D. Graph and Queries
data structures; dsu; graphs; implementation; trees
You are given an undirected graph consisting of \(n\) vertices and \(m\) edges. Initially there is a single integer written on every vertex: the vertex \(i\) has \(p_i\) written on it. All \(p_i\) are distinct integers from \(1\) to \(n\).You have to process \(q\) queries of two types: \(1\) \(v\) — among all vertices reachable from the vertex \(v\) using the edges of the graph (including the vertex \(v\) itself), find a vertex \(u\) with the largest number \(p_u\) written on it, print \(p_u\) and replace \(p_u\) with \(0\); \(2\) \(i\) — delete the \(i\)-th edge from the graph. Note that, in a query of the first type, it is possible that all vertices reachable from \(v\) have \(0\) written on them. In this case, \(u\) is not explicitly defined, but since the selection of \(u\) does not affect anything, you can choose any vertex reachable from \(v\) and print its value (which is \(0\)).
The first line contains three integers \(n\), \(m\) and \(q\) (\(1 \le n \le 2 \cdot 10^5\); \(1 \le m \le 3 \cdot 10^5\); \(1 \le q \le 5 \cdot 10^5\)).The second line contains \(n\) distinct integers \(p_1\), \(p_2\), ..., \(p_n\), where \(p_i\) is the number initially written on vertex \(i\) (\(1 \le p_i \le n\)).Then \(m\) lines follow, the \(i\)-th of them contains two integers \(a_i\) and \(b_i\) (\(1 \le a_i, b_i \le n\), \(a_i \ne b_i\)) and means that the \(i\)-th edge connects vertices \(a_i\) and \(b_i\). It is guaranteed that the graph does not contain multi-edges.Then \(q\) lines follow, which describe the queries. Each line is given by one of the following formats: \(1\) \(v\) — denotes a query of the first type with a vertex \(v\) (\(1 \le v \le n\)). \(2\) \(i\) — denotes a query of the second type with an edge \(i\) (\(1 \le i \le m\)). For each query of the second type, it is guaranteed that the corresponding edge is not deleted from the graph yet.
For every query of the first type, print the value of \(p_u\) written on the chosen vertex \(u\).