【poj3237】【link-cut tree】Tree

题目大意:

给你一颗树，要求支持下列3个操作：

     1.询问两点之间路径的边中边权最大的；

     2.把两点之间的路径的边权全部取反；

     3.修改某条边的边权。

很明显的动态树模型，首先要把边权转化为点权，并且要在dfs的时候记录每条边的权值在哪个点里面。

操作1和3是常规操作。

对于操作2，我们对每个节点记录Max和Min，取反就等价于Max = -Min,Min = -Max

代码:

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn = 10000 + 10;
const int inf = 0x3f3f3f3f;
struct Edge
{
int pos,cost;
int next;
}E[maxn<<2];
int head[maxn];
int Max[maxn],Min[maxn],w[maxn];
int ch[maxn][2],pre[maxn],belong[maxn<<2];
bool neg[maxn];
int T,NE,n;
void init()
{
freopen("poj3237.in","r",stdin);
freopen("poj3237.out","w",stdout);
}

inline int min(int a,int b)
{
return a < b ? a : b;
}

inline int max(int a,int b)
{
return a > b ? a : b;
}

void swap(int &a,int &b)
{
int t = a;a = b;b = t;
}

void add(int u,int v,int w)
{
++NE;
E[NE].pos = v;E[NE].cost = w;
E[NE].next = head[u];head[u] = NE;
}

void Init()
{
memset(E,0,sizeof(E));
memset(head,-1,sizeof(head));
memset(Min,0x3f,sizeof(Min));
memset(Max,~0x3f,sizeof(Max));
memset(w,0,sizeof(w));
memset(neg,false,sizeof(neg));
memset(ch,0,sizeof(ch));
memset(pre,0,sizeof(pre));
NE = 0;w[1] = -inf;
}

void dfs(int u,int f)
{
for(int i = head[u];i != -1;i = E[i].next)
{
int v = E[i].pos;
if(v == f)continue;
belong[(i + 1) >> 1] = v;
w[v] = E[i].cost;
pre[v] = u;
dfs(v,u);
}
}

void update(int x)
{
Min[x] = min(w[x],min(Min[ ch[x][0] ],Min[ ch[x][1] ]));
Max[x] = max(w[x],max(Max[ ch[x][0] ],Max[ ch[x][1] ]));
}

void makeneg(int x)
{
if(x != 0)
{
neg[x] = !neg[x];
w[x] = -w[x];
int t = Max[x];
Max[x] = -Min[x];Min[x] = -t;
}
}

void push_down(int x)
{
if(neg[x])
{
makeneg(ch[x][0]);
makeneg(ch[x][1]);
neg[x] = false;
}
}

bool isroot(int x)
{
return ch[pre[x]][0] != x && ch[pre[x]][1] != x;
}

void down_all(int x)
{
if(!isroot(x))down_all(pre[x]);
push_down(x);
}

void Rotate(int x,int f)
{
int y = pre[x];
ch[y][!f] = ch[x][f];
pre[ ch[x][f] ] = y;
pre[x] = pre[y];
if(ch[ pre[y] ][0] == y)ch[ pre[y] ][0] = x;
else if(ch[ pre[y] ][1] == y)ch[ pre[y] ][1] = x;
pre[y] = x;
ch[x][f] = y;
update(y);
}

void splay(int x)
{
down_all(x);
while(!isroot(x))
{
if(isroot(pre[x]))Rotate(x,ch[ pre[x] ][0] == x);
else
{
int y = pre[x],z = pre[y];
int f = (ch[z][0] == y);
if(ch[y][f] == x)Rotate(x,!f),Rotate(x,f);
else Rotate(y,f),Rotate(x,f);
}
}
update(x);
}

void access(int u)
{
for(int v = 0;u;v = u,u = pre[u])
{
splay(u);
ch[u][1] = v;
update(u);
}
}

void modify(int p,int key)
{
splay(p);
w[p] = key;
update(p);
}

int query(int a,int b)
{
int x = a,y = b;
access(y);
for(y = 0;x;y = x,x = pre[x])
{
splay(x);
if(!pre[x])return max(Max[ ch[x][1] ],Max[y]);
ch[x][1] = y;
update(x);
}
return 0;
}

void negate(int a,int b)
{
int x = a,y = b;
access(y);
for(y = 0;x;y = x,x = pre[x])
{
splay(x);
if(!pre[x])
{
makeneg(ch[x][1]);
makeneg(y);
return;
}
ch[x][1] = y;
update(x);
}
}

void readdata()
{
scanf("%d",&T);
while(T--)
{
Init();
scanf("%d",&n);
for(int i = 1;i < n;i++)
{
int u,v,w;
scanf("%d%d%d",&u,&v,&w);
add(u,v,w);
add(v,u,w);
}
dfs(1,-1);
char op[10];
while(true)
{
scanf("%s",op);
int a,b;
if(!strcmp(op,"DONE"))break;
scanf("%d%d",&a,&b);
if(!strcmp(op,"CHANGE"))a = belong[a],modify(a,b);
if(!strcmp(op,"QUERY"))printf("%d\n",query(a,b));
if(!strcmp(op,"NEGATE"))negate(a,b);
}
}
}

int main()
{
init();
readdata();
return 0;
}