poj 1827 A Bunch Of Monsters 贪心（并查集优化）

Background 
Jim is a brave explorer. One day, he set out for his next destination, a mysterious hill. When he arrived at the foot of the hill, he was told that there were a bunch of monsters living in that hill, and was dissuaded from continuing his trip by the residents near the hill. Nevertheless, our Jim was so brave that he would never think of giving up his exploration. 
The monsters do exist! When he got into that hill, he was caught by a bunch of fearful monsters. 
Fortunately, the monsters didn’t plan to kill him or eat him for they were planning a big party. They wanted to invite Jim, a clever human being, to their party, in order to let human beings know that the monsters also have wonderful parties. 
Problem 
At the end of the party, the monsters promised that, after the last game, they would set Jim free. The game is described as follow: 
1. There are a great many boxes of treasure, which are numbered from 1 to X. One box has the only one number; one number can only appear on one box. Furthermore, we can assume that X is INFINITY, because the monsters have got a lot of treasure from the men they caught. 
2. There are N monsters in this game. Each picks up a card randomly. After that, he / she (it?) opens it, getting a positive integer number d[i], and cannot change it or pick up another card again. The range of d[i] is from 1 to M. If the i-th monster get the number d[i], he can only get the treasure box numbered equal to or less than d[i]. What’s more, one box only can be distributed to one monster; one monster can only get one box. 
3. Of course, there are many ways to distribute the boxes to the monsters when N monsters get their numbers; and not every monster can get a box in many cases. Jim has the right to make the arrangement; however, he also knows that the monsters that don’t get the boxes will also punish him. 
Jim knows the strength of the N monsters. The i-th one has the strength s[i]. We call the sum of strength s[i] of all the monsters that don’t get the boxes --- the DAMAGE to Jim. Your task is to help Jim find out the minimum DAMAGE to him. 

The input consists of several test cases. In the first line of each test case, there are two positive integers N and M (1<=N<=50000, 1<=M<=50000), indicating the number of monsters and the range of numbers the monsters possibly get on the cards. Then there are N integers d[i] (1<=d[i]<=M) in the following lines, which are the numbers those monsters got. And in the rest lines of one test case, there are other N positive integers s[i] (1<=s[i]<=20000), indicating the strength of each monsters. The test case starting with 2 zeros is the final test case and has no output.

For each test case, print your answer, the minimum DAMAGE, in one line without any redundant spaces.

1 1
1
1
7 7
6 4 4 2 3 4 3
10 70 20 60 30 50 40
0 0

0
50

题意及分析：

n个怪，每个怪有一个号码d[i]，伤害值为s[i]，怪需要分配一个箱子（分配箱子的编号<=d[i]），箱子编号为1-INF。一个怪一个箱子，一个箱子只分配一次。

贪心的思想在这里：1，怪的伤害越高，就应该首先被满足。2，如果有足够的箱子，那么第i的怪获得的箱子就得是d[i]（这样才能尽可能的利用），如果这个箱子已经被分配，就寻找编号小的箱子。所以按怪物的伤害排序就好了。

未优化的的代码如下：

贪心的思想没变，利用并查集优化其实是利用里面找根节点的函数。根节点的数值（也就是fun（d[i]）代表d[i]最近的可以利用的那个编号。这样每次就可以直接找到现行的可以利用的箱子，而不是用for循环一个一个的往前找。

代码如下：