Count of Subsequences forming Palindrome with Binary representations

Last Updated : 20 May, 2022

Given an array A[]. The task is to count the number of subsequences such that concatenation of binary representation of the numbers represents palindrome.

Examples:

Input: A[] = {1, 2, 3}
Output: 4
Explanation: Binary representation of all elements are {1, 10, 11}
here the concatenation of {1, 3} => 111 makes palindrome
similarly, concatenation of {1, 2, 3} => 11011 makes palindrome, and
element {1} and {3} already have a palindromic binary form
Hence, total 4 subsequences are possible whose binary concatenation makes palindrome

Input: A[ ] = {4, 9, 3, 15, 23}
Output: 6

Approach: The problem can be solved by checking each subsequence for palindrome after converting the given array into the binary representation of each element.

Follow the steps to solve the problem:

Firstly, replace all the integers of the array into their binary representation and store it into a vector of string.
Now, find all the subsequence of the vector of string:
- Check, if the subsequence is a palindrome or not.
- If true, then increment the count.
Lastly, print the count.

Below is the implementation of the above approach:

C++

// C++ implementation of above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to convert array element into
// their binary representation
vector<string> convert(vector<int> arr,
                       int n)
{
 
    vector<string> v;
    int i, x;
    for (i = 0; i < n; i++) {
        x = arr[i];
        string s;
 
        // Convert into binary one by one
        while (x) {
 
            int r = x % 2;
            s += to_string(r);
            x /= 2;
        }
 
        // Reverse the string and store
        // into vector v
        reverse(s.begin(), s.end());
 
        v.push_back(s);
    }
    return v;
}
 
// Function to check palindrome
bool palindrome(string a, int i, int j)
{
    while (i < j) {
 
        // If the integer at i is
        // not equal to j
        // then return false
        if (a[i] != a[j])
            return false;
 
        i++;
        j--;
    }
 
    // All a[i] is equal to a[j]
    // then return true
    return true;
}
 
// Function to count palindromic subsequences
void countSubsequences(vector<string> arr,
                       int i, string s,
                       int& count)
{
    // Check the condition of palindrome
    // if it is the leaf of recursion tree
    if (i == arr.size()) {
        int l = s.length();
 
        // Check for palindrome and
        // increment count
        if (l > 0 && palindrome(s, 0, l - 1)) {
 
            count++;
        }
    }
    else {
 
        // Subsequence without including
        // the element at current index
        countSubsequences(arr, i + 1, s, count);
 
        // Concatenate string
        s += (arr[i]);
 
        // Subsequence including the element
        // at current index
        countSubsequences(arr, i + 1,
                          s, count);
    }
    return;
}
 
// Function to find all the subsequences
int solve(vector<int>& arr)
{
    int count = 0, i = 0;
    vector<string> v = convert(arr, arr.size());
 
    // Recursive function call
    countSubsequences(v, i, "", count);
    return count;
}
 
// Driver code
int main()
{
    vector<int> arr = { 4, 9, 3, 15, 23 };
 
    // First replace all the array element
    // to their binary form
    int count = solve(arr);
 
    cout << count;
    return 0;
}

Java

// Java program for the above approach
import java.io.*; 
import java.util.*; 
 
class GFG
{
 
  static int count = 0;
 
  static String reverse(String str)
  {
    char[] chars = str.toCharArray();
    for (int i = 0, j = str.length() - 1; i < j;
         i++, j--) {
      char c = chars[i];
      chars[i] = chars[j];
      chars[j] = c;
    }
    return new String(chars);
  }
 
  // Function to convert array element into
  // their binary representation
  static ArrayList convert(int[] arr, int n)
  {
 
    ArrayList<String> v = new ArrayList<String>();
    int i = 0, x = 0;
    for (i = 0; i < n; i++) {
      x = arr[i];
      String s = "";
 
