POJ 1988 并查集 妙用deep数组

[align=center]Cube Stacking[/align]

Time Limit: 2000MS		Memory Limit: 30000K
Total Submissions: 23635		Accepted: 8281
Case Time Limit: 1000MS

Description
Farmer John and Betsy are playing a game with N (1 <= N <= 30,000)identical cubes labeled 1 through N. They start with N stacks, each containing a single cube. Farmer John asks Betsy to perform P (1<= P <= 100,000) operation. There
are two types of operations:

moves and counts.

* In a move operation, Farmer John asks Bessie to move the stack containing cube X on top of the stack containing cube Y.

* In a count operation, Farmer John asks Bessie to count the number of cubes on the stack with cube X that are under the cube X and report that value.

Write a program that can verify the results of the game.

Input
* Line 1: A single integer, P

* Lines 2..P+1: Each of these lines describes a legal operation. Line 2 describes the first operation, etc. Each line begins with a 'M' for a move operation or a 'C' for a count operation. For move operations, the line also contains two integers: X and Y.For
count operations, the line also contains a single integer: X.

Note that the value for N does not appear in the input file. No move operation will request a move a stack onto itself.

Output
Print the output from each of the count operations in the same order as the input file.

Sample Input

6
M 1 6
C 1
M 2 4
M 2 6
C 3
C 4

Sample Output

1
0
2

题意：搬箱子和架箱子，如果箱子上面有箱子，则再不打乱顺序的条件下把整体搬过去

先普及下基础：并查集就是在路径压缩的条件下找根，每次在函数返回的时候，顺带把路上遇到的人的BOSS改为最后找到的祖宗编号。这样可以提高今后找到最高领导人（也就是树的祖先）的速度。然后再merge中判断是不是在一个连通分量，若不是，则连通，把一个连通图的根赋给另一个连通图，靠这样的方式去合并一个连通分量。

看了网上大牛的思路做出来的，在并查集的基础上加一个deep数组，用来存旧根的深度，旧根的深度等于新根上一次的节点数，这里就是一个线树，最后输出的时候，查根，减去改节点的深度，再减去本身，就得到下面的箱子，很巧妙啊，整体分为了根的节点数，本身，本身的深度三部分，思路实在巧妙。

如 给出这个数据：

#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;
const int N =30010;
int father
, jiedian
, deep
;

int find(int x)
{
int temp;
if(x == father[x])
return x;
temp = father[x];
father[x] = find(temp);
deep[x] += deep[temp]; //与根结点的距离
return father[x];
}

int main()
{
//freopen("in.txt","r",stdin);
int p;
char ope;
int a, b;
int query;
int root1, root2;
scanf("%d", &p);
for(int i = 1; i < N; ++i) //init
{
father[i] = i;
jiedian[i] = 1;
deep[i] = 0;
}
for(int i = 0; i < p; ++i)
{
scanf("%*c%c", &ope);
if(ope == 'M')
{
scanf("%d%d", &a, &b);
root1 = find(a);
root2 = find(b);
if(root1 != root2)
{
father[root2] = root1;
deep[root2] = jiedian[root1]; //更新深度,这里的深度指的是root2箱子上箱子的个数，因为root1架在上面，离根的距离
jiedian[root1] += jiedian[root2]; //更新结点数，根下面的节点，包括根
}
}
else
{
scanf("%d", &query);
printf("%d\n", jiedian[find(query)] - deep[query] - 1); //减去自己
}
}
return 0;
}