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Occurrences of a pattern in binary representation of a number

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  • Difficulty Level : Medium
  • Last Updated : 11 Aug, 2021

Given a string pat and an integer N, the task is to find the number of occurrences of the pattern pat in binary representation of N.
Examples: 
 

Input: N = 2, pat = “101” 
Output:
Pattern “101” doesn’t occur in the binary representation of 2 (10).
Input: N = 10, pat = “101” 
Output:
Binary representation of 10 is 1010 and the given pattern occurs only once. 
 

 

Naive Approach: Convert the number into its binary string representation and then use a pattern matching algorithm to check the number of times the pattern has occurred in the binary representation.
Efficient Approach: 
 

  1. Convert the binary pattern into it’s decimal representation.
  2. Take an integer all_ones, whose binary representation consists of all set bits (equal to the number of bits in the pattern).
  3. Performing N & all_ones now will leave only the last k bits unchanged (others will be 0) where k is the number of bits in the pattern.
  4. Now if N = pattern, it means that N contained the pattern in the end in its binary representation. So update count = count + 1.
  5. Right shift N by 1 and repeat the previous two steps until N ≥ pattern & N > 0.
  6. Print the count in the end.

Below is the implementation of the above approach: 
 

C++




// C++ program to find the number of times
// pattern p occurred in binary representation
// on n.
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the count of occurrence
// of pat in binary representation of n
int countPattern(int n, string pat)
{
    // To store decimal value of the pattern
    int pattern_int = 0;
 
    int power_two = 1;
 
    // To store a number that has all ones in
    // its binary representation and length
    // of ones equal to length of the pattern
    int all_ones = 0;
 
    // Find values of pattern_int and all_ones
    for (int i = pat.length() - 1; i >= 0; i--) {
        int current_bit = pat[i] - '0';
        pattern_int += (power_two * current_bit);
        all_ones = all_ones + power_two;
        power_two = power_two * 2;
    }
 
    int count = 0;
    while (n && n >= pattern_int) {
 
        // If the pattern occurs in the last
        // digits of n
        if ((n & all_ones) == pattern_int) {
            count++;
        }
 
        // Right shift n by 1 bit
        n = n >> 1;
    }
    return count;
}
 
// Driver code
int main()
{
    int n = 500;
    string pat = "10";
    cout << countPattern(n, pat);
}

Java




// Java program to find the number of times
// pattern p occurred in binary representation
// on n.
import java.util.*;
 
class solution
{
 
// Function to return the count of occurrence
// of pat in binary representation of n
static int countPattern(int n, String pat)
{
    // To store decimal value of the pattern
    int pattern_int = 0;
 
    int power_two = 1;
 
    // To store a number that has all ones in
    // its binary representation and length
    // of ones equal to length of the pattern
    int all_ones = 0;
 
    // Find values of pattern_int and all_ones
    for (int i = pat.length() - 1; i >= 0; i--) {
        int current_bit = pat.charAt(i) - '0';
        pattern_int += (power_two * current_bit);
        all_ones = all_ones + power_two;
        power_two = power_two * 2;
    }
 
    int count = 0;
    while (n!=0 && n >= pattern_int) {
 
        // If the pattern occurs in the last
        // digits of n
        if ((n & all_ones) == pattern_int) {
            count++;
        }
 
        // Right shift n by 1 bit
        n = n >> 1;
    }
    return count;
}
 
// Driver code
public static void main(String args[])
{
    int n = 500;
    String pat = "10";
    System.out.println(countPattern(n, pat));
}
}

Python3




# Python 3 program to find the number of times
# pattern p occurred in binary representation
# on n.
 
# Function to return the count of occurrence
# of pat in binary representation of n
def countPattern(n, pat):
     
    # To store decimal value of the pattern
    pattern_int = 0
 
    power_two = 1
 
    # To store a number that has all ones in
    # its binary representation and length
    # of ones equal to length of the pattern
    all_ones = 0
 
    # Find values of pattern_int and all_ones
    i = len(pat) - 1
    while(i >= 0):
        current_bit = ord(pat[i]) - ord('0')
        pattern_int += (power_two * current_bit)
        all_ones = all_ones + power_two
        power_two = power_two * 2
        i -= 1
     
    count = 0
    while (n != 0 and n >= pattern_int):
         
