Check if an encoding represents a unique binary string

Given an encoding of a binary string of length k, the task is to find if the given encoding uniquely identifies a binary string or not. The encoding has counts of contiguous 1s (separated by 0s).

For example, encoding of 11111 is {5}, encoding of 01101010 is {2, 1, 1} and encoding of 111011 is {3, 2}.

Examples :

Input: encoding[] = {3, 3, 3} 
       Length, k = 12 
Output: No

Explanation: There are more than one possible 
binary strings. The strings are 111011101110
and 011101110111. Hence “No” 

Input: encoding[] = {3, 3, 2} 
       Length, k = 10 
Output: Yes

Explanation: There is only one possible encoding 
that is 1110111011

A naive approach is to take an empty string and traverse through the n integers to no of 1s as given in encoding[0] and then add 1 zero to it, then encoding[1] 1s, and at the end check if the string length is equal to k then print “Yes” or print “No”

An efficient approach will be to add all the n integers to sum, and then add (n-1) to sum and check if it is equal to K, as n-1 will be the number of zeros in between every 1’s. Check if sum is equal to k, to get exactly one string or else there are more or none.

C++

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// C++ program to check if given encoding
// represents a single string.
#include <bits/stdc++.h>
using namespace std;
  
bool isUnique(int a[], int n, int k)
{
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += a[i];
      
    sum += n - 1; 
      
    // Return true if sum becomes k
    return (sum == k); 
}
  
// Driver Code
int main() 
{
  
int a[] = {3, 3, 3};
int n = sizeof(a) / sizeof(a[0]);
int k = 12;
if (isUnique(a, n, k))
    cout << "Yes";
else
    cout << "No";
return 0;
}

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Java

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// Java program to check if given encoding
// represents a single string.
import java.io.*;
  
class GFG
{
    static boolean isUnique(int []a, int n, int k)
    {
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += a[i];
          
        sum += n - 1
          
        // Return true if sum becomes k
        return (sum == k); 
    }
      
    // Driver Code
    static public void main (String[] args)
    {
        int []a = {3, 3, 3};
        int n = a.length;
        int k = 12;
        if (isUnique(a, n, k))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
  
// This code is contributed by vt_m

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Python3

# Python 3 program to check if given
# encoding represents a single string.

def isUnique(a, n, k):
sum = 0
for i in range(0, n, 1):
sum += a[i]

sum += n – 1

# Return true if sum becomes k
return (sum == k)

# Driver Code
if __name__ == ‘__main__’:
a = [3, 3, 3]
n = len(a)
k = 12
if (isUnique(a, n, k)):
print(“Yes”)
else:
print(“No”)

# This code is contributed by
# Surndra_Gangwar

C#

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// C# program to check if given encoding
// represents a single string.
using System;
  
class GFG
{
    static bool isUnique(int []a, int n, int k)
    {
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += a[i];
          
        sum += n - 1; 
          
        // Return true if sum becomes k
        return (sum == k); 
    }
      
    // Driver Code
    static public void Main ()
    {
        int []a = {3, 3, 3};
        int n = a.Length;
        int k = 12;
        if (isUnique(a, n, k))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
                  
    }
}
  
// This code is contributed by vt_m

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PHP

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<?php
// PHP program to check
// if given encoding 
// represents a single string
  
function isUnique( $a, $n, $k)
{
    $sum = 0;
    for ($i = 0; $i < $n; $i++)
        $sum += $a[$i];
      
    $sum += $n - 1; 
      
    // Return true if
    // sum becomes k
    return ($sum == $k); 
}
  
// Driver Code
$a = array(3, 3, 3);
$n = count($a);
$k = 12;
if (isUnique($a, $n,$k))
    echo"Yes";
else
    echo "No";
      
// This code is contributed by anuj_67.
?>

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Output :

No

Time complexity : O(n)
Auxiliary Space : O(1)

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Improved By : vt_m, SURENDRA_GANGWAR



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