【AtCoder2134】ZigZag MST

题面

https://www.luogu.org/problem/AT2134

题解

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
#define ri register int
#define N 200500

struct edge{
  int u,v,l;
  bool operator < (const edge &rhs) const {
    return l<rhs.l;
  }
} e[N<<1];
int f[N],v[N];
int n,m;
LL ans;

int findroot(int x){
  if (f[x]==x) return x;
  return f[x]=findroot(f[x]);
}

using namespace std;
int main(){
  scanf("%d %d",&n,&m);
  for (ri i=0;i<n;i++) v[i]=2000000000;
  for (ri i=1;i<=m;i++) {
    scanf("%d %d %d",&e[i].u,&e[i].v,&e[i].l);
    v[e[i].u]=min(e[i].l+1,v[e[i].u]);
    v[e[i].v]=min(e[i].l+2,v[e[i].v]);
  }
  for (ri i=0;i<n;i++) f[i]=i;
  for (ri i=0;i<2*n;i++) v[(i+1)%n]=min(v[(i+1)%n],v[i%n]+2);
  int cc=m;
  for (ri i=0;i<n-1;i++) e[++cc]=(edge){i,i+1,v[i]};
  e[++cc]=(edge){n-1,0,v[n-1]};
  sort(e+1,e+cc+1);

  for (ri i=1;i<=cc;i++) {
    int r1=findroot(e[i].u),r2=findroot(e[i].v);
    if (r1==r2) continue;
    f[r1]=r2;
    ans+=e[i].l;
  }
  cout<<ans<<endl;
}