HDU 5521 Meeting (最短路 + 拆点)

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题目点我点我点我



题目大意:有N个点,给定M个集合,集合Si里面的点两两之间的距离都为Ti,集合里面的所有点数之和<=1e6。两个人分别从1和n出发,要求相遇的最短距离,并输出相遇的点(可能多个)。



解题思路:首先无疑是最短路,然后因为同一个点可能属于两个或多个集合,故需要拆点。除了n个点外,每一个集合建一个新的点与集合中的点相连,集合中的点要到集合中的另一个点要先经过新建的点,所以走的路变成了2倍,分别从1和n各走一遍最短路,最后答案除以2即可。


/* ***********************************************┆  ┏┓   ┏┓ ┆┆┏┛┻━━━┛┻┓ ┆┆┃       ┃ ┆┆┃   ━   ┃ ┆┆┃ ┳┛ ┗┳ ┃ ┆┆┃       ┃ ┆┆┃   ┻   ┃ ┆┆┗━┓ 马 ┏━┛ ┆┆  ┃ 勒 ┃  ┆      ┆  ┃ 戈 ┗━━━┓ ┆┆  ┃ 壁     ┣┓┆┆  ┃ 的草泥马  ┏┛┆┆  ┗┓┓┏━┳┓┏┛ ┆┆   ┃┫┫ ┃┫┫ ┆┆   ┗┻┛ ┗┻┛ ┆************************************************ */#include <stdio.h>#include <string.h>#include <iostream>#include <algorithm>#include <vector>#include <queue>#include <stack>#include <set>#include <map>#include <string>#include <math.h>#include <stdlib.h>#include <bitset>using namespace std;#define rep(i,a,b) for (int i=(a),_ed=(b);i<=_ed;i++)#define per(i,a,b) for (int i=(b),_ed=(a);i>=_ed;i--)#define pb push_back#define mp make_pairconst int inf_int = 2e9;const long long inf_ll = 2e18;#define inf_add 0x3f3f3f3f#define mod 1000000007#define LL long long#define ULL unsigned long long#define MS0(X) memset((X), 0, sizeof((X)))#define SelfType intSelfType Gcd(SelfType p,SelfType q){return q==0?p:Gcd(q,p%q);}SelfType Pow(SelfType p,SelfType q){SelfType ans=1;while(q){if(q&1)ans=ans*p;p=p*p;q>>=1;}return ans;}#define Sd(X) int (X); scanf("%d", &X)#define Sdd(X, Y) int X, Y; scanf("%d%d", &X, &Y)#define Sddd(X, Y, Z) int X, Y, Z; scanf("%d%d%d", &X, &Y, &Z)#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())#define all(a) a.begin(), a.end()typedef pair<int, int> pii;typedef pair<long long, long long> pll;typedef vector<int> vi;typedef vector<long long> vll;inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1;while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-')fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,rx=getchar();return ra*fh;}//#pragma comment(linker, "/STACK:102400000,102400000")const int N = 2e6 + 5;struct Edge{    int to,nx;    LL w;}edge[N*2];int cnt,head[N];void addedge(int u,int v,LL w){    edge[cnt] = {v,head[u],w};    head[u] = cnt++;}struct node{    int p;    LL d;    bool operator < (const node &a) const    {        return d>a.d;    }};LL da[N],db[N];int vis[N],n,m,z;void dijkstra(int s,LL d[]){    priority_queue<node>q;    for(int i=0;i<=z;i++)    {        vis[i] = 0;        d[i] = inf_ll;    }    d[s] = 0;    q.push(node{s,d[s]});    while(!q.empty())    {        node t = q.top();        q.pop();        int u = t.p;        if(vis[u])continue;        vