Check if a number is Bleak
A number ‘n’ is called Bleak if it cannot be represented as sum of a positive number x and set bit count in x, i.e., x + countSetBits(x) is not equal to n for any non-negative number x.
Examples :
Input : n = 3 Output : false 3 is not Bleak as it can be represented as 2 + countSetBits(2). Input : n = 4 Output : true 4 is t Bleak as it cannot be represented as sum of a number x and countSetBits(x) for any number x.
Method 1 (Simple)
bool isBleak(n)
1) Consider all numbers smaller than n
a) If x + countSetBits(x) == n
return false
2) Return true
Below is the implementation of the simple approach.
C++
// A simple C++ program to check Bleak Number #include <bits/stdc++.h> using namespace std; /* Function to get no of set bits in binary representation of passed binary no. */int countSetBits(int x) { unsigned int count = 0; while (x) { x &= (x - 1); count++; } return count; } // Returns true if n is Bleak bool isBleak(int n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for (int x = 1; x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code int main() { isBleak(3) ? cout << "Yes\n" : cout << "No\n"; isBleak(4) ? cout << "Yes\n" : cout << "No\n"; return 0; } |
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Java
// A simple Java program to check Bleak Number import java.io.*; class GFG { /* Function to get no of set bits in binary representation of passed binary no. */ static int countSetBits(int x) { int count = 0; while (x != 0) { x &= (x - 1); count++; } return count; } // Returns true if n is Bleak static boolean isBleak(int n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for (int x = 1; x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code public static void main(String args[]) { if (isBleak(3)) System.out.println("Yes"); else System.out.println("No"); if (isBleak(4)) System.out.println("Yes"); else System.out.println("No"); } } /*This code is contributed by Nikita Tiwari.*/ |
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Python3
# A simple Python 3 program # to check Bleak Number # Function to get no of set # bits in binary # representation of passed # binary no. def countSetBits(x) : count = 0 while (x) : x = x & (x-1) count = count + 1 return count # Returns true if n # is Bleak def isBleak(n) : # Check for all numbers 'x' # smaller than n. If x + # countSetBits(x) becomes # n, then n can't be Bleak. for x in range(1, n) : if (x + countSetBits(x) == n) : return False return True # Driver code if(isBleak(3)) : print( "Yes") else : print("No") if(isBleak(4)) : print("Yes") else : print( "No") # This code is contributed by Nikita Tiwari. |
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C#
// A simple C# program to check // Bleak Number using System; class GFG { /* Function to get no of set bits in binary representation of passed binary no. */ static int countSetBits(int x) { int count = 0; while (x != 0) { x &= (x - 1); count++; } return count; } // Returns true if n is Bleak static bool isBleak(int n) { // Check for all numbers // 'x' smaller than n. If // x + countSetBits(x) // becomes n, then n can't // be Bleak for (int x = 1; x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code public static void Main() { if (isBleak(3)) Console.Write("Yes"); else Console.WriteLine("No"); if (isBleak(4)) Console.Write("Yes"); else Console.Write("No"); } } // This code is contributed by // Nitin mittal |
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PHP
<?php // A simple PHP program // to check Bleak Number // Function to get no of // set bits in binary // representation of // passed binary no. function countSetBits( $x) { $count = 0; while ($x) { $x &= ($x - 1); $count++; } return $count; } // Returns true if n is Bleak function isBleak( $n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for($x = 1; $x < $n; $x++) if ($x + countSetBits($x) == $n) return false; return true; } // Driver code if(isBleak(3)) echo "Yes\n" ; else echo "No\n"; if(isBleak(4)) echo "Yes\n" ; else echo "No\n"; // This code is contributed by anuj_67. ?> |
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Output :
No Yes
Time complexity of above solution is O(n Log n).
Method 2 (Efficient)
The idea is based on the fact that the largest count of set bits in any number smaller than n cannot exceed ceiling of Log2n. So we need to check only numbers from range n – ceilingLog2(n) to n.
bool isBleak(n)
1) Consider all numbers n - ceiling(Log2n) to n-1
a) If x + countSetBits(x) == n
return false
2) Return true
Below is the implementation of the idea.
