Recover and Decode XORed Array in Python

Suppose we have a hidden array arr with n non-negative integers. Now this array is encoded into another array enc of length n-1. So here enc[i] = arr[i] XOR arr[i+1]. If we have the encoded enc array and an integer first, that is the first element of actual array, we have to find the original array.

So, if the input is like enc = [8,3,2,7], first = 4, then the output will be [4, 12, 15, 13, 10].

To solve this, we will follow these steps −

• arr := an array with only one element first

• for i in range 0 to size of enc - 1, do

  • insert arr[i] XOR enc[i] at the end of arr

• return arr

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

def solve(enc, first):
   arr = [first]
   for i in range(0, len(enc)):
      arr.append(arr[i] ^ enc[i])
   return arr

enc = [8,3,2,7]
first = 4
print(solve(enc, first))

Input

[8,3,2,7], 4

Output

[4, 12, 15, 13, 10]