Program to find decode XORed permutation in Python

PythonServer Side ProgrammingProgramming

Suppose we have an array enc. There is an array perm that is a permutation of the first n(odd) positive integers. This list will be encoded into array enc of length n-1, such that enc[i] = perm[i] XOR perm[i+1]. We have to find the original array perm.

So, if the input is like enc = [2,5,6,3], then the output will be [7, 5, 0, 6, 5], here [7 XOR 5 XOR 0 XOR 6 XOR 5] = [2, 5, 6, 3]

To solve this, we will follow these steps −

  • n := size of enc
  • result := an array of size (n+1) and fill with 0
  • x := 0
  • for i in range 1 to n+1, do
    • x := x XOR i
  • result[0] := x
  • for i in range 1 to n, increase by 2, do
    • result[0] := result[0] XOR enc[i]
  • for i in range 1 to n, do
    • result[i] := result[i-1] XOR enc[i-1]
  • return result

Example

Let us see the following implementation to get better understanding −

def solve(enc):
   n = len(enc)
   result = [0] * (n+1)
   x = 0
   for i in range(1, n+2):
      x ^= i
   result[0] = x
   for i in range(1, n+1, 2):
      result[0] ^= enc[i]
   for i in range(1, n+1):
      result[i] = result[i-1] ^ enc[i-1]
   return result

enc = [2,5,6,3]
print(solve(enc))

Input

[2,5,6,3]

Output

[7, 5, 0, 6, 5]
raja
Published on 07-Oct-2021 11:04:03
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