baylor 6622 Absurdistan Roads( NWERC Contest)

ACM

原题pdf:click here

##Description
The people of Absurdistan discovered how to build roads only last year. After the discovery, every city
decided to build their own road connecting their city with another city. Each newly built road can be
used in both directions.

Absurdistan is full of surprising coincidences. It took all N cities precisely one year to build their
roads. And even more surprisingly, in the end it was possible to travel from every city to every other
city using the newly built roads.

HDU 2874 Connections between cities

ACM

Connections between cities

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4759 Accepted Submission(s): 1341

Problem Description

After World War X, a lot of cities have been seriously damaged, and we need to rebuild those cities. However, some materials needed can only be produced in certain places. So we need to transport these materials from city to city. For most of roads had been totally destroyed during the war, there might be no path between two cities, no circle exists as well.
Now, your task comes. After giving you the condition of the roads, we want to know if there exists a path between any two cities. If the answer is yes, output the shortest path between them.

内网2073 城主GeassCode

ACM

##Description

GeassCode凭借自己在topcoder上的超凡表现,赢得了国王的喜爱,国王赏赐他一座城池。这座城池里有n个 村子,m条路连接这些村子。坐上城主的GeassCode决定要修路,他打算用最少的代价把所以的村子连在一起。据探子回报,有些村子之间虽然原来没有路 径,但是可以强行的去建一条路。GeassCode想知道,如果强行在某两个村子之间建一条路,最后的总花费是多少?

POJ1989 Distance Queries

ACM

##Description

Farmer John’s cows refused to run in his marathon since he chose a path much too long for their leisurely lifestyle. He therefore wants to find a path of a more reasonable length. The input to this problem consists of the same input as in “Navigation Nightmare”,followed by a line containing a single integer K, followed by K “distance queries”. Each distance query is a line of input containing two integers, giving the numbers of two farms between which FJ is interested in computing distance (measured in the length of the roads along the path between the two farms). Please answer FJ’s distance queries as quickly as possible!

POJ1330 Nearest Common Ancestors

ACM

Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 17734 Accepted: 9405

##Description
A rooted tree is a well-known data structure in computer science and engineering. An example is shown below:

In the figure, each node is labeled with an integer from {1, 2,…,16}. Node 8 is the root of the tree. Node x is an ancestor of node y if node x is in the path between the root and node y. For example, node 4 is an ancestor of node 16. Node 10 is also an ancestor of node 16. As a matter of fact, nodes 8, 4, 10, and 16 are the ancestors of node 16. Remember that a node is an ancestor of itself. Nodes 8, 4, 6, and 7 are the ancestors of node 7. A node x is called a common ancestor of two different nodes y and z if node x is an ancestor of node y and an ancestor of node z. Thus, nodes 8 and 4 are the common ancestors of nodes 16 and 7. A node x is called the nearest common ancestor of nodes y and z if x is a common ancestor of y and z and nearest to y and z among their common ancestors. Hence, the nearest common ancestor of nodes 16 and 7 is node 4. Node 4 is nearer to nodes 16 and 7 than node 8 is.