31. 0/1 Knapsack

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Input: amount = 5, coins = [1, 2, 5]

Output: 4

Explanation: The combinations are: [5], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1].

Input: amount = 3, coins = [2]

Output: 0

Explanation: It's impossible to make an amount of 3 using only coins of denomination 2.

Input: amount = 10, coins = [10]

Output: 1

Explanation: There is only one way to make an amount of 10 using coins of denomination 10.

Time Complexity

O(nW)

Space Complexity

O(nW)