Single source shortest path, negative weights


The input consists of several test cases. Each test case starts with a line with four non-negative integers, $1 \le n \le 1000$, $0 \le m \le 5000$, $1 \le q \le 100$ 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 three (space-separated) integers $u$, $v$ and $w$ indicating that there is an edge from $u$ to $v$ in the graph with weight $-2000 \le w \le 2000$. 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.


For each query, output a single line containing the minimum distance from node $s$ to the node specified in the query, the word “Impossible” if there is no path from $s$ to that node, or “-Infinity” if there are arbitrarily short paths 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
5 4 3 0
0 1 999
1 2 -2
2 1 1
0 3 2
2 1 1 0
0 1 -100
0 0 0 0

CPU Time limit 3 seconds
Memory limit 1024 MB
Difficulty 4.8medium
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License Creative Commons License (cc by)

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