My first instinct was to just throw DP at it with floats and call it a day.
Convert all decimal denominations and the target amount to integer cents by multiplying by 100 and rounding to avoid floating-point errors. Then apply a standard dynamic programming approach for the unbounded coin change problem on the integer values, returning the minimum number of coins or -1 if impossible.
Pro tip: Mention that using integers (cents) is crucial for exactness and performance, and that you can optimize space by using a 1D DP array. Also, note that if the target is large, a BFS approach might be more efficient for finding the minimum coins.
Confirm that denominations and target are decimal values, then convert them to integer cents by multiplying by 100 and rounding to the nearest integer to avoid floating-point precision issues.
Check for invalid inputs: if target is 0, return 0; if any denomination is 0 or negative, or if target is negative, return -1. Also, if the target is not reachable, return -1.
Use dynamic programming with a 1D array of size target+1, initialized to infinity (or a large number), with dp[0] = 0. For each coin, iterate through the array and update dp[i] = min(dp[i], dp[i - coin] + 1).
Discuss time and space complexity: O(target * number of denominations) time and O(target) space. Mention potential optimizations like using BFS for sparse targets or pruning denominations larger than target.
After filling the DP array, if dp[target] is still infinity, return -1; otherwise, return dp[target] as the minimum number of coins.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.