Decode Ways
A message containing letters A-Z can be encoded as numbers: 'A' -> "1", 'B' -> "2", ..., 'Z' -> "26".
Given a string s containing only digits, return the number of ways to decode it.
Example:
226
3
- The input string
226can be decoded as follows:2as 'B',2as 'B',6as 'F', resulting in one possible decoding: 'BBF'.
- Another possible decoding is:
22as 'V',6as 'F', resulting in 'VF'.
- A third possible decoding is:
2as 'B',26as 'Z', resulting in 'BZ'.
- The total number of ways to decode
226is the sum of these possibilities, which is 1+1+1=3. - The final output is 3.
Constraints:
- 1 <= len(s) <= 100
- s contains only digits and may contain leading zeros
Background Knowledge
The "Decode Ways" problem is a classic example of a Dynamic Programming problem. Dynamic Programming is a method for solving complex problems by breaking them down into simpler subproblems, solving each subproblem only once, and storing the solutions to subproblems to avoid redundant computation. In the context of this problem, we need to understand how to break down the string s into smaller subproblems and use the solutions to these subproblems to compute the total number of ways to decode the string.
To approach this problem, we also need to understand the encoding scheme used to map letters to numbers. The scheme is based on the standard ordering of the alphabet, where 'A' corresponds to 1, 'B' corresponds to 2, and so on, up to 'Z' corresponding to 26. This means that a single digit can represent a letter (e.g., '1' -> 'A'), and two digits can also represent a letter (e.g., '11' -> 'AA' or '1' -> 'A' and '1' -> 'A'). We need to consider both cases when decoding the string.
The key to solving this problem lies in recognizing the overlapping subproblems that arise when decoding the string. For example, when decoding the string "12", we need to consider the possibilities for the first digit ('1' -> 'A') and the second digit ('2' -> 'B'), as well as the possibility that the first two digits represent a single letter ('12' -> 'L'). By breaking down the problem into smaller subproblems and solving each subproblem only once, we can efficiently compute the total number of ways to decode the string.
Algorithm/Approach
The general approach to solving this problem is to use a bottom-up dynamic programming strategy. This involves creating a table to store the solutions to subproblems and filling in the table in a systematic way. The table will store the number of ways to decode each prefix of the string s. By using this table, we can avoid redundant computation and efficiently compute the total number of ways to decode the string.
Continue the full explanation
You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.
Editor locked
The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.