Count House Segments After Sequential Demolitions

## Problem Distinct houses occupy integer positions on a number line. Houses at consecutive positions belong to the same segment. Remove houses in the given query order and return the number of remaining segments after each removal. ### Function Contract Implement `segment_counts_after_removals(houses, queries) -> list[int]`. ### Constraints - `1 <= len(houses) <= 200000` and all positions are distinct. - Every query position occurs in `houses`, and query positions are distinct. - `1 <= len(queries) <= len(houses)`. - House positions are integers in `[-10^9, 10^9]`. ### Examples - `houses = [1,2,3,6,7,9]`, `queries = [6,3,7,2,9,1]` returns `[3,3,2,2,1,0]`. - Removing the only house returns `[0]`. ```hint Inspect immediate neighbors Removing one active house changes only the adjacency relationships with positions one less and one greater. ``` ```hint Or process in reverse Adding queried houses back in reverse turns deletion into a union operation; remember that houses never queried remain active initially. ``` ### Edge Cases - Removing an isolated house reduces the segment count by one. - Removing the middle of a segment splits it into two and increases the count by one. - Removing an endpoint leaves the number of segments unchanged unless it was a one-house segment.