AtCoder abc352

E

Problem Statement

You are given a weighted undirected graph $G$ with $N$ vertices, numbered $1$ to $N$. Initially, $G$ has no edges.

You will perform $M$ operations to add edges to $G$. The $i$-th operation $$(1\le i\le M)$$ is as follows:

• You are given a subset of vertices $S_i=\{A_{i,1},A_{i,2},\dots ,A_{i,K_i}\}$ consisting of $K_i$ vertices. For every pair $u,v$ such that $u,v\in S_i$ and $u<v$, add an edge between vertices $u$ and $$v$$ with weight $$C_i$$.

After performing all $M$ operations, determine whether $G$ is connected. If it is, find the total weight of the edges in a minimum spanning tree of $G$.

---

赛时用并查集做连通图的判断，用优先队列维护每一个点的最小连接边（仅值），但想不出如何生成最小生成树，维护信息不足

---

F

Problem Statement

There are $N$ people, numbered $1$ to $N$.

A competition was held among these $N$ people, and they were ranked accordingly. The following information is given about their ranks:

• Each person has a unique rank.
• For each $1\le i\le M$, if person $A_i$ is ranked $x$-th and person $B_i$ is ranked $y$-th, then $x-y=C_i$.

The given input guarantees that there is at least one possible ranking that does not contradict the given information.

Answer $N$ queries. The answer to the $i$-th query is an integer determined as follows:

• If the rank of person $i$ can be uniquely determined, return that rank. Otherwise, return $-1$.

这应该是真的难题，赛时也才过了480个人，初步想法为带权并查集维护一条奇怪的链，带着缺口的链，然后几根链子来判断最后的答案