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Check if binary representations of 0 to N are present as substrings in given binary string
  • Last Updated : 31 Jul, 2020

Give binary string str and an integer N, the task is to check if the substrings of the string contain all binary representations of non-negative integers less than or equal to the given integer N.

Examples: 

Input: str = “0110″, N = 3 
Output: True 
Explanation: 
Since substrings “0″, “1″, “10″, and “11″ can be formed from given string. Hence all binary representations of 0 to 3 are present as substrings in given binary string.

Input: str = “0110”, N = 4 
Output: False 
Explanation: 
Since substrings “0″, “1″, “10″, and “11″ can be formed from given string, but not “100”. Hence the answer is False

 

Approach:  
The above problem can be solved using BitSet and HashMap. Follow the steps given below to solve the problem

  • Initialize a map[] to mark the strings and take a bit-set variable ans to convert the number from decimal to binary.
  • Take one more variable count as zero.
  • run the loop from N to 1 using the variable i and check the corresponding numbers are marked in a map or not.
  • if number i is not marked in a map[] then convert the current number into binary using the bit-set variable ans.
  • then check if converted binary string is substring of the given string or not.
  • if it is not a substring then
  • run while loop unless i is not marked and binary number becomes zero
    • mark the i in a map
    • increment the count
    • do the right shift of converted number. This is done because if any string x is converted into binary (say 111001) and this substring is already marked in map, then 11100 will already be marked automatically. 
      This is based on the fact that if i exists, i>>1 also exists.
  • Finally check if count ? N + 1, then print True 
    Else print False

Below is the implementation of above approach:

C++




// C++ program for the above approach 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to convert decimal to binary 
// representation 
string decimalToBinary(int N) 
  
    string ans = ""
  
    // Iterate over all bits of N 
    while (N > 0) { 
  
        // If bit is 1 
        if (N & 1) { 
            ans = '1' + ans; 
        
        else
            ans = '0' + ans; 
        
  
        N /= 2; 
    
  
    // Return binary representation 
    return ans; 
  
// Function to check if binary conversion 
// of numbers from N to 1 exists in the 
// string as a substring or not 
string checkBinaryString(string& str, int N) 
  
    // To store the count of number 
    // exists as a substring 
    int map[N + 10], cnt = 0; 
  
    memset(map, 0, sizeof(map)); 
  
    // Traverse from N to 1 
    for (int i = N; i > 0; i--) { 
  
        // If current number is not 
        // present in map 
        if (!map[i]) { 
  
            // Store current number 
            int t = i; 
  
            // Find binary of t 
            string s = decimalToBinary(t); 
  
            // If the string s is a 
            // substring of str 
            if (str.find(s) != str.npos) { 
  
                while (t && !map[t]) { 
  
                    // Mark t as true 
                    map[t] = 1; 
  
                    // Increment the count 
                    cnt++; 
  
                    // Update for t/2 
                    t >>= 1; 
                
            
        
    
  
    // Special judgment '0' 
    for (int i = 0; i < str.length(); i++) { 
        if (str[i] == '0') { 
            cnt++; 
            break
        
    
    // If the count is N+1, return "yes" 
    if (cnt == N + 1) 
        return "True"
    else
        return "False"
  
// Driver Code 
int main() 
    // Given String 
    string str = "0110"
  
    // Given Number 
    int N = 3; 
  
    // Function Call 
    cout << checkBinaryString(str, N); 
    return 0; 

Java




// Java program for the above approach 
import java.util.*;
  
class GFG{ 
  
// Function to convert decimal to binary 
// representation 
static String decimalToBinary(int N) 
    String ans = ""
  
    // Iterate over all bits of N 
    while (N > 0
    
          
        // If bit is 1 
        if (N % 2 == 1)
        
            ans = '1' + ans; 
        
        else
        
            ans = '0' + ans; 
        
        N /= 2
    
  
    // Return binary representation 
    return ans; 
  
// Function to check if binary conversion 
// of numbers from N to 1 exists in the 
// String as a subString or not 
static String checkBinaryString(String str, int N) 
      
    // To store the count of number 
    // exists as a subString 
    int []map = new int[N + 10];
    int cnt = 0
  
    // Traverse from N to 1 
    for(int i = N; i > 0; i--)
    
  
        // If current number is not 
        // present in map 
        if (map[i] == 0)
        
              
            // Store current number 
            int t = i; 
  
            // Find binary of t 
            String s = decimalToBinary(t); 
  