      // Convert into binary one by one
      while (x > 0) {
 
        int r = x % 2;
        s += Integer.toString(r);
        x /= 2;
      }
 
      // Reverse the String and store
      // into vector v
      s = reverse(s);
 
      v.add(s);
    }
    return v;
  }
 
  // Function to check palindrome
  static boolean palindrome(String a, int i, int j)
  {
    while (i < j) {
 
      // If the integer at i is
      // not equal to j
      // then return false
      if (a.charAt(i) != a.charAt(j)) {
        return false;
      }
 
      i++;
      j--;
    }
 
    // All a[i] is equal to a[j]
    // then return true
    return true;
  }
 
  // Function to count palindromic subsequences
  static void countSubsequences(ArrayList<String> arr, int i,
                                String s)
  {
 
    // Check the condition of palindrome
    // if it is the leaf of recursion tree
    if (i == arr.size()) {
      int l = s.length();
 
      // Check for palindrome and
      // increment count
      if (l > 0 && palindrome(s, 0, l - 1) == true) {
 
        count++;
      }
    }
    else {
 
      // Subsequence without including
      // the element at current index
      countSubsequences(arr, i + 1, s);
 
      // Concatenate String
      s += (arr.get(i));
 
      // Subsequence including the element
      // at current index
      countSubsequences(arr, i + 1, s);
    }
    return;
  }
 
  // Function to find all the subsequences
  static int solve(int[] arr)
  {
    int i = 0;
    ArrayList<String> v = convert(arr, arr.length);
 
    // Recursive function call
    countSubsequences(v, i, "");
    return count;
  }
 
  // Driver Code
  public static void main(String args[])
  {
    int[] arr = { 4, 9, 3, 15, 23 };
 
    // First replace all the array element
    // to their binary form
    int c = solve(arr);
 
    System.out.print(c);
  }
}
 
// This code is contributed by sanjoy_62.

Python3

# Python3 code for the above approach
 
# Taking count as a global variable
count = 0
 
# Function to convert array element into
# their binary representation
def convert(arr, n):
    v = []
    for i in range(n):
        x = arr[i]
        s = ""
         
        # Convert into binary one by one
        while(x > 0):
            r = x % 2
            s = s + str(r)
            x = x // 2
        # Reverse the string and store
        # into list v
        s = s[::-1]
        v.append(s)
    return v
 
# Function to check palindrome
def palindrome(a, i, j):
    while(i < j):
       
        # If the integer at i is
        # not equal to j
        # then return false
        if(a[i] != a[j]):
            return False
        i = i + 1
        j = j - 1
    # All a[i] is equal to a[j]
    # then return true
    return True
     
# Function to count palindromic subsequences
def countSubsequences(arr, i, s):
    global count
     
    # Check the condition of palindrome
    # if it is the leaf of recursion tree
    if(i == len(arr)):
        l = len(s)  
        # Check for palindrome and
        # increment count
        if(l > 0 and palindrome(s, 0, l - 1)):
            count = count + 1
    else:
        # Subsequence without including
        # the element at current index
        countSubsequences(arr, i + 1, s)
         
        # Concatenate string
        s = s + arr[i]
         
        # Subsequence including the element
        # at current index
        countSubsequences(arr, i + 1, s)
    return
 
def solve(arr):
    i = 0
    v = convert(arr, len(arr))
    # Recursive function call
    countSubsequences(v, i, "")
    return count
     
# Driver code
arr = [4, 9, 3, 15, 23]
 
# First replace all the array element
# to their binary form
count = solve(arr)
print(count)
 
# This code is contributed by Pushpesh Raj

C#

// C# implementation of above approach
using System;
using System.Collections;
 
class GFG {
 
  static int count = 0;
 
  static string reverse(string str)
  {
    char[] chars = str.ToCharArray();
    for (int i = 0, j = str.Length - 1; i < j;
         i++, j--) {
      char c = chars[i];
      chars[i] = chars[j];
      chars[j] = c;
    }
    return new string(chars);
  }
 
