Decode Ways in Python

Suppose we have a message containing letters from A to Z is being encoded to numbers using the following mapping − 'A' → 1, 'B' → 2 ... 'Z' → 26. So if we have one non-empty string, containing only digits, then we have to find, in how many ways that can be decoded. So if the string is like “12”, then that can be made from “AB”, or “L”, so there are two possible ways. So the answer will be 2.

To solve this, we will follow these steps −

• We will solve this using dynamic programming.
• n := length of s
• dp := an array with n number of 0s
• if s[0] is not ‘0’, then dp[0] := 1
• for i in range 1 to n – 1
  • x := s[i] as integer, y := substring of s from index i – 1 to i + 1 as integer
  • if x >= 1 and y <= 9, then dp[i] := dp[i] + dp[i – 1]
  • if y >= 10 and y <= 26
    • if i – 2 >= 0, then dp[i] := dp[i] + dp[i – 2], otherwise increase dp[i] by 1
• return last element of dp

Example(Python)

Let us see the following implementation to get a better understanding −

 Live Demo

class Solution(object):
   def numDecodings(self, s):
      n = len(s)
      dp = [0 for i in range(n)]
      if s[0]!='0':
         dp[0]=1
      for i in range(1,n):
         x = int(s[i])
         y = int(s[i-1:i+1])
         if x>=1 and x<=9:
            dp[i]+=dp[i-1]
         if y>=10 and y<=26:
            if i-2>=0:
               dp[i]+=dp[i-2]
            else:
               dp[i]+=1
      return dp[-1]
ob1 = Solution()
print(ob1.numDecodings("226"))

Input

"226"

Output

3