D. ShortestPath Query

Codeforces

IDCF10057D

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

De Prezer loves troyic paths.Consider we have a graph with n vertices and m edges.Edges are directed in one way.And there is at most one edge from any vertex to any other vertex.If there is an edge from v to u, then c(v, u) is its color and w(v, u) is its length.Otherwise,c(v, u) = w(v, u) = - 1. A sequence p1, p2, ..., pk is a troyic path is and only if for each 1 ≤ i ≤ k, 1 ≤ pi ≤ n and if i < k, then c(pi, pi + 1) > - 1 and if i + 1 < k, then c(pi, pi + 1) ≠ c(pi + 1, pi + 2) . The length of such troyic path is and it's called a p1 - pk path. In such graph, length of the shortest path from vertex v to u is the minimum length of all v - u paths.(The length of the shortest path from any vertex to itself equals 0) De Prezer gives you a graph like above and a vertex s. De Prezer also loves query. So he gives you q queries and in each query, gives you number t and you should print the length of the shortest path from s to t (or - 1 if there is no troyic path from s to t) The first line of input contains three integers n and m and C, the number of vertices, the numbers of edges and the number of valid colors. The next m lines, each line contains 4 integers v, u, w(v, u), c(v, u) (1 ≤ v, u ≤ n and v ≠ u and 1 ≤ w(v, u) ≤ 109 and 1 ≤ c(v, u) ≤ C). The line after that contains integer s and q. The next q lines, each line contains information of one query, number t. 1 ≤ n, m, C, q ≤ 105 m ≤ n(n - 1) 1 ≤ s, t ≤ n For each query, print the answer. ## Input The first line of input contains three integers n and m and C, the number of vertices, the numbers of edges and the number of valid colors.The next m lines, each line contains 4 integers v, u, w(v, u), c(v, u) (1 ≤ v, u ≤ n and v ≠ u and 1 ≤ w(v, u) ≤ 109 and 1 ≤ c(v, u) ≤ C).The line after that contains integer s and q.The next q lines, each line contains information of one query, number t.1 ≤ n, m, C, q ≤ 105m ≤ n(n - 1)1 ≤ s, t ≤ n ## Output For each query, print the answer. [samples]

**Definitions** Let $ a, b \in \mathbb{Z}^+ $ with $ 1 \leq a, b \leq 10^5 $. **Objective** Compute $ c = \gcd(a, b) $, and store $ c $ in storage location 1.

API Response (JSON)

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