What is the optimal time complexity of solving Decode Ways?

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 Decode Ways?

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 Decode Ways?

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 Decode Ways?

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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Decode Ways

Learn how to solve the 'Decode Ways' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

A message containing letters from A-Z can be encoded into numbers using the following mapping:

'A' -> "1"

'B' -> "2"

...

'Z' -> "26"

To decode an encoded message, all the digits must be grouped then mapped back into letters using the reverse mapping above. For example, "11106" can be mapped into:

- "AAJF" with the grouping (1 1 10 6)

- "KJF" with the grouping (11 10 6)

Note that the grouping (1 11 06) is invalid because "06" cannot be mapped into 'F' since "6" is different from "06".

Given a string s containing only digits, return the number of ways to decode it.

Write a function numDecodings(s: str) -> int.

Constraints

•1 <= len(s) <= 100
•s contains only digits and may contain leading zero(s)

Examples

Example 1

Input

s = "12"

Output

Explanation

"12" could be decoded as "AB" (1 2) or "L" (12).

Example 2

Input

s = "226"

Output

Explanation

"226" could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).

Example 3

Input

s = "06"

Output

Explanation

"06" cannot be mapped to 'F' because of the leading zero.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

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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