Find the largest number smaller than integer N with maximum number of set bits

Difficulty Level : Medium
Last Updated : 08 Jun, 2020

Given an integer N, the task is to find the largest number smaller than N having the maximum number of set bits.

Examples:

Input : N = 345
Output : 255
Explanation:
345 in binary representation is 101011001 with 5 set bits, and 255 is 11111111 with maximum number of set bits less than the integer N.

Input : N = 2
Output : 1
Explanation:
2 in binary representation is 10 with 1 set bit, and 1 has maximum number of set bits less than the integer N.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach:

The naive way to solve the above problem is to iterate till the integer N and find the number of set bits of each number and store the number having the largest set bits at each step.

Below is the implementation of the above approach:

C++

// C++ implementation to Find the 
// largest number smaller than integer 
// N with maximum number of set bits 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to return the largest 
// number less than N 
int largestNum(int n) 
{ 
    int num = 0; 
  
    int max_setBits = 0; 
  
    // Iterate through all the numbers 
    for (int i = 0; i <= n; i++) { 
  
        // Find the number of set bits 
        // for the current number 
        int setBits = __builtin_popcount(i); 
  
        // Check if this number has the  
        // highest set bits 
        if (setBits >= max_setBits) { 
            num = i; 
            max_setBits = setBits; 
        } 
    } 
  
    // Return the result 
    return num; 
} 
  
// Driver code 
int main() 
{ 
    int N = 345; 
  
    cout << largestNum(N); 
  
    return 0; 
} 

Java

// Java implementation to Find the 
// largest number smaller than integer 
// N with maximum number of set bits 
class GFG  
{ 
          
    /* Function to get no of set  
    bits in binary representation  
    of positive integer n */
    static int countSetBits(int n)  
    {  
        int count = 0;  
        while (n > 0)  
        {  
            count += n & 1;  
            n >>= 1;  
        }  
        return count;  
    }  
      
    // Function to return the largest 
    // number less than N 
    static int largestNum(int n) 
    { 
        int num = 0; 
      
        int max_setBits = 0; 
      
        // Iterate through all the numbers 
        for (int i = 0; i <= n; i++) 
        { 
      
            // Find the number of set bits 
            // for the current number 
            int setBits = countSetBits(i); 
      
            // Check if this number has the  
            // highest set bits 
            if (setBits >= max_setBits)  
            { 
                num = i; 
                max_setBits = setBits; 
            } 
        } 
      
        // Return the result 
        return num; 
    } 
      
    // Driver code 
    public static void main (String[] args) 
    { 
        int N = 345; 
      
        System.out.println(largestNum(N)); 
    } 
} 
  
// This code is contributed by AnkitRai01 

Python3

# Python3 implementation to find the  
# largest number smaller than integer  
# N with maximum number of set bits  
  
# Function to return the largest  
# number less than N  
def largestNum(n):  
  
    num = 0;  
    max_setBits = 0;  
  
    # Iterate through all the numbers  
    for i in range(n + 1): 
  
        # Find the number of set bits  
        # for the current number  
        setBits = bin(i).count('1');  
  
        # Check if this number has the  
        # highest set bits  
        if (setBits >= max_setBits): 
            num = i;  
            max_setBits = setBits;  
  
    # Return the result  
    return num;  
  
# Driver code  
if __name__ == "__main__" :  
  
    N = 345;  
  
    print(largestNum(N));  
  
# This code is contributed by AnkitRai01 

C#

// C# implementation to Find the 
// largest number smaller than integer 
// N with a maximum number of set bits 
using System; 
      
class GFG{     
      
// Function to get no of set  
// bits in binary representation  
// of positive integer n  
static int countSetBits(int n)  
{  
    int count = 0;  
    while (n > 0)  
    {  
        count += n & 1;  
        n >>= 1;  
    }  
    return count;  
}  
      
// Function to return the largest 
// number less than N 
static int largestNum(int n) 
{ 
    int num = 0; 
    int max_setBits = 0; 
      