            // If the String s is a 
            // subString of str 
            if (str.contains(s))
            
                while (t > 0 && map[t] == 0)
                
                      
                    // Mark t as true 
                    map[t] = 1
  
                    // Increment the count 
                    cnt++; 
  
                    // Update for t/2 
                    t >>= 1
                
            
        
    
  
    // Special judgment '0' 
    for(int i = 0; i < str.length(); i++)
    
        if (str.charAt(i) == '0')
        
            cnt++; 
            break
        
    }
      
    // If the count is N+1, return "yes" 
    if (cnt == N + 1
        return "True"
    else
        return "False"
  
// Driver Code 
public static void main(String[] args) 
      
    // Given String 
    String str = "0110"
  
    // Given number 
    int N = 3
  
    // Function call 
    System.out.print(checkBinaryString(str, N)); 
}
  
// This code is contributed by 29AjayKumar

Python3




# Python3 implementation of
# the above approach
  
# Function to convert decimal to 
# binary representation
def decimalToBinary(N):
  
    ans = ""
  
    # Iterate over all bits of N
    while(N > 0):
  
        # If bit is 1
        if(N & 1):
            ans = '1' + ans
        else:
            ans = '0' + ans
  
        N //= 2
  
    # Return binary representation
    return ans
  
# Function to check if binary conversion
# of numbers from N to 1 exists in the
# string as a substring or not
def checkBinaryString(str, N):
  
    # To store the count of number
    # exists as a substring
    map = [0] * (N + 10)
    cnt = 0
  
    # Traverse from N to 1
    for i in range(N, -1, -1):
  
        # If current number is not
        # present in map
        if(not map[i]):
  
            # Store current number
            t = i
  
            # Find binary of t
            s = decimalToBinary(t)
  
            # If the string s is a
            # substring of str
            if(s in str):
                while(t and not map[t]):
                      
                    # Mark t as true
                    map[t] = 1
  
                    # Increment the count
                    cnt += 1
  
                    # Update for t/2
                    t >>= 1
  
    # Special judgment '0'
    for i in range(len(str)):
        if(str[i] == '0'):
            cnt += 1
            break
  
    # If the count is N+1, return "yes" 
    if(cnt == N + 1):
        return "True"
    else:
        return "False"
  
# Driver Code
if __name__ == '__main__':
  
    # Given String
    str = "0110"
  
    # Given Number
    N = 3
  
    # Function Call
    print(checkBinaryString(str, N))
  
# This code is contributed by Shivam Singh

C#




// C# program for the above approach 
using System;
  
class GFG{ 
  
// Function to convert decimal to binary 
// representation 
static String decimalToBinary(int N) 
    String ans = ""
  
    // Iterate over all bits of N 
    while (N > 0) 
    
          
        // If bit is 1 
        if (N % 2 == 1)
        
            ans = '1' + ans; 
        
        else
        
            ans = '0' + ans; 
        
        N /= 2; 
    
  
    // Return binary representation 
    return ans; 
  
// Function to check if binary conversion 
// of numbers from N to 1 exists in the 
// String as a subString or not 
static String checkBinaryString(String str, int N) 
      
    // To store the count of number 
    // exists as a subString 
    int []map = new int[N + 10];
    int cnt = 0; 
  
    // Traverse from N to 1 
    for(int i = N; i > 0; i--)
    
  
        // If current number is not 
        // present in map 
        if (map[i] == 0)
        
              
            // Store current number 
            int t = i; 
  
            // Find binary of t 
            String s = decimalToBinary(t); 
  
            // If the String s is a 
            // subString of str 
            if (str.Contains(s))
            
                while (t > 0 && map[t] == 0)
                
                      
                    // Mark t as true 
                    map[t] = 1; 
  
                    // Increment the count 
                    cnt++; 
  
                    // Update for t/2 
                    t >>= 1; 
                
            
        
    
  
    // Special judgment '0' 
    for(int i = 0; i < str.Length; i++)
    
        if (str[i] == '0')
        
            cnt++; 
            break
        
    }
      
    // If the count is N+1, return "yes" 
    if (cnt == N + 1) 
        return "True"
    else
        return "False"
  
// Driver Code 
public static void Main(String[] args) 
      
    // Given String 
    String str = "0110"
  
    // Given number 
    int N = 3; 
  
    // Function call 
    Console.Write(checkBinaryString(str, N)); 
}
  
// This code is contributed by PrinciRaj1992
Output: 
True

 




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