bzoj 3732 Network (kruskal重构树)

Posted 2021-12-23 uid001

大意: 无向图, 多组询问, 求从A点走到B点的所有路径中，最长的边最小值是多少.

 

kruskal重构树板子题, 最小值一定是最小生成树上的最长边, 转化为求kruskal重构树lca的点权.

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <queue>
#define REP(i,a,n) for(int i=a;i<=n;++i)
#define pb push_back
using namespace std;
const int N = 1e6+10;
int n, m, k;
int fa[N], son[N], dep[N], s[N];
int sz[N], top[N], val[N], vis[N];
struct _ int u,v,w; e[N];
vector<int> g[N];
void add(int u, int v) 
    g[u].pb(v),g[v].pb(u);

int Find(int x) return s[x]?s[x]=Find(s[x]):x;
 
void dfs(int x, int f, int d) 
    fa[x]=f,dep[x]=d,sz[x]=1;
    int mx = -1;
	for (int i=0;i<g[x].size();++i)  
		int y = g[x][i];
		if (y==f) continue;
        dfs(y,x,d+1),sz[x]+=sz[y];
        if (sz[y]>mx) sz[y]=mx,son[x]=y;
    

void dfs2(int x, int tf) 
    top[x]=tf;
    if (son[x]) dfs2(son[x],tf);
	for (int i=0;i<g[x].size();++i)  
		int y = g[x][i];
		if (!top[y]) dfs2(y,y);
	

int lca(int x, int y) 
    while (top[x]!=top[y]) 
        if (dep[top[x]]<dep[top[y]]) swap(x,y);
        x = fa[top[x]];
    
    if (dep[x]>dep[y]) swap(x,y);
    return x;

bool cmp(_ a, _ b) 
	return a.w<b.w;

int main() 
    scanf("%d%d%d", &n, &m, &k);
    REP(i,1,m) scanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);
    sort(e+1,e+1+m,cmp);
    int tot = n;
    REP(i,1,m) 
        int u=Find(e[i].u),v=Find(e[i].v);
        if (u!=v) 
            s[u] = s[v] = ++tot;
            val[tot] = e[i].w;
            add(tot,u),add(tot,v);
            if (tot==2*n-1) break;
        
    
    dfs(tot,0,0),dfs2(tot,tot);
	while (k--) 
		int x, y;
		scanf("%d%d", &x, &y);
		printf("%d\n", val[lca(x,y)]);