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++
#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 printedvoid 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 // Calculate 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 numbervoid 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;} |
Java
class GFG{ // 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 public static void decodeUtil(int P[], int n, int first) { // Array to store decoded bit pattern int S[] = new int[n]; // The first number is always // the given number S[0] = first; // Initialize second int second = 0; // Calculate 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) { System.out.println("NONE"); return; } second = first; first = S[i]; } // Print the output array for(int i = 0; i < n; i++) { System.out.print(S[i]); } System.out.println();}// Driver codepublic static void main(String []args){ int P[] = { 0, 1, 2, 3, 2, 1, 0 }; int n = P.length; // This function decodes P[] using // two techniques 1) Starts with 0 // as first number 2) Starts 1 as // first number decodeUtil(P, n, 0); decodeUtil(P, n, 1);}}// This code is contributed by avanitrachhadiya2155 |
Python3
# This function prints decoding of P[] with # first decoded number as 'first'. If the # decoded numbers contain anything other# than 0, then "NONE" is printeddef 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 numberdef decode(P, n): decodeUtil(P, n, 0) decodeUtil(P, n, 1)# Driver Codeif __name__ == '__main__': P = [0, 1, 2, 3, 2, 1, 0] n = len(P) decode(P, n) # This code is contributed by# Shashank_Sharma |
C#
using System;class GFG{ // 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 static void decodeUtil(int[] P, int n, int first){ // Array to store decoded bit pattern int[] S = new int[n]; // The first number is always // the given number S[0] = first; // Initialize second int second = 0; // Calculate 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) { Console.WriteLine("NONE"); return; } second = first; first = S[i]; } // Print the output array for(int i = 0; i < n; i++) { Console.Write(S[i]); } Console.WriteLine();}// Driver codestatic public void Main(){ int[] P = { 0, 1, 2, 3, 2, 1, 0 }; int n = P.Length; // This function decodes P[] using // two techniques 1) Starts with 0 // as first number 2) Starts 1 as // first number decodeUtil(P, n, 0); decodeUtil(P, n, 1);}}// This code is contributed by rag2127 |
PHP
<?php// This function prints decoding// of P[] with first decoded// number as 'first'. If the // decoded numbers contain anything// other than 0, then "NONE" is printedfunction decodeUtil($P, $n, $first){ // The first number is always // the given number $S[0] = $first; // Initialize second $second = 0; // Calculate all bits starting // from second for ($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 numberfunction 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?> |
Javascript
<script> // 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) { // Array to store decoded bit pattern let S = new Array(n); // The first number is always // the given number S[0] = first; // Initialize second let second = 0; // Calculate all bits starting // from second for(let i = 1; i < n; i++) { S[i] = P[i] - first - second; if (S[i] != 1 && S[i] != 0) { document.write("NONE" + "</br>"); return; } second = first; first = S[i]; } // Print the output array for(let i = 0; i < n; i++) { document.write(S[i]); } document.write("</br>"); } let P = [ 0, 1, 2, 3, 2, 1, 0 ]; let n = P.length; // This function decodes P[] using // two techniques 1) Starts with 0 // as first number 2) Starts 1 as // first number decodeUtil(P, n, 0); decodeUtil(P, n, 1);</script> |
Output
0111000 NONE
Time Complexity: O(n)
Auxiliary Space: O(n)
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