解题思路
(lct)维护最小生成树。我们首先按照(a)排序,然后每次加入一条边,在图中维护一棵最小生成树。用并查集判断一下(1)与(n)是否联通,如果联通的话就尝试更新答案。
代码
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<algorithm>
using namespace std;
const int MAXN = 50005;
const int MAXM = 1000005;
inline int rd(){
int x=0,f=1;char ch=getchar();
while(!isdigit(ch)) {f=ch=='-'?0:1;ch=getchar();}
while(isdigit(ch)) {x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
return f?x:-x;
}
int n,m,ans=1e9,F[MAXN],val[MAXN+MAXM],num;
int xx[MAXN+MAXM],yy[MAXN+MAXM];
struct Edge{
int x,y,a,b;
friend bool operator<(const Edge A,const Edge B){
return A.a<B.a;
}
}edge[MAXM];
int Find(int x){
if(x==F[x]) return x;
return F[x]=Find(F[x]);
}
namespace lct{
int fa[MAXN+MAXM],ch[MAXN+MAXM][2],Max[MAXN+MAXM];
bool tag[MAXN+MAXM];
inline void pushup(int x){
Max[x]=x;
if(val[Max[ch[x][0]]]>val[Max[x]]) Max[x]=Max[ch[x][0]];
if(val[Max[ch[x][1]]]>val[Max[x]]) Max[x]=Max[ch[x][1]];
}
inline void pushdown(int x){
if(tag[x]){
tag[x]^=1;swap(ch[x][0],ch[x][1]);
if(ch[x][0]) tag[ch[x][0]]^=1;
if(ch[x][1]) tag[ch[x][1]]^=1;
}
}
inline bool isroot(int x){
return (x!=ch[fa[x]][0] && x!=ch[fa[x]][1]);
}
inline bool check(int x){
return (x==ch[fa[x]][1]);
}
void pd(int x){
if(!isroot(x)) pd(fa[x]);pushdown(x);
}
inline void rotate(int x){
int y=fa[x],z=fa[y];bool chk=check(x);
if(!isroot(y)) ch[z][check(y)]=x;
ch[y][chk]=ch[x][chk^1];fa[ch[x][chk^1]]=y;
ch[x][chk^1]=y;fa[y]=x;fa[x]=z;pushup(y);pushup(x);
}
inline void splay(int x){
pd(x);
for(;!isroot(x);rotate(x))
if(!isroot(fa[x])) rotate(check(fa[x])==check(x)?fa[x]:x);
}
inline void access(int x){
for(int y=0;x;y=x,x=fa[x])
splay(x),ch[x][1]=y,pushup(x);
}
inline void makeroot(int x){
access(x);splay(x);tag[x]^=1;
}
inline void link(int x,int y){
makeroot(x);fa[x]=y;pushup(y);
}
inline void split(int x,int y){
makeroot(x);access(y);splay(x);
}
inline void cut(int x,int y){
makeroot(x);access(y);splay(y);
fa[x]=ch[y][0]=0;pushup(y);
}
}
int main(){
n=rd(),m=rd();int x,y,a,b,A,u,v;
for(int i=1;i<=n;i++) F[i]=i;num=n;
for(int i=1;i<=m;i++){
x=rd(),y=rd(),a=rd(),b=rd();
edge[i].x=x,edge[i].y=y,edge[i].a=a,edge[i].b=b;
}
sort(edge+1,edge+1+m);
for(int i=1;i<=m;i++){
A=edge[i].a;x=edge[i].x,y=edge[i].y;
u=Find(edge[i].x);v=Find(edge[i].y);
if(u!=v){
val[++num]=edge[i].b;lct::link(x,num);lct::link(num,y);
xx[num]=x;yy[num]=y;F[u]=v;
}
else {
lct::split(x,y);
if(val[lct::Max[x]]>edge[i].b) {
a=lct::Max[x];b=yy[lct::Max[x]];val[++num]=edge[i].b;
lct::cut(xx[lct::Max[x]],lct::Max[x]);lct::cut(a,b);
lct::link(x,num),lct::link(num,y);xx[num]=x;yy[num]=y;
}
}
if(Find(1)==Find(n)){
lct::split(1,n);
ans=min(ans,A+val[lct::Max[1]]);
}
}
if(ans!=1e9) printf("%d
",ans);
else puts("-1");
return 0;
}