Check if given number is a power of d where d is a power of 2
Given an integer n, find whether it is a power of d or not, where d is itself a power of 2.
Examples:
Input : n = 256, d = 16 Output : Yes Input : n = 32, d = 16 Output : No
Method 1 Take log of the given number on base d, and if we get an integer then number is power of d.
Method 2 Keep dividing the number by d, i.e, do n = n/d iteratively. In any iteration, if n%d becomes non-zero and n is not 1 then n is not a power of d, otherwise n is a power of d.
Method 3(Bitwise)
A number n is a power of d if following conditions are met.
a) There is only one bit set in the binary representation of n (Note : d is a power of 2)
b) The count of zero bits before the (only) set bit is a multiple of log2(d).
For example: For n = 16 (10000) and d = 4, 16 is a power of 4 because there is only one bit set and count of 0s before the set bit is 4 which is a multiple of log2(4).
C++
// CPP program to find if a number is power // of d where d is power of 2. #include<stdio.h> unsigned int Log2n(unsigned int n) { return (n > 1)? 1 + Log2n(n/2): 0; } bool isPowerOfd(unsigned int n, unsigned int d) { int count = 0; /* Check if there is only one bit set in n*/if (n && !(n&(n-1)) ) { /* count 0 bits before set bit */ while (n > 1) { n >>= 1; count += 1; } /* If count is a multiple of log2(d) then return true else false*/ return (count%(Log2n(d)) == 0); } /* If there are more than 1 bit set then n is not a power of 4*/return false; } /* Driver program to test above function*/int main() { int n = 64, d = 8; if (isPowerOfd(n, d)) printf("%d is a power of %d", n, d); else printf("%d is not a power of %d", n, d); return 0; } |
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Java
// Java program to find if // a number is power of d // where d is power of 2. class GFG { static int Log2n(int n) { return (n > 1)? 1 + Log2n(n / 2): 0; } static boolean isPowerOfd(int n, int d) { int count = 0; /* Check if there is only one bit set in n*/if (n > 0 && (n & (n - 1)) == 0) { /* count 0 bits before set bit */ while (n > 1) { n >>= 1; count += 1; } /* If count is a multiple of log2(d) then return true else false*/ return (count % (Log2n(d)) == 0); } /* If there are more than 1 bit set then n is not a power of 4*/return false; } // Driver Code public static void main(String[] args) { int n = 64, d = 8; if (isPowerOfd(n, d)) System.out.println(n + " is a power of " + d); else System.out.println(n + " is not a power of " + d); } } // This code is contributed by mits |
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Python3
# Python3 program to find if a number # is power of d where d is power of 2. def Log2n(n): return (1 + Log2n(n / 2)) if (n > 1) else 0; def isPowerOfd(n, d): count = 0; # Check if there is only # one bit set in n if (n and (n & (n - 1))==0): # count 0 bits # before set bit while (n > 1): n >>= 1; count += 1; # If count is a multiple of log2(d) # then return true else false return (count%(Log2n(d)) == 0); # If there are more than 1 bit set # then n is not a power of 4 return False; # Driver Code n = 64; d = 8; if (isPowerOfd(n, d)): print(n,"is a power of",d); else: print(n,"is not a power of",d); # This code is contributed by mits |
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C#
// C# program to find if // a number is power of d // where d is power of 2. using System; class GFG { static int Log2n(int n) { return (n > 1)? 1 + Log2n(n / 2): 0; } static bool isPowerOfd(int n, int d) { int count = 0; /* Check if there is only one bit set in n*/if (n > 0 && (n & (n - 1)) == 0) { /* count 0 bits before set bit */ while (n > 1) { n >>= 1; count += 1; } /* If count is a multiple of log2(d) then return true else false*/ return (count % (Log2n(d)) == 0); } /* If there are more than 1 bit set then n is not a power of 4*/return false; } // Driver Code static void Main() { int n = 64, d = 8; if (isPowerOfd(n, d)) Console.WriteLine("{0} is a " + "power of {1}", n, d); else Console.WriteLine("{0} is not a"+ " power of {1}", n, d); } // This code is contributed by mits } |
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PHP
<?php // PHP program to find if a number // is power of d where d is power of 2. function Log2n($n) { return ($n > 1)? 1 + Log2n($n / 2): 0; } function isPowerOfd($n, $d) { $count = 0; // Check if there is only // one bit set in n if ($n && !($n & ($n - 1))) { // count 0 bits // before set bit while ($n > 1) { $n >>= 1; $count += 1; } /* If count is a multiple of log2(d) then return true else false*/ return ($count%(Log2n($d)) == 0); } /* If there are more than 1 bit set then n is not a power of 4*/ return false; } // Driver Code $n = 64; $d = 8; if (isPowerOfd($n, $d)) echo $n," ","is a power of ", $d; else echo $n," ","is not a power of ", $d; // This code is contributed by m_kit ?> |
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Output:
64 is a power of 8
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