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.
Vincoli
1 ≤ number of coins ≤ 200,000. Each value is between 1 and 1,000,000,000.
Esempi
Input:
coins = [1, 1, 4]
Output atteso:
expected = 3Input:
std::vector<long long> coins = {1, 1, 4};
Output atteso:
long long expected = 3;Input:
long[] coins = new long[] {1, 1, 4};
Output atteso:
long expected = 3;Spiegazione
Amounts 1 and 2 use the one-valued coins. No available subset totals 3.
Input:
coins = [2, 3]
Output atteso:
expected = 1Input:
std::vector<long long> coins = {2, 3};
Output atteso:
long long expected = 1;Input:
long[] coins = new long[] {2, 3};
Output atteso:
long expected = 1;Spiegazione
There is no way to make 1 because every coin is worth at least 2.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
Sort the coins and build the smallest reachable sum from smallest upward.
Suggerimento 2
If the next coin is larger than the first unreachable amount, that amount can never be formed.
Suggerimento 3
Duplicates help only when they extend the currently reachable range without gaps.
Complessità attesa
O(n log n) time, O(1) extra space, excluding sorting implementation details
Riferimenti
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