Count Complete Digit-to-Letter Decodings
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
The codes `"1"` through `"26"` represent the letters A through Z. Given a digit string `s`, count how many ways its entire sequence can be divided into valid one- or two-digit codes. A code cannot begin with zero: `"6"` is valid, `"06"` is not, and `"0"` has no letter.
Return 0 if there is no complete decoding. The input cases guarantee that the final answer fits a signed 32-bit integer.
```cpp
int numDecodings(string s);
```
### Examples
```text
Input: s = "121"
Output: 3
```
The groupings are `1|2|1`, `12|1`, and `1|21`.
```text
Input: s = "100"
Output: 0
```
Neither the final zero on its own nor `00` is a valid code.
### Constraints
- `1 <= s.length <= 100`.
- `s` contains digits only and may start with zeros.
- The final number of complete decodings is at most 2147483647.
Overview: Count complete digit-to-letter decodings with valid zero handling and safe intermediate arithmetic under a final signed32 answer guarantee.