        # If the pattern occurs in the last
        # digits of n
        if ((n & all_ones) == pattern_int):
            count += 1
         
        # Right shift n by 1 bit
        n = n >> 1
     
    return count
 
# Driver code
if __name__ == '__main__':
    n = 500
    pat = "10"
    print(countPattern(n, pat))
 
# This code is contributed by
# Surendra_Gangwar

C#




// C# program to find the number of times
// pattern p occurred in binary representation
// on n.
using System ;
 
class GFG
{
 
// Function to return the count of occurrence
// of pat in binary representation of n
static int countPattern(int n, string pat)
{
    // To store decimal value of the pattern
    int pattern_int = 0;
 
    int power_two = 1;
 
    // To store a number that has all ones in
    // its binary representation and length
    // of ones equal to length of the pattern
    int all_ones = 0;
 
    // Find values of pattern_int and all_ones
    for (int i = pat.Length - 1; i >= 0; i--)
    {
        int current_bit = pat[i] - '0';
        pattern_int += (power_two * current_bit);
        all_ones = all_ones + power_two;
        power_two = power_two * 2;
    }
 
    int count = 0;
    while (n != 0 && n >= pattern_int)
    {
 
        // If the pattern occurs in the last
        // digits of n
        if ((n & all_ones) == pattern_int)
        {
            count++;
        }
 
        // Right shift n by 1 bit
        n = n >> 1;
    }
    return count;
}
 
// Driver code
public static void Main()
{
    int n = 500;
    string pat = "10";
    Console.WriteLine(countPattern(n, pat));
}
}
 
// This code is contributed by Ryuga

PHP




<?php
// PHP program to find the number of times
// pattern pat occurred in binary representation
// of n.
 
// Function to return the count of occurrence
// of pat in binary representation of n
function countPattern($n, $pat)
{
    // To store decimal value of the pattern
    $pattern_int = 0;
 
    $power_two = 1;
 
    // To store a number that has all ones in
    // its binary representation and length
    // of ones equal to length of the pattern
    $all_ones = 0;
 
    // Find values of $pattern_int and $all_ones
    for ($i = strlen($pat) - 1; $i >= 0; $i--)
    {
        $current_bit = $pat[$i] - '0';
        $pattern_int += ($power_two * $current_bit);
        $all_ones = $all_ones + $power_two;
        $power_two = $power_two * 2;
    }
 
    $count = 0;
    while ($n && $n >= $pattern_int)
    {
 
        // If the pattern occurs in the last
        // digits of $n
        if (($n & $all_ones) == $pattern_int)
        {
            $count++;
        }
 
        // Right shift $n by 1 bit
        $n = $n >> 1;
    }
    return $count;
}
 
// Driver code
$n = 500;
$pat = "10";
echo countPattern($n, $pat);
 
// This code is contributed by ihritik
?>

Javascript




<script>
 
// Javascript program to find the number of times
// pattern p occurred in binary representation
// on n.
 
 
// Function to return the count of occurrence
// of pat in binary representation of n
function countPattern( n, pat)
{
    // To store decimal value of the pattern
    let pattern_int = 0;
 
    let power_two = 1;
 
    // To store a number that has all ones in
    // its binary representation and length
    // of ones equal to length of the pattern
    let all_ones = 0;
 
    // Find values of pattern_int and all_ones
    for (let i = pat.length - 1; i >= 0; i--) {
        let current_bit = pat.charAt(i) - '0';
        pattern_int += (power_two * current_bit);
        all_ones = all_ones + power_two;
        power_two = power_two * 2;
    }
 
    let count = 0;
    while (n!=0 && n >= pattern_int) {
 
        // If the pattern occurs in the last
        // digits of n
        if ((n & all_ones) == pattern_int) {
            count++;
        }
 
        // Right shift n by 1 bit
        n = n >> 1;
    }
    return count;
}
 
// Driver Code
 
let n = 500;
let pat = "10";
document.write(countPattern(n, pat));
 
</script>

Output: 

2

 

Time Complexity: O(N)
Auxiliary Space: O(1)


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