Expert · Dynamic programming · 214 of 264
Fewest coins
Pay an amount exactly with the fewest coins; every coin value can be used as often as you like. Greedy does not always work (try 1 3 4 and 6).
Input: the coin values on one line, then the amount (up to 10000). Output: the fewest coins, or -1 if it is impossible.
Examples
Input
1 3 4 6
Output
2
Input
2 3
Output
-1
Input
1 5 10 25 63
Output
6
2 more tests check other inputs when you press Check.
Stuck? The idea behind dynamic programming
Break the problem into smaller ones that repeat, and keep each answer in a table so it is worked out only once.
Decide what one cell of the table means ("the best total using the first i items"), how it follows from earlier cells, and where it starts.
n = 10
ways = [0] * (n + 1)
ways[0] = 1
for i in range(1, n + 1):
ways[i] = ways[i - 1] + (ways[i - 2] if i >= 2 else 0)
print(ways[n]) # climbing 10 stairs, 1 or 2 at a timeWatch for: Fill the table in an order where every cell it needs is already filled.