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Check if an encoding represents a unique binary string

  • Difficulty Level : Easy
  • Last Updated : 27 Apr, 2021

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

 

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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++




// 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;
}

Java




// 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

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#




// 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

PHP




<?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.
?>

Javascript




<script>
// javascript program to check if given encoding
// represents a single string.
    function isUnique(a , n , k)
    {
        var 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
        var a = [ 3, 3, 3 ];
        var n = a.length;
        var k = 12;
        if (isUnique(a, n, k))
            document.write("Yes");
        else
            document.write("No");
 
// This code is contributed by Rajput-Ji
</script>

Output : 
 

No

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