  // Function to convert array element into
  // their binary representation
  static ArrayList convert(int[] arr, int n)
  {
 
    ArrayList v = new ArrayList();
    int i = 0, x = 0;
    for (i = 0; i < n; i++) {
      x = arr[i];
      string s = "";
 
      // Convert into binary one by one
      while (x > 0) {
 
        int r = x % 2;
        s += r.ToString();
        x /= 2;
      }
 
      // Reverse the string and store
      // into vector v
      s = reverse(s);
 
      v.Add(s);
    }
    return v;
  }
 
  // Function to check palindrome
  static bool palindrome(string a, int i, int j)
  {
    while (i < j) {
 
      // If the integer at i is
      // not equal to j
      // then return false
      if (a[i] != a[j]) {
        return false;
      }
 
      i++;
      j--;
    }
 
    // All a[i] is equal to a[j]
    // then return true
    return true;
  }
 
  // Function to count palindromic subsequences
  static void countSubsequences(ArrayList arr, int i,
                                string s)
  {
     
    // Check the condition of palindrome
    // if it is the leaf of recursion tree
    if (i == arr.Count) {
      int l = s.Length;
 
      // Check for palindrome and
      // increment count
      if (l > 0 && palindrome(s, 0, l - 1) == true) {
 
        count++;
      }
    }
    else {
 
      // Subsequence without including
      // the element at current index
      countSubsequences(arr, i + 1, s);
 
      // Concatenate string
      s += (arr[i]);
 
      // Subsequence including the element
      // at current index
      countSubsequences(arr, i + 1, s);
    }
    return;
  }
 
  // Function to find all the subsequences
  static int solve(int[] arr)
  {
    int i = 0;
    ArrayList v = convert(arr, arr.Length);
 
    // Recursive function call
    countSubsequences(v, i, "");
    return count;
  }
 
  // Driver code
  public static void Main()
  {
    int[] arr = { 4, 9, 3, 15, 23 };
 
    // First replace all the array element
    // to their binary form
    int c = solve(arr);
 
    Console.Write(c);
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
 
// Taking count as a global variable
let count = 0
 
// Function to convert array element into
// their binary representation
function convert(arr, n){
    let v = []
    for(let i = 0; i < n; i++){
        let x = arr[i]
        let s = ""
         
        // Convert into binary one by one
        while(x > 0){
            let r = x % 2
            s += r.toString()
            x = Math.floor(x / 2)
        }
        // Reverse the string and store
        // into list v
        s = s.split("").reverse().join("")
        v.push(s)
    }
    return v
}
 
// Function to check palindrome
function palindrome(a, i, j){
    while(i < j){
       
        // If the integer at i is
        // not equal to j
        // then return false
        if(a[i] != a[j])
            return false
        i = i + 1
        j = j - 1
    }
     
    // All a[i] is equal to a[j]
    // then return true
    return true
}
     
// Function to count palindromic subsequences
function countSubsequences(arr, i, s){
     
    // Check the condition of palindrome
    // if it is the leaf of recursion tree
    if(i == arr.length){
        let l = s.length 
         
        // Check for palindrome and
        // increment count
        if(l > 0 && palindrome(s, 0, l - 1))
            count = count + 1
    }
    else
    {
     
        // Subsequence without including
        // the element at current index
        countSubsequences(arr, i + 1, s)
         
        // Concatenate string
        s = s + arr[i]
         
        // Subsequence including the element
        // at current index
        countSubsequences(arr, i + 1, s)
    }
    return
}
 
function solve(arr){
    let i = 0
    let v = convert(arr, arr.length)
     
    // Recursive function call
    countSubsequences(v, i, "")
    return count
}
     
// Driver code
let arr = [4, 9, 3, 15, 23]
 
// First replace all the array element
// to their binary form
count = solve(arr)
document.write(count,"</br>")
 
// This code is contributed by shinjanpatra
 
</script>