標籤：acm hdu
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 strongly-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 strongly-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 strongly-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.
題意：將圖的點分成S和T集合，要求對任意的分法X<=Y始終成立
思路：其實可以將X看成流量的下界，將Y看成流量的上界，可以將問題轉化為求一個無源無匯的有上下界的最大流
這個建圖可以這樣來： 對於任意的節點i，令flow=∑流入的下界流量-∑流出的下界流量 1.flow>0 說明節點i一定要流入flow的流量，則從附加源點向i連邊，流量為flow 2.flow<0 說明節點i一定要流出flow的流量，則從i向附加匯點連邊，流量為flow
然後跑最大流，跑完之後檢查附加源點的每條邊是否滿流即可，如果滿流則滿足
