Smallest Missing Integer Greater Than Sequential Prefix Sum

For the LeetCode-style version, first find the longest prefix beginning at index zero such that each value is exactly one greater than the previous value. Add those prefix values to sum. Then build a hash set containing every number in the array. The answer is the smallest integer strictly greater than sum that is absent, so begin with candidate = sum + 1 and increment while the set contains it. This is a direct simulation of the statement; do not confuse “sequential prefix” with any increasing subsequence later in the array. The prefix scan is O(n), set construction is O(n), and the candidate loop is amortized O(n) because at most the number of present values can be skipped. Space is O(n). Clarify behavior if the prompt allows negatives or duplicates: duplicates do not affect set membership, and the algorithm still follows the same definition.