[BZOJ 2049] [Sdoi2008] Cave 洞穴勘测 【LCT】

题目链接：BZOJ - 2049

题目分析

LCT的基本模型，包括 Link ，Cut 操作和判断两个点是否在同一棵树内。

Link(x, y) : Make_Root(x); Splay(x); Father[x] = y;

Cut(x, y) : Make_Root(x); Access(y); 断掉 y 和 Son[y][0]; 注意修改 Son[y][0] 的 isRoot 和 Father

判断 x, y 是否在同一棵数内，我们就看两个点所在树的根是否相同，使用 Find_Root();

Find_Root(x) : Access(x); Splay(x); while (Son[x][0] != 0) x = Son[x][0]; 然后 x 就是树根了。

代码

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

inline void Read(int &Num)
{
	char c = getchar();
	bool Neg = false;
	while (c < '0' || c > '9')
	{
		if (c == '-') Neg = true;
		c = getchar();
	}
	Num = c - '0'; c = getchar();
	while (c >= '0' && c <= '9')
	{
		Num = Num * 10 + c - '0';
		c = getchar();
	}
	if (Neg) Num = -Num;
}

const int MaxN = 10000 + 5;

int n, m;
int Father[MaxN], Son[MaxN][2];

bool isRoot[MaxN], Rev[MaxN];

inline void Reverse(int x)
{
	Rev[x] = !Rev[x];
	swap(Son[x][0], Son[x][1]);
}

inline void PushDown(int x)
{
	if (!Rev[x]) return;
	Rev[x] = false;
	if (Son[x][0]) Reverse(Son[x][0]);
	if (Son[x][1]) Reverse(Son[x][1]);
}

void Rotate(int x)
{
	int y = Father[x], f;
	PushDown(y); PushDown(x);
	if (x == Son[y][0]) f = 1;
	else f = 0;
	if (isRoot[y])
	{
		isRoot[y] = false;
		isRoot[x] = true;
	}
	else
	{
		if (y == Son[Father[y]][0]) Son[Father[y]][0] = x;
		else Son[Father[y]][1] = x;
	}
	Father[x] = Father[y];
	Son[y][f ^ 1] = Son[x][f];
	if (Son[x][f]) Father[Son[x][f]] = y;
	Son[x][f] = y;
	Father[y] = x;
}

void Splay(int x)
{
	int y;
	while (!isRoot[x])
	{
		y = Father[x];
		if (isRoot[y])
		{
			Rotate(x);
			break;
		}
		if (y == Son[Father[y]][0])
		{
			if (x == Son[y][0])
			{
				Rotate(y);
				Rotate(x);
			}
			else
			{
				Rotate(x);
				Rotate(x);
			}
		}
		else
		{
			if (x == Son[y][1])
			{
				Rotate(y);
				Rotate(x);
			}
			else
			{
				Rotate(x);
				Rotate(x);
			}
		}
	}
}

int Access(int x)
{
	int y = 0;
	while (x != 0)
	{
		Splay(x);
		PushDown(x);
		isRoot[Son[x][1]] = true;
		Son[x][1] = y;
		if (y) isRoot[y] = false;
		y = x;
		x = Father[x];
	}
	return y;
}

void Make_Root(int x)
{
	int t = Access(x);
	Reverse(t);
}

int Find_Root(int x)
{
	int t = Access(x);
	while (Son[t][0] != 0) t = Son[t][0];
	return t;
}

int main()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; ++i)
	{
		isRoot[i] = true;
		Father[i] = 0;
	}
	char Str[10];
	int a, b, x, y;
	for (int i = 1; i <= m; ++i)
	{
		scanf("%s", Str);
		Read(a); Read(b);
		if (strcmp(Str, "Connect") == 0)
		{
			Make_Root(a);
			Splay(a);
			Father[a] = b;
		}
		else if (strcmp(Str, "Destroy") == 0)
		{
			Make_Root(a);
			Access(b);
			Splay(b);
			PushDown(b);
			isRoot[Son[b][0]] = true;
			Father[Son[b][0]] = 0;
			Son[b][0] = 0;
		}
		else
		{
			x = Find_Root(a);
			y = Find_Root(b);
			if (x == y) printf("Yes\n");
			else printf("No\n");
		}
	}
	return 0;
}