Count Coin Combinations

Use any number of each supplied denomination to make amount exactly. Count combinations, not orderings: two arrangements using the same counts of each coin are the same way. Denominations are distinct and positive.

Implement coin_sums(amount, coins).

Input

amount: The total amount to make.

coins: The available distinct denominations.

Output

Return the number of unordered combinations.

Restricciones

0 ≤ amount ≤ 200. There are 0 through 10 distinct denominations, each from 1 through 200. All counts fit signed 64-bit. Amount 0 has one way: choose no coins.

Ejemplos

Entrada:
coins = [1, 2]
amount = 4

Salida esperada:
expected = 3

Entrada:
std::vector<long long> coins = {1, 2};
long long amount = 4;

Salida esperada:
long long expected = 3;

Entrada:
long[] coins = new long[] {1, 2};
long amount = 4;

Salida esperada:
long expected = 3;

Entrada:
coins = [2]
amount = 3

Salida esperada:
expected = 0

Entrada:
std::vector<long long> coins = {2};
long long amount = 3;

Salida esperada:
long long expected = 0;

Entrada:
long[] coins = new long[] {2};
long amount = 3;

Salida esperada:
long expected = 0;

Referencias

Este reto está adaptado para CodeUtility. Sigue el enunciado y las restricciones indicadas arriba.

• #31 Coin Sums