Problema
You may select any subset of the supplied coins. Each individual coin may be used at most once, even when multiple coins share a value. Find the smallest positive integer amount that no selection can produce.
Implement missing_coin_sum(coins).
Input
coins: The values of the available coins; duplicates represent separate coins.
Output
Return the smallest positive impossible amount.
Restricciones
1 ≤ number of coins ≤ 200,000. Each value is between 1 and 1,000,000,000.
Ejemplos
Entrada:
coins = [1, 1, 4]
Salida esperada:
expected = 3Entrada:
std::vector<long long> coins = {1, 1, 4};
Salida esperada:
long long expected = 3;Entrada:
long[] coins = new long[] {1, 1, 4};
Salida esperada:
long expected = 3;Explicación
Amounts 1 and 2 use the one-valued coins. No available subset totals 3.
Entrada:
coins = [2, 3]
Salida esperada:
expected = 1Entrada:
std::vector<long long> coins = {2, 3};
Salida esperada:
long long expected = 1;Entrada:
long[] coins = new long[] {2, 3};
Salida esperada:
long expected = 1;Explicación
There is no way to make 1 because every coin is worth at least 2.
Cómo abordarlo
Inténtalo primero por tu cuenta y luego abre las pistas una a una.
Pista 1
Sort the coins and build the smallest reachable sum from smallest upward.
Pista 2
If the next coin is larger than the first unreachable amount, that amount can never be formed.
Pista 3
Duplicates help only when they extend the currently reachable range without gaps.
Complejidad esperada
O(n log n) time, O(1) extra space, excluding sorting implementation details
Referencias
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