The thematic wrapper fooled me for a second.
Recognize this as an unbounded knapsack/coin change problem where you need to find the minimum number of items to sum exactly to X. Use dynamic programming with a 1D array of size X+1, initialized to infinity except dp[0]=0, and iterate through all durations to update dp values. Return dp[X] if finite, else -1.
Pro tip: Mention that since durations are decimals, convert them to integers by multiplying by a common factor (e.g., 10 or 100) to avoid floating-point precision issues, then scale X accordingly. Also, discuss time and space complexity and potential optimizations like BFS for minimum coins.
Restate the problem to ensure understanding: given a target X and a list of decimal durations, find the minimum number of bookings (with repetition allowed) to sum exactly to X. Ask about constraints (e.g., X up to what value, number of experiences, precision of decimals) to determine the appropriate algorithm.
Convert all durations and X to integers by multiplying by a power of 10 (e.g., 100) to avoid floating-point errors. This transforms the problem into an integer coin change problem.
Use dynamic programming (bottom-up) for minimum coins: create an array dp of size X+1, initialize dp[0]=0 and others to infinity. For each amount from 1 to X, iterate through durations and update dp[amount] = min(dp[amount], dp[amount - duration] + 1). Alternatively, use BFS for unweighted shortest path.
Write code carefully, handling edge cases (X=0, no durations, impossible cases). Test with small examples and consider time/space complexity (O(X * N) time, O(X) space).
Mention alternative approaches like BFS (which can be more efficient if X is small) or mathematical insights (e.g., if all durations share a gcd that doesn't divide X, return -1). Discuss how to handle large X or many experiences.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.