Interview Questions/Coding/First Unmakeable Coin Sum

First Unmakeable Coin Sum

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First Unmakeable Coin Sum

A shopkeeper has coins with different positive values. Using each coin at most once, some totals can be formed and some cannot. Return the smallest positive total that cannot be formed from the available coins.

Examples

Example 1
Input:
1 2 3
Output:
7

Approach hint

If all sums from 1 to x - 1 are possible, a coin of value at most x extends the reachable range.

Common mistake

Skipping assumptions, edge cases, or trade-offs can make an otherwise good answer feel incomplete.

solution.cpp