The recursive part came to me pretty fast.
Start by explaining the recursive backtracking solution with two pointers, clearly defining the base cases and the branching logic for '?' and '*'. Then discuss the exponential time complexity and how memoization or DP can optimize it to O(m*n) by caching overlapping subproblems.
Pro tip: Mention that the greedy two-pointer approach with backtracking for '*' can achieve O(m*n) time and O(1) space, but the DP solution is more straightforward to reason about and less error-prone under pressure.
Confirm that '?' matches exactly one character and '*' matches any sequence including empty. Discuss edge cases like empty string or pattern, consecutive stars, and patterns starting with '*'.
Describe a function that takes indices i and j for s and p. If p[j] is '?' or matches s[i], recurse on i+1, j+1. If p[j] is '*', recurse on i+1, j (match one or more) or i, j+1 (match empty). Define base cases: if j reaches end, return i == len(s); if i reaches end, return all remaining in p are '*'.
Explain that the naive recursion has exponential time complexity due to overlapping subproblems, especially with multiple '*'. Mention that the recursion tree can be pruned but worst-case remains exponential.
Introduce memoization by caching results of (i, j) in a 2D array to avoid recomputation, reducing time to O(m*n). Alternatively, present a bottom-up DP table where dp[i][j] indicates if s[0..i) matches p[0..j), with transitions similar to recursion.
Compare memoization (top-down, easier to implement) vs DP (bottom-up, iterative). Mention space optimization for DP to O(n) using two rows. Also note the greedy two-pointer approach with backtracking for O(1) space, but highlight its complexity in reasoning.
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