L3 · FAANGDynamic programming~15 min · 7 tests

Decode Ways (A=1 … Z=26)

Count the ways to decode a digit string where A=1 … Z=26 using a two-variable DP in O(n), handling the tricky zeros. A frequent Meta and Google question.

The problem

Letters are encoded as "1" → A … "26" → Z. Return the number of ways to decode the digit string s. A part like "06" is not valid.

Examples

Example 1
Input
```
num_decodings('12')
```
Expected output
```
2
```
Example 2
Input
```
num_decodings('226')
```
Expected output
```
3
```

+ 5 hidden tests on Submit — leading zero.

Edge cases to ask about

Leading zero
'10' and '20'
'30' is invalid

Hints

0/3

How an interviewer scores this

0/9

1. Understand the problemRestate it, ask about edge cases and input size.
2. Write a brute-force solutionCorrect first, clever later.
3. Get the correct outputautoAll visible examples pass.
4. Analyse time complexityautoCommit to a Big-O in the Complexity Lab.
5. Analyse space complexityautoExtra memory, not the input.
6. Identify the bottleneckautoMeasure your code — where does it bend?
7. OptimiseUsually: a set or dict instead of a scan.
8. Explain why it worksSay it out loud to Solvi.
9. Test the edge casesautoSubmit passes every hidden test.

Python 3.13 · num_decodings

def num_decodings(s):
    """Number of ways to decode s with A=1 ... Z=26."""
    # Write your solution here
    pass

⌘/Ctrl + Enter runs the examples

Your code runs in real CPython inside your browser — nothing is sent anywhere. The first run downloads the interpreter (about 6 MB, once). Your code is saved on this device as you type.

Complexity Lab

What does this cost as n grows?

Interviewers score the analysis as much as the code. Commit to an answer first — then check it, and measure your code against the optimal one at growing input sizes.

Time complexity of the optimal solution

Space complexity (extra memory)

Pick both to reveal the answer.

Measure it

Runs the function on inputs of size 250 up to 16,000 and records the time and peak memory. Slow solutions stop early — a short curve is itself the answer.

From brute force to optimal

The progression an interviewer wants to hear, one step at a time.

Approach	Time	Space	Idea
Recursion over 1- and 2-digit steps	O(2ⁿ)	O(n)
bestDP like Fibonacci	O(n)	O(1)	ways[i] = ways[i−1] (if s[i] ≠ '0') + ways[i−2] (if s[i−1:i+1] is 10–26).

Walkthrough of the optimal approach (try it yourself first)

ways[i] = number of decodings of the first i + 1 digits. The last step used either one digit (valid if it isn't "0") or two (valid if 10–26), so ways[i] = ways[i−1]·[single ok] + ways[i−2]·[pair ok]. Only the previous two values matter — Fibonacci-shaped, O(1) space.

Zeros are the whole difficulty: "10" → 1, "100" → 0, "06" → 0.

Complexity: O(n) time, O(1) space. One pass; only the last two counts are kept.

Reveal the reference solution

def num_decodings(s):
    if not s:
        return 0
    two_back, one_back = 1, 1 if s[0] != "0" else 0
    for i in range(1, len(s)):
        cur = 0
        if s[i] != "0":
            cur += one_back
        if 10 <= int(s[i - 1:i + 1]) <= 26:
            cur += two_back
        two_back, one_back = one_back, cur
    return one_back

Follow-ups interviewers ask

'*' can be any digit 1–9 (Decode Ways II).

Frequently asked interview questions

Core interview concepts, complexities, and follow-ups scored by hiring teams.

What is the time complexity of Decode Ways (A=1 … Z=26) in Python?

The optimal solution runs in O(n) time and O(1) auxiliary space. One pass; only the last two counts are kept.

What is the brute-force approach, and how do you optimise it?

Recursion over 1- and 2-digit steps: O(2ⁿ) time, O(n) space. DP like Fibonacci: O(n) time, O(1) space. ways[i] = ways[i−1] (if s[i] ≠ '0') + ways[i−2] (if s[i−1:i+1] is 10–26).

What follow-up questions do interviewers ask about Decode Ways (A=1 … Z=26)?

'*' can be any digit 1–9 (Decode Ways II).