Took me an embarrassingly long time to realize this was just longest common subsequence with a story wrapped around it.
Recognize this as the Longest Common Subsequence (LCS) problem: find the longest sequence of restaurant IDs that appears in both drivers' lists in the same relative order. Explain the dynamic programming approach, including the recurrence and how to reconstruct the actual route, and discuss time/space complexity and possible optimizations.
Pro tip: After presenting the DP solution, mention that if the lists are large and the alphabet of restaurant IDs is small, you can optimize space to O(min(m,n)) and use Hirschberg's algorithm to reconstruct the LCS in linear space. This shows you understand practical trade-offs beyond the basic solution.
Restate the problem to confirm understanding: we need the longest sequence of restaurant IDs that appears in both lists in the same order. Ask about constraints (list sizes, possible duplicates) and expected output (length or actual route).
State that this is the Longest Common Subsequence (LCS) problem, a classic dynamic programming problem. Explain why it fits: we need to preserve order and find the longest common subsequence.
Define dp[i][j] as the length of LCS of the first i elements of list A and first j elements of list B. Give the recurrence: if A[i-1] == B[j-1], dp[i][j] = dp[i-1][j-1] + 1; else dp[i][j] = max(dp[i-1][j], dp[i][j-1]). Base cases: dp[0][j] = dp[i][0] = 0.
Describe how to backtrack through the DP table to reconstruct the actual route. State time complexity O(m*n) and space complexity O(m*n), and mention space optimization to O(min(m,n)) if only length is needed.
Mention alternative approaches (e.g., if one list is much smaller, use it as the DP dimension; if duplicates are rare, use a hash map to find matching indices and reduce complexity). Discuss Hirschberg's algorithm for linear-space reconstruction.
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