Problem
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.
Constraints
1 ≤ number of coins ≤ 200,000. Each value is between 1 and 1,000,000,000.
Examples
Input:
coins = [1, 1, 4]
Expected output:
expected = 3Input:
std::vector<long long> coins = {1, 1, 4};
Expected output:
long long expected = 3;Input:
long[] coins = new long[] {1, 1, 4};
Expected output:
long expected = 3;Explanation
Amounts 1 and 2 use the one-valued coins. No available subset totals 3.
Input:
coins = [2, 3]
Expected output:
expected = 1Input:
std::vector<long long> coins = {2, 3};
Expected output:
long long expected = 1;Input:
long[] coins = new long[] {2, 3};
Expected output:
long expected = 1;Explanation
There is no way to make 1 because every coin is worth at least 2.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Sort the coins and build the smallest reachable sum from smallest upward.
Hint 2
If the next coin is larger than the first unreachable amount, that amount can never be formed.
Hint 3
Duplicates help only when they extend the currently reachable range without gaps.
Expected complexity
O(n log n) time, O(1) extra space, excluding sorting implementation details
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.