Total Ways To Decode A String - Recursive Dynamic Programming Approach ("Decode Ways" on LeetCode)

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Question: A message containing letters from A-Z is being encoded to numbers using the following mapping: 'A' - 1 'B' - 2 ... 'Z' - 26. Given a non-empty string containing only digits, determine the total number of ways to decode it.

Examples:

1
Input: "12"
Output: 2
Explanation: It could be decoded as "AB" (1 2) or "L" (12).

2
Input: "226"
Output: 3
Explanation: It could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).
Complexities:

n is the total digits in the input string

Time: O( n )
Memoization prunes our recursion tree and we will do a linear amount of work to solve the problem.

Space: O( n )
We will need to store the answer to up to n subproblems that we will need to calculate
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