What is the optimal time complexity of solving Count possible decoding of a given digit sequence?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Count possible decoding of a given digit sequence?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Count possible decoding of a given digit sequence?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Count possible decoding of a given digit sequence?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Count possible decoding of a given digit sequence

Learn how to solve the 'Count possible decoding of a given digit sequence' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function count_decodings(digits) that takes a string of digits and returns the number of possible ways to decode it, where 'A' = 1, 'B' = 2, ..., 'Z' = 26.

For example, '12' can be decoded as 'AB' (1, 2) or 'L' (12), giving 2 ways.

If the string contains '0' in an invalid position (e.g., leading '0' or '30'), those paths are invalid and should not be counted.

Constraints

•1 <= len(digits) <= 20
•digits contains only characters '0' through '9'

Examples

Example 1

Input

count_decodings('12')

Output

Explanation

'12' can be decoded as 'AB' (1,2) or 'L' (12). So 2 ways.

Example 2

Input

count_decodings('226')

Output

Explanation

'226' can be decoded as 'BBF' (2,2,6), 'BZ' (2,26), or 'VF' (22,6). So 3 ways.

Example 3

Input

count_decodings('06')

Output

Explanation

'06' cannot be decoded because '0' has no letter mapping and '06' is not a valid code.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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