Decode Ways:

A message containing letters fromA-Zis being encoded to numbers using the following mapping:

'A' -> 1
'B' -> 2
...
'Z' -> 26

Given an encoded message containing digits, determine the total number of ways to decode it.

For example,
Given encoded message"12", it could be decoded as"AB"(1 2) or"L"(12).

The number of ways decoding"12"is 2.

Solution

1. state: # of decede ways up till state i. Easy
2. Function: how to increment to next state. hard. See code. Best to find it with examples.
3. init.
4. return. end

what should the middle function be to next state?

class Solution(object):
    def numDecodings(self, s):
        """
        :type s: str
        :rtype: int
        """
        if s == None or len(s) == 0 or s[0] == "0":
            return 0

        # init
        n = len(s)
        dp = [1] * (n + 1)


        # function from top down approach
        for i in range(1, n):

            # case 1:
            if s[i] == "0": 
                if s[i - 1] == "1" or s[i - 1] == "2":
                    dp[i + 1]  = dp[i - 1]
                else:
                    return 0

            # case 2:
            elif s[i - 1] != "0" and int(s[i-1:i+1]) <= 26:
                dp[i + 1] = dp[i] + dp[i-1]

            # case 3:
            else:
                dp[i + 1] = dp[i]

        return dp[-1]