    // Iterate through all the numbers 
    for(int i = 0; i <= n; i++) 
    { 
         
       // Find the number of set bits 
       // for the current number 
       int setBits = countSetBits(i); 
         
       // Check if this number has  
       // the  highest set bits 
       if (setBits >= max_setBits)  
       { 
           num = i; 
           max_setBits = setBits; 
       } 
    } 
      
    // Return the result 
    return num; 
} 
      
// Driver code 
public static void Main(String[] args)  
{ 
    int N = 345; 
      
    Console.Write(largestNum(N)); 
} 
} 
  
// This code is contributed by shivanisinghss2110 

Output:

Efficient Approach: To optimize the above solution we have to observe that the number with the highest set bits will surely be of form 2^k – 1. So we only need to iterate over the possible values of k and find the highest value just less than the integer N. Since we are iterating over the exponent variable therefore at most log(N) steps will be required.

Below is the implementation of the above approach:

C++

// C++ implementation to Find the 
// largest number smaller than integer 
// N with maximum number of set bits 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to return the largest 
// number less than N 
int largestNum(int n) 
{ 
  
    int num = 0; 
  
    // Iterate through all possible values 
    for (int i = 0; i <= 32; i++) 
    { 
        // Multiply the number by 2 i times 
        int x = (1 << i); 
  
        if ((x - 1) <= n) 
            num = (1 << i) - 1; 
  
        else
            break; 
    } 
  
    // Return the final result 
    return num; 
} 
  
// Driver code 
int main() 
{ 
    int N = 345; 
  
    cout << largestNum(N); 
  
    return 0; 
} 

Java

// Java implementation to Find the 
// largest number smaller than integer 
// N with maximum number of set bits 
import java.util.*; 
class GFG{ 
  
// Function to return the largest 
// number less than N 
static int largestNum(int n) 
{ 
    int num = 0; 
  
    // Iterate through all possible values 
    for (int i = 0; i <= 32; i++) 
    { 
        // Multiply the number by 2 i times 
        int x = (1 << i); 
  
        if ((x - 1) <= n) 
            num = (1 << i) - 1; 
  
        else
            break; 
    } 
  
    // Return the final result 
    return num; 
} 
  
// Driver code 
public static void main(String args[]) 
{ 
    int N = 345; 
  
    System.out.print(largestNum(N)); 
} 
} 
  
// This code is contributed by Akanksha_Rai 

Python3

# Python3 implementation to find the 
# largest number smaller than integer 
# N with the maximum number of set bits 
  
# Function to return the largest 
# number less than N 
def largestNum(n): 
  
    num = 0; 
  
    # Iterate through all possible 
    # values 
    for i in range(32): 
  
        # Multiply the number by 
        # 2 i times 
        x = (1 << i); 
  
        if ((x - 1) <= n): 
            num = (1 << i) - 1; 
        else: 
            break; 
  
    # Return the final result 
    return num; 
  
# Driver code 
if __name__ == "__main__": 
  
    N = 345; 
  
    print(largestNum(N)); 
  
# This code is contributed by AnkitRai01 

C#

// C# implementation to Find the 
// largest number smaller than integer 
// N with maximum number of set bits 
using System; 
class GFG{ 
  
// Function to return the largest 
// number less than N 
static int largestNum(int n) 
{ 
    int num = 0; 
  
    // Iterate through all possible values 
    for (int i = 0; i <= 32; i++) 
    { 
        // Multiply the number by 2 i times 
        int x = (1 << i); 
  
        if ((x - 1) <= n) 
            num = (1 << i) - 1; 
  
        else
            break; 
    } 
  
    // Return the final result 
    return num; 
} 
  
// Driver code 
public static void Main() 
{ 
    int N = 345; 
  
    Console.Write(largestNum(N)); 
} 
} 
  
// This code is contributed by Nidhi_Biet 

Output:

Time Complexity: O(log N)

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My Personal Notes

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Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

C++

Java

Python3

C#