math.Pow(2, pos); } // Function to return the lowest power // of 2 close to given negative number static int powOfNegative( int n) { // Ceil function is used for negative numbers // as -1 > -4. It would be opposite // to positive numbers where 1 < 4 int pos = ( int )Math.Ceiling((Math.Log(n)/Math.Log(2))); return ( int )(-1 * Math.Pow(2, pos)); } // Function to find the highest power of 2 static void highestPowerOf2( int n) { // To check if the given number // is positive or negative if (n > 0) { Console.WriteLine(powOfPositive(n)); } else { // If the number is negative, // then the ceil of the positive number // is calculated and // negative sign is added n = -n; Console.WriteLine(powOfNegative(n)); } } // Driver code public static void Main() { int n = -24; highestPowerOf2(n); } } // This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the above approach from math import floor,ceil,log2 # Function to return the lowest power # of 2 close to given positive number def powOfPositive(n) : # Floor function is used to determine # the value close to the number pos = floor(log2(n)); return 2 * * pos; # Function to return the lowest power # of 2 close to given negative number def powOfNegative(n) : # Ceil function is used for negative numbers # as -1 > -4. It would be opposite # to positive numbers where 1 < 4 pos = ceil(log2(n)); return ( - 1 * pow ( 2 , pos)); # Function to find the highest power of 2 def highestPowerOf2(n) : # To check if the given number # is positive or negative if (n > 0 ) : print (powOfPositive(n)); else : # If the number is negative, # then the ceil of the positive number # is calculated and # negative sign is added n = - n; print (powOfNegative(n)); # Driver code if __name__ = = "__main__" : n = - 24 ; highestPowerOf2(n); # This code is contributed by AnkitRai01 |
Javascript
<script> // Javascript implementation of the above approach // Function to return the lowest power // of 2 close to given positive number function powOfPositive(n) { // Floor function is used to determine // the value close to the number let pos = Math.floor(Math.log2(n)); return Math.pow(2, pos); } // Function to return the lowest power // of 2 close to given negative number function powOfNegative(n) { // Ceil function is used for negative numbers // as -1 > -4. It would be opposite // to positive numbers where 1 < 4 let pos = Math.ceil(Math.log2(n)); return (-1 * Math.pow(2, pos)); } // Function to find the highest power of 2 function highestPowerOf2(n) { // To check if the given number // is positive or negative if (n > 0) { document.write(powOfPositive(n)); } else { // If the number is negative, // then the ceil of the positive number // is calculated and // negative sign is added n = -n; document.write(powOfNegative(n)); } } // Driver code let n = -24; highestPowerOf2(n); // This code is contributed by mohit kumar 29 </script> |
Output:
-32