Decode a given pattern in two ways (Flipkart Interview Question)

A sender sends a binary string to a receiver meanwhile he encrypt the digits. You are given a encrypted form of string. Now, the receiver needs to decode the string, and while decoding there were 2 approaches.

Let the encrypted binary string be P[] and actual string be S[].

First, receiver starts with first character as 0; 
S[0] = 0 // First decoded bit is 1
Remaining bits or S[i]s are decoded using following formulas.
P[1] = S[1] + S[0] 
P[2] = S[2] + S[1] + S[0] 
P[3] = S[3] + S[2] + S[1] 
and so on ...

Second, Receiver starts with first character as 1; 
S[0] = 1 // First decoded bit is 1
Remaining bits or S[i]s are decoded using following formulas.
P[1] = S[1] + S[0]  
P[2] = S[2] + S[1] + S[0] 
P[3] = S[3] + S[2] + S[1] 
and so on ... 

You need to print two string generated using two different after evaluation from both first and second technique. If any string contains other that binary numbers you need to print NONE.

Input1; 0123210
Output: 0111000, NONE

Explanation for first output
S[0] = 0, 
P[1] = S[1] + S[0], S[1] = 1
P[2] = S[2] + S[1] + S[0], S[2] = 1
P[3] = S[3] + S[2] + S[1], S[3] = 1
P[4] = S[4] + S[3] + S[2], S[4] = 0 
P[5] = S[5] + S[4] + S[3], S[5] = 0
P[6] = S[6] + S[5] + S[4], S[6] = 0

Explanation for second output 
S[0] = 1,
P[1] = S[1] + S[0], S[1] = 0
P[2] = s[2] + S[1] + S[0], S[2] = 1
P[3] = S[3] + S[2] + S[1], S[3] = 2, not a binary character so NONE.

Source: Flipkart Interview | Set 9 (On-Campus)

The idea to solve this problem is simple, we keep track of last two decoded bits. The current bit S[i] can always be calculated by subtracting last two decoded bits from P[i].

Following is the implementation of above idea. We store last two decoded bits in ‘first’ and ‘second’.

C++

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#include<iostream>
using namespace std;
  
// This function prints decoding of P[] with first decoded
// number as 'first'. If the decoded numbers contain anything
// other than 0, then "NONE" is printed
void decodeUtil(int P[], int n, int first)
{
    int S[n];  // array to store decoded bit pattern
    S[0] = first;  // The first number is always the given number
  
    int second = 0;  // Initialize second
  
    // Caclulate all bits starting from second
    for (int i = 1; i < n; i++)
    {
        S[i] = P[i] -  first - second;
        if (S[i] != 1 && S[i] != 0)
        {
            cout << "NONE\n";
            return;
        }
        second = first;
        first = S[i];
    }
  
    // Print the output array
    for (int i = 0; i < n; i++)
       cout << S[i];
    cout << endl;
}
  
// This function decodes P[] using two techniques
// 1) Starts with 0 as first number 2) Starts 1 as first number
void decode(int P[], int n)
{
    decodeUtil(P, n, 0);
    decodeUtil(P, n, 1);
}
  
int main()
{
    int P[] = {0, 1, 2, 3, 2, 1, 0};
    int n = sizeof(P)/sizeof(P[0]);
    decode(P, n);
    return 0;
}

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Python3

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# Python3 program to Decode a given
# pattern in two ways
  
# This function prints decoding of P[] with 
# first decoded number as 'first'. If the 
# decoded numbers contain anything other
# than 0, then "NONE" is printed
def decodeUtil(P, n, first):
    S = [0 for i in range(n)]
      
    # array to store decoded bit pattern
    S[0] = first # The first number is 
                 # always the given number
  
    second = 0
      
    # Initialize second
  
    # Calculate all bits starting from second
    for i in range(1, n, 1):
        S[i] = P[i] - first - second
        if (S[i] != 1 and S[i] != 0):
            print("NONE")
            return
      
        second = first
        first = S[i]
  
    # Print the output array
    for i in range(0, n, 1):
        print(S[i], end = "")
    print("\n", end = "")
  
# This function decodes P[] using
# two techniques
# 1) Starts with 0 as first number
# 2) Starts 1 as first number
def decode(P, n):
    decodeUtil(P, n, 0)
    decodeUtil(P, n, 1)
  
# Driver Code
if __name__ == '__main__':
    P = [0, 1, 2, 3, 2, 1, 0]
    n = len(P)
    decode(P, n)
      
# This code is contributed by
# Shashank_Sharma

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PHP

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<?php
// PHP program to Decode a 
// given pattern in two ways
  
// This function prints decoding
// of P[] with first decoded
// number as 'first'. If the 
// decoded numbers contain anything
// other than 0, then "NONE" is printed
function decodeUtil($P, $n, $first)
{
      
    // The first number is always
    // the given number
    $S[0] = $first
  
    // Initialize second
    $second = 0; 
  
    // Caclulate all bits starting
    // from second
    for ($i = 1; $i < $n; $i++)
    {
        $S[$i] = $P[$i] - $first - $second;
        if ($S[$i] != 1 && $S[$i] != 0)
        {
            echo "NONE\n";
            return;
        }
        $second = $first;
        $first = $S[$i];
    }
  
    // Print the output array
    for ($i = 0; $i < $n; $i++)
    echo $S[$i];
    echo "\n";
}
  
// This function decodes P[] 
// using two techniques
// 1) Starts with 0 as first number 
// 2) Starts 1 as first number
function decode($P, $n)
{
    decodeUtil($P, $n, 0);
    decodeUtil($P, $n, 1);
}
  
    // Driver Code
    $P=array (0, 1, 2, 3, 2, 1, 0);
    $n = sizeof($P);
    decode($P, $n);
  
// This code is contributed by ajit
?>

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Output:

0111000
NONE

Time Complexity: O(n)

This article is contributed by Abhishek. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



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Improved By : jit_t, Shashank_Sharma



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