Started doing DP straight on the float values and got maybe halfway through before the interviewer nudged me about precision.
First, clarify the problem requirements: whether to just determine feasibility or find the minimum number of coins, and whether unlimited coins of each denomination are available. Then, address the floating-point issue by converting all values to integers (e.g., cents) to avoid precision errors. Finally, discuss dynamic programming for the general case, noting that for canonical coin systems a greedy approach may work, but DP is safer.
Pro tip: Mention that in real-world systems like Airbnb, coin denominations are often canonical, but you should still handle non-canonical cases robustly. Also, emphasize the importance of integer conversion to avoid floating-point errors, which is a common pitfall in financial computations.
Ask whether the goal is to check feasibility or find the minimum number of coins, and whether coin supply is unlimited. Also confirm if denominations can be used multiple times.
Convert all denominations and the target to integers by multiplying by a common factor (e.g., 100 for cents) to avoid floating-point errors. Discuss rounding and precision considerations.
For small targets, use dynamic programming (unbounded knapsack) to find the minimum coins or feasibility. For large targets, consider greedy if the coin system is canonical, but verify or use DP with optimizations.
Implement DP with a 1D array of size target+1, initializing with infinity and dp[0]=0. Time complexity O(target * number of denominations), space O(target).
Compare greedy vs DP in terms of time and correctness. Mention edge cases: target=0, unreachable target, negative values, and very large targets requiring alternative approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.