POJ 1149 PIGS

DescriptionMirko works on a pig farm that consists of M locked pig-houses and Mirko can't unlock any pighouse because he doesn't have the keys. Customers come to the farm one after another. Each of them has keys to some pig-houses and wants to buy a certain number of pigs. All data concerning customers planning to visit the farm on that particular day are available to Mirko early in the morning so that he can make a sales-plan in order to maximize the number of pigs sold. More precisely, the procedure is as following: the customer arrives, opens all pig-houses to which he has the key, Mirko sells a certain number of pigs from all the unlocked pig-houses to him, and, if Mirko wants, he can redistribute the remaining pigs across the unlocked pig-houses. An unlimited number of pigs can be placed in every pig-house. Write a program that will find the maximum number of pigs that he can sell on that day.InputThe first line of input contains two integers M and N, 1 <= M <= 1000, 1 <= N <= 100, number of pighouses and number of customers. Pig houses are numbered from 1 to M and customers are numbered from 1 to N. The next line contains M integeres, for each pig-house initial number of pigs. The number of pigs in each pig-house is greater or equal to 0 and less or equal to 1000. The next N lines contains records about the customers in the following form ( record about the i-th customer is written in the (i+2)-th line): A K1 K2 ... KA B It means that this customer has key to the pig-houses marked with the numbers K1, K2, ..., KA (sorted nondecreasingly ) and that he wants to buy B pigs. Numbers A and B can be equal to 0.OutputThe first and only line of the output should contain the number of sold pigs.Sample Input3 33 1 102 1 2 22 1 3 31 2 6Sample Output7

题意：M个猪圈，N个顾客，每个顾客有一些的猪圈的钥匙，只能购买这些有钥匙的猪圈里的猪，而且要买一定数量的猪，每个猪圈有已知数量的猪，
但是猪圈可以重新打开，将猪的个数，重新分配，以达到卖出的猪的数量最多。

思路：刚学网络流，表示很菜很菜很菜~~
①构造网络，将顾客看成源点和汇点以外的结点，并设另外两个节点：源点和汇点。
②源点和每个猪圈的第一个顾客连边，边的权是开始时候猪圈中猪的数量。
③ 若源点和某个节点之间有重边，则将权合并
④顾客j紧跟顾客i之后打开某个猪圈，则<i.j>的权是正无穷。
⑤每个顾客和会点之间连边，边的权值是顾客所希望购买的猪的数量。
例如：样例中的就可以建立如图

自己的理解：

①每个猪圈在被使用后，它只会直接影响它的下一次被使用（影响下一个顾客），而并不会对以后的使用造成直接影响，

因此将使用同一个猪圈的相邻两个人(i, j)相连。

②本题的关键就在于两个相邻操作某个猪圈的顾客之间，前者直接影响后者，注意这和顾客的到来顺序有关，因此在

构图的时候要体现这样的特点。

网络流构图化简规则：规律 1. 如果几个节点的流量的来源完全相同，且流量为+∞，则可以把它们合并成一个。规律 2. 如果几个节点的流量的去向完全相同，且流量为+∞，则可以把它们合并成一个。规律 3. 如果从点 u 到点 v 有一条容量为 +∞ 的边，并且 u 是 v 的唯一流量来源，或者 v 是 u 的唯一流量去向，则可以把 u 和 v 合并成一个节点。

对于简化规则的应用：

①直观上可以如下构图：

根据简化规则消除一些无穷大的边，同时消去一些点。

经验：

网络流的题目重在构图，以后应该首先着眼于如何建模，并且根据简化规则对图进行必要的简化。