Destroy Transportation System
Time Limit: 2000/1000 MS (Java/others) memory limit: 131072/131072 K (Java/Others)
Total submission (s): 114 accepted submission (s): 83
Problem descriptiontom is a commander, his task is destroying his enemy's transportation system.
Let's represent his enemy's transportation system as a simple directed graph G with N nodes and m edges. each node is a city and each directed edge is a directed Road. each edge from node u to node v is associated with two values D and B, D is the cost to destroy/remove such edge, B is the cost to build an undirected edge between u and v.
His enemy can deliver supplies from City U to city V if and only if there is a directed path from u to v. at first they can deliver supplies from any city to any other cities. so the graph is a stronugly-connected graph.
He will choose a non-empty proper subset of cities, let's denote this set as S. let's denote the complement set of S as T. he will command his soldiers to destroy all the edges (u, v) that u belongs to set S and v belongs to set T.
To destroy an edge, he must pay the related cost D. The total cost he will pay is X. You can use this formula to calculate X:
After that, all the edges from S to t are destroyed. in order to deliver huge number of supplies from S to T, his enemy will change all the remained directed edges (u, v) that u belongs to set T and V belongs to set S into undirected edges. (surely, those edges exist because the original graph is stronugly-connected)
To change an edge, they must remove the original directed edge at first, whose cost is d, then they have to build a new undirected edge, whose cost is B. the total cost they will pay is Y. you can use this formula to calculate Y:
At last, if y> = x, Tom will achieve his goal. but Tom is so lazy that he is unwilling to take a cup of time to choose a set S to make y> = x, he hope to choose set S randomly! So he asks you if there is a set S, such that Y <X. if such set exists, he will feel unhappy, because he must choose set S carefully, otherwise he will become very happy.
Inputthere are multiply test cases.
The first line contains an integer T (t <= 200), indicates the number of cases.
For each test case, the first line has two numbers N and M.
Next m lines describe each edge. Each line has four numbers U, V, D, B.
(2 = <n <= 200, 2 = <m <= 5000, 1 = <u, v <= N, 0 = <D, B <= 100000)
The meaning of all characters are described above. It is guaranteed that the input graph is stronugly-connected.
Outputfor each case, output "case # X:" First, X is the case number starting from 1.if such set doesn't exist, print "happy", else print "unhappy ".
Sample Input
23 31 2 2 22 3 2 23 1 2 23 31 2 10 22 3 2 23 1 2 2
Sample output
Case #1: happyCase #2: unhappyHintIn first sample, for any set S, X=2, Y=4. In second sample. S= {1}, T= {2, 3}, X=10, Y=4.
The points in the graph are divided into S and T sets, and any division x <= y is always valid.
Train of Thought: in fact, we can regard X as the lower bound of traffic, and Y as the upper bound of traffic. We can convert the problem into finding the maximum stream with the upper and lower bound of a passive and no sink.
This figure can be shown as follows: For any node I, the flow = Σ inflow lower bound traffic-Σ outflow lower bound traffic 1. flow> 0 indicates that node I must flow into the flow, and then from the additional source point to the I edge, the flow is 2. flow <0 indicates that node I must flow the flow, and the flow is
Then run the largest stream. After running, check whether each edge of the additional source point is full. If the stream is full
