What is the optimal time complexity of solving Distinct Subsequences?

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 Distinct Subsequences?

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 Distinct Subsequences?

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 Distinct Subsequences?

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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Distinct Subsequences

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

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Problem Statement

Medium

Given two strings s and t, return the number of distinct subsequences of s which equals t.

A string's subsequence is a new string formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Write a function numDistinct(s: str, t: str) -> int.

Constraints

•1 <= len(s), len(t) <= 1000
•s and t consist of English letters

Examples

Example 1

Input

s = "rabbbit", t = "rabbit"

Output

Explanation

There are 3 ways you can generate "rabbit" from s: **rab**b**bit**, **ra**b**bbit**, **rab**bb**it**.

Example 2

Input

s = "babgbag", t = "bag"

Output

Explanation

There are 5 ways you can generate "bag" from s.

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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