分类目录归档:图论

[BZOJ3482][COCI2013]hiperprostor

Orz Claris菊苣

对于这道题我们发现q很小,那么大概率是让你在线去做

然后我们知道n,m也很小,大概率是用n,m做一个dp

所以设f[i][j]表示从s出发,到达i,恰好经过jx边的最短路,利用spfa求出。

如果对于任意的i都有f[t][i]=\infty,则答案为无解。

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Topcoder SRM705

SuperUserDo

Problem Statement

Fox Ciel just used the command "sudo" (super-user do) to gain administrative privileges in the UNIX-based operating system on her computer. She now wants to install several new programs. Each program has some dependencies: in addition to the program, the package manager has to install some libraries used by the program.
The package repository contains exactly 1000 libraries. For simplicity, we will number them from 1 to 1000, inclusive.
You are given the information about the dependencies of the programs Fox Ciel wants to install. More precisely, you are given the int[]s A and B, both containing the same number of elements. For each valid i, one of the programs needs all libraries that have numbers between A[i] and B[i], inclusive. Note that the programs may have overlapping dependences: multiple programs may require the same library to be installed. Of course, in such cases it is sufficient to install such a library once.
Calculate and return the total number of libraries that need to be installed.

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[bzoj 1880][Sdoi2009]Elaxia的路线

Description

最近,Elaxia和w**的关系特别好,他们很想整天在一起,但是大学的学习太紧张了,他们 必须合理地安排两个人在一起的时间。Elaxia和w**每天都要奔波于宿舍和实验室之间,他们 希望在节约时间的前提下,一起走的时间尽可能的长。 现在已知的是Elaxia和w**所在的宿舍和实验室的编号以及学校的地图:地图上有N个路 口,M条路,经过每条路都需要一定的时间。 具体地说,就是要求无向图中,两对点间最短路的最长公共路径。

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[bzoj 1295][SCOI2009]最长距离

Description

windy有一块矩形土地,被分为 N*M 块 1*1 的小格子。 有的格子含有障碍物。 如果从格子A可以走到格子B,那么两个格子的距离就为两个格子中心的欧几里德距离。 如果从格子A不可以走到格子B,就没有距离。 如果格子X和格子Y有公共边,并且X和Y均不含有障碍物,就可以从X走到Y。 如果windy可以移走T块障碍物,求所有格子间的最大距离。 保证移走T块障碍物以后,至少有一个格子不含有障碍物。

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[codeforces 76A] Gift

Description

The kingdom of Olympia consists of N cities and M bidirectional roads. Each road connects exactly two cities and two cities can be connected with more than one road. Also it possible that some roads connect city with itself making a loop.

All roads are constantly plundered with bandits. After a while bandits became bored of wasting time in road robberies, so they suggested the king of Olympia to pay off. According to the offer, bandits want to get a gift consisted of gold and silver coins. Offer also contains a list of restrictions: for each road it is known gi — the smallest amount of gold and si — the smallest amount of silver coins that should be in the gift to stop robberies on the road. That is, if the gift contains a gold and b silver coins, then bandits will stop robberies on all the roads that gi ≤ a and si ≤ b.

Unfortunately kingdom treasury doesn't contain neither gold nor silver coins, but there are Olympian tugriks in it. The cost of one gold coin in tugriks is G, and the cost of one silver coin in tugriks is S. King really wants to send bandits such gift that for any two cities there will exist a safe path between them. Your task is to find the minimal cost in Olympian tugriks of the required gift.

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[codeforces 734E] Anton and Tree

Description

Anton is growing a tree in his garden. In case you forgot, the tree is a connected acyclic undirected graph.

There are n vertices in the tree, each of them is painted black or white. Anton doesn't like multicolored trees, so he wants to change the tree such that all vertices have the same color (black or white).

To change the colors Anton can use only operations of one type. We denote it as paint(v), where v is some vertex of the tree. This operation changes the color of all vertices u such that all vertices on the shortest path from v to u have the same color (including v andu). For example, consider the tree

and apply operation paint(3) to get the following:

Anton is interested in the minimum number of operation he needs to perform in order to make the colors of all vertices equal.

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[codeforces 733F] Drivers Dissatisfaction

Description

In one kingdom there are n cities and m two-way roads. Each road connects a pair of cities, and for each road we know the level of drivers dissatisfaction — the value wi.

For each road we know the value ci — how many lamziks we should spend to reduce the level of dissatisfaction with this road by one. Thus, to reduce the dissatisfaction with the i-th road by k, we should spend k·ci lamziks. And it is allowed for the dissatisfaction to become zero or even negative.

In accordance with the king's order, we need to choose n - 1 roads and make them the main roads. An important condition must hold: it should be possible to travel from any city to any other by the main roads.

The road ministry has a budget of S lamziks for the reform. The ministry is going to spend this budget for repair of some roads (to reduce the dissatisfaction with them), and then to choose the n - 1 main roads.

Help to spend the budget in such a way and then to choose the main roads so that the total dissatisfaction with the main roads will be as small as possible. The dissatisfaction with some roads can become negative. It is not necessary to spend whole budget S.

It is guaranteed that it is possible to travel from any city to any other using existing roads. Each road in the kingdom is a two-way road.

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