Kruskal重构树(货车运输)

。。。
和Kruskal生成树一样

本来是u,v连一条f的边

现在变成新建一个点,点权为f,u v都像它连无边权的边

(实际上应该是u的根和v的根)

这样树有一些性质:

1.二叉树

2.原树与新树两点间路径上边权(点权)的最大(最小)值相等

3.子节点的边权(大于等于)小于等于父亲节点

4.原树中两点之间路径上边权的最大(最小)值等于新树上两点的LCA的点权

# include <iostream>
# include <stdio.h>
# include <stdlib.h>
# include <algorithm>
# include <string.h>
# define IL inline
# define ll long long
# define Fill(a, b) memset(a, b, sizeof(a));
using namespace std; IL ll Read(){
char c = '%'; ll x = 0, z = 1;
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0';
return x * z;
} const int MAXN = 20001, MAXM = 200001;
int ft[MAXN], n, m, cnt, fa[MAXN][20], w[MAXN], deep[MAXN], Fa[MAXN], num;
struct Edge{
int to, nt;
} edge[MAXM];
struct Kruskal{
int u, v, f;
IL bool operator <(Kruskal b) const{
return f > b.f;
}
} road[MAXM]; IL int Find(int x){
return Fa[x] == x ? x : Fa[x] = Find(Fa[x]);
} IL void Add(int u, int v){
edge[cnt] = (Edge){v, ft[u]}; ft[u] = cnt++;
edge[cnt] = (Edge){u, ft[v]}; ft[v] = cnt++;
} IL void Dfs(int u){
for(int e = ft[u]; e != -1; e = edge[e].nt){
int v = edge[e].to;
if(!deep[v]){
deep[v] = deep[u] + 1;
fa[v][0] = u;
Dfs(v);
}
}
} IL int LCA(int u, int v){
if(Find(u) != Find(v)) return -1;
if(deep[u] < deep[v]) swap(u, v);
for(int i = 18; i >= 0; i--)
if(deep[fa[u][i]] >= deep[v]) u = fa[u][i];
if(u == v) return w[u];
for(int i = 18; i >= 0; i--)
if(fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i];
return w[fa[u][0]];
} int main(){
Fill(ft, -1);
num = n = Read(); m = Read();
for(int i = 1; i <= 2 * n; i++)
Fa[i] = i;
for(int i = 1; i <= m; i++)
road[i] = (Kruskal){Read(), Read(), Read()};
sort(road + 1, road + m + 1);
for(int i = 1, tot = 0; i <= m && tot < n; i++){
int u = Find(road[i].u), v = Find(road[i].v);
if(u != v){
tot++;
w[++num] = road[i].f;
Fa[u] = Fa[v] = num;
Add(u, num); Add(v, num);
}
}
for(int i = num; i; i--)
if(!deep[i]) deep[i] = 1, Dfs(i);
for(int i = 1; i <= 18; i++)
for(int j = 1; j <= num; j++)
fa[j][i] = fa[fa[j][i - 1]][i - 1];
int Q = Read();
while(Q--){
int u = Read(), v = Read();
printf("%d\n", LCA(u, v));
}
return 0;
}
上一篇:Failed to start bean 'stompBrokerRelayMessageHandler'; nested exception is java.lang.NoClassDefFoundError: reactor/io/codec/Codec


下一篇:POJ 1002 487-3279 Trie解读