图论 - cool's Blog
[有向图最小生成树-朱刘算法]
做题的时候看到了这个算法，决定学习一下。
[费用流训练]
一直不会费用流，每天用单纯形骗分，被大骂一通，开始学习费用流。
费用流什么原理不是很清楚，但板子还是很好背的。
[CF652E]Pursuit For Artifacts
Johnny is playing a well-known computer game. The game are in some country, where the player can freely travel, pass quests and gain an experience.
In that country there are n islands and m bridges between them, so you can travel from any island to any other. In the middle of some bridges are lying ancient powerful artifacts. Johnny is not interested in artifacts, but he can get some money by selling some artifact.
At the start Johnny is in the island a and the artifact-dealer is in the island b (possibly they are on the same island). Johnny wants to find some artifact, come to the dealer and sell it. The only difficulty is that bridges are too old and destroying right after passing over them. Johnnie's character can't swim, fly and teleport, so the problem became too difficult.
Note that Johnny can't pass the half of the bridge, collect the artifact and return to the same island.
Determine if Johnny can find some artifact and sell it.
The first line contains two integers n and m (1 ≤ n ≤ 3·105, 0 ≤ m ≤ 3·105) — the number of islands and bridges in the game.
Each of the next m lines contains the description of the bridge — three integers xi, yi, zi (1 ≤ xi, yi ≤ n, xi ≠ yi, 0 ≤ zi ≤ 1), where xi andyi are the islands connected by the i-th bridge, zi equals to one if that bridge contains an artifact and to zero otherwise. There are no more than one bridge between any pair of islands. It is guaranteed that it's possible to travel between any pair of islands.
The last line contains two integers a and b (1 ≤ a, b ≤ n) — the islands where are Johnny and the artifact-dealer respectively.
If Johnny can find some artifact and sell it print the only word "YES" (without quotes). Otherwise print the word "NO" (without quotes).
[二分图匹配]bzoj1143
1143: [CTSC2008]祭祀river
Time Limit: 10 Sec Memory Limit: 162 MBSubmit: 1870 Solved: 932
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Description
在遥远的东方，有一个神秘的民族，自称Y族。他们世代居住在水面上，奉龙王为神。每逢重大庆典， Y族都会在水面上举办盛大的祭祀活动。我们可以把Y族居住地水系看成一个由岔口和河道组成的网络。每条河道连接着两个岔口，并且水在河道内按照一个固定的方向流动。显然，水系中不会有环流（下图描述一个环流的例子）。
由于人数众多的原因，Y族的祭祀活动会在多个岔口上同时举行。出于对龙王的尊重，这些祭祀地点的选择必须非常慎重。准确地说，Y族人认为，如果水流可以从一个祭祀点流到另外一个祭祀点，那么祭祀就会失去它神圣的意义。族长希望在保持祭祀神圣性的基础上，选择尽可能多的祭祀的地点。
Input
第一行包含两个用空格隔开的整数N、M，分别表示岔口和河道的数目，岔口从1到N编号。接下来M行，每行包含两个用空格隔开的整数u、v，描述一条连接岔口u和岔口v的河道，水流方向为自u向v。
Output
第一行包含一个整数K，表示最多能选取的祭祀点的个数。
Sample Input
1 2
3 4
3 2
4 2
Sample Output
【样例说明】
在样例给出的水系中，不存在一种方法能够选择三个或者三个以上的祭祀点。包含两个祭祀点的测试点的方案有两种：
选择岔口1与岔口3（如样例输出第二行），选择岔口1与岔口4。
水流可以从任意岔口流至岔口2。如果在岔口2建立祭祀点，那么任意其他岔口都不能建立祭祀点
但是在最优的一种祭祀点的选取方案中我们可以建立两个祭祀点，所以岔口2不能建立祭祀点。对于其他岔口
至少存在一个最优方案选择该岔口为祭祀点，所以输出为2。