문제
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.
제약 조건
1 ≤ number of coins ≤ 200,000. Each value is between 1 and 1,000,000,000.
예시
입력:
coins = [1, 1, 4]
예상 출력:
expected = 3입력:
std::vector<long long> coins = {1, 1, 4};
예상 출력:
long long expected = 3;입력:
long[] coins = new long[] {1, 1, 4};
예상 출력:
long expected = 3;설명
Amounts 1 and 2 use the one-valued coins. No available subset totals 3.
입력:
coins = [2, 3]
예상 출력:
expected = 1입력:
std::vector<long long> coins = {2, 3};
예상 출력:
long long expected = 1;입력:
long[] coins = new long[] {2, 3};
예상 출력:
long expected = 1;설명
There is no way to make 1 because every coin is worth at least 2.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
Sort the coins and build the smallest reachable sum from smallest upward.
힌트 2
If the next coin is larger than the first unreachable amount, that amount can never be formed.
힌트 3
Duplicates help only when they extend the currently reachable range without gaps.
예상 복잡도
O(n log n) time, O(1) extra space, excluding sorting implementation details
참고 자료
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