C++
// An efficient C++ program to check Bleak Number #include <bits/stdc++.h> using namespace std; /* Function to get no of set bits in binary representation of passed binary no. */int countSetBits(int x) { unsigned int count = 0; while (x) { x &= (x - 1); count++; } return count; } // A function to return ceiling of log x // in base 2. For example, it returns 3 // for 8 and 4 for 9. int ceilLog2(int x) { int count = 0; x--; while (x > 0) { x = x >> 1; count++; } return count; } // Returns true if n is Bleak bool isBleak(int n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for (int x = n - ceilLog2(n); x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code int main() { isBleak(3) ? cout << "Yes\n" : cout << "No\n"; isBleak(4) ? cout << "Yes\n" : cout << "No\n"; return 0; } |
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Java
// An efficient Java program to // check Bleak Number import java.io.*; class GFG { /* Function to get no of set bits in binary representation of passed binary no. */ static int countSetBits(int x) { int count = 0; while (x != 0) { x &= (x - 1); count++; } return count; } // A function to return ceiling of log x // in base 2. For example, it returns 3 // for 8 and 4 for 9. static int ceilLog2(int x) { int count = 0; x--; while (x > 0) { x = x >> 1; count++; } return count; } // Returns true if n is Bleak static boolean isBleak(int n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for (int x = n - ceilLog2(n); x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code public static void main(String[] args) { if (isBleak(3)) System.out.println("Yes"); else System.out.println("No"); if (isBleak(4)) System.out.println("Yes"); else System.out.println("No"); } } // This code is contributed by Prerna Saini |
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Python3
# An efficient Python 3 program # to check Bleak Number import math # Function to get no of set # bits in binary representation # of passed binary no. def countSetBits(x) : count = 0 while (x) : x = x & (x - 1) count = count + 1 return count # A function to return ceiling # of log x in base 2. For # example, it returns 3 for 8 # and 4 for 9. def ceilLog2(x) : count = 0 x = x - 1 while (x > 0) : x = x>>1 count = count + 1 return count # Returns true if n is Bleak def isBleak(n) : # Check for all numbers 'x' # smaller than n. If x + # countSetBits(x) becomes n, # then n can't be Bleak for x in range ((n - ceilLog2(n)), n) : if (x + countSetBits(x) == n) : return False return True # Driver code if(isBleak(3)) : print("Yes") else : print( "No") if(isBleak(4)) : print("Yes") else : print("No") # This code is contributed by Nikita Tiwari. |
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C#
// An efficient C# program to check // Bleak Number using System; class GFG { /* Function to get no of set bits in binary representation of passed binary no. */ static int countSetBits(int x) { int count = 0; while (x != 0) { x &= (x - 1); count++; } return count; } // A function to return ceiling // of log x in base 2. For // example, it returns 3 for 8 // and 4 for 9. static int ceilLog2(int x) { int count = 0; x--; while (x > 0) { x = x >> 1; count++; } return count; } // Returns true if n is Bleak static bool isBleak(int n) { // Check for all numbers // 'x' smaller than n. If // x + countSetBits(x) // becomes n, then n // can't be Bleak for (int x = n - ceilLog2(n); x < n; x++) if (x + countSetBits(x) == n) return false; return true; } // Driver code public static void Main() { if (isBleak(3)) Console.WriteLine("Yes"); else Console.WriteLine("No"); if (isBleak(4)) Console.WriteLine("Yes"); else Console.WriteLine("No"); } } // This code is contributed by anuj_67. |
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PHP
<?php // An efficient PHP program // to check Bleak Number /* Function to get no of set bits in binary representation of passed binary no. */function countSetBits( $x) { $count = 0; while ($x) { $x &= ($x - 1); $count++; } return $count; } // A function to return ceiling of log x // in base 2. For example, it returns 3 // for 8 and 4 for 9. function ceilLog2( $x) { $count = 0; $x--; while ($x > 0) { $x = $x >> 1; $count++; } return $count; } // Returns true if n is Bleak function isBleak( $n) { // Check for all numbers 'x' smaller // than n. If x + countSetBits(x) // becomes n, then n can't be Bleak for ($x = $n - ceilLog2($n); $x < $n; $x++) if ($x + countSetBits($x) == $n) return false; return true; } // Driver code if(isBleak(3)) echo "Yes\n" ; else echo "No\n"; if(isBleak(4)) echo "Yes\n" ; else echo "No\n"; // This code is contributed by anuj_67 ?> |
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Output :
No Yes
Time Complexity: O(Log n * Log n)
Note: In GCC, we can directly count set bits using __builtin_popcount(). So we can avoid a separate function for counting set bits.
// C++ program to demonstrate __builtin_popcount() #include <iostream> using namespace std; int main() { cout << __builtin_popcount(4) << endl; cout << __builtin_popcount(15); return 0; } |
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Output :
1 4
This article is contributed by Rahuain. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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