gistfile1.txt

using System;

class Solution
{
    public static string Decrypt(string word)
    {
      if(word == null || word.Length == 0)
        return "";
      
      var length = word.Length; 
      
      var source = new char[length];
      var firstChar = word[0];
      source[0] = firstChar == 'a' ? 'z' : (char)(word[0] - 1); // a -> z 
      
      for(int i = 1; i < length; i++)
      {
         //line 39 - (encrypt[i] - encrypt[i - 1]) + 26 * m -> a - z, for i >= 1
         int diff = word[i] - word[i-1]; // 10 -> 10 + 26 * 4 = 114
                                         // 111 - 110 + 26 * 4 = 105
         while(diff < 'a')
         {
           diff += 26;
         }
        
        source[i] = (char)diff;        
      }
      
      return new string(source); 
    }

    static void Main(string[] args)
    {

    }
}
/*
        c   r        i            m      e 
       99  114      105          109    101  
step 2 100 100+114  224 + 105 
            214      319              <- encrypt[i] = encrypt[i - 1] + source[i], i >= 1  -- Formula 1
step 3: 100  214 -26 * x        
          
        d    a - z
        d    n        o         t       q
  based on formula 1, I can imply that 
  
  source[i] = (char)(encrypt[i] - 1),   i = 0
            = (encrypt[i] - encrypt[i - 1]) + 26 * m -> a - z, for i >= 1
            
            */