UKSPC22 Practice Graphs

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2022-01-08 08:00 AKST

## UKSPC22 Practice Graphs

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2022-01-14 08:00 AKST
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# Problem JSingle source shortest path, time table

## Input

The input consists of several test cases. Each test case starts with a line with four non-negative integers, $1 \le n \le 10\, 000$, $0 \le m \le 20\, 000$, $1 \le q \le 100$ and $0 \le s < n$, separated by single spaces, where $n$ is the numbers of nodes in the graph, $m$ the number of edges, $q$ the number of queries and $s$ the index of the starting node. Nodes are numbered from $0$ to $n-1$. Then follow $m$ lines, each line consisting of five (space-separated) integers $u$, $v$, $t_{0}$, $P$ and $d$ indicating that there is an edge from $u$ to $v$ in the graph which can be traversed at time $t_{0} + t \cdot P$ for all nonnegative integers $t$, and that it takes $d$ time units to traverse the edge. You may assume $0 \le t_0, P, d \le 1000$.

For instance, the edge 3 8 15 10 5 indicates that at time $15, 25, 35, 45, \ldots$, we can travel from node $3$ to node $8$ in $5$ time units. Note that it is possible to stand still at a node, to wait for an edge to become available. Also, note that if $P = 0$, the edge can be used only at time $t_{0}$ and never again.

Then follow $q$ lines of queries, each consisting of a single non-negative integer, asking for the minimum distance from node $s$ to the node number given on the query line.

Input will be terminated by a line containing four zeros, this line should not be processed.

## Output

For each query, output a single line containing the minimum time to reach the node queried, assuming we start in node $s$ at time $0$, or the word “Impossible” if there is no path from $s$ to that node. For clarity, the sample output has a blank line between the output for different cases.

Sample Input 1 Sample Output 1
4 4 4 0
0 1 15 10 5
1 2 15 10 5
0 2 5 5 30
3 0 0 1 1
0
1
2
3
2 1 1 0
0 1 100 0 5
1
0 0 0 0

0
20
30
Impossible

105