Tutorial by Examples

Given coins of different denominations and a total, in how many ways can we combine these coins to get the total? Let's say we have coins = {1, 2, 3} and a total = 5, we can get the total in 5 ways: 1 1 1 1 1 1 1 1 2 1 1 3 1 2 2 2 3 The problem is closely related to knapsack problem. The o...

Given coins of different denominations and a total, how many coins do we need to combine to get the total if we use minimum number of coins? Let's say we have coins = {1, 5, 6, 8} and a total = 11, we can get the total using 2 coins which is {5, 6}. This is indeed the minimum number of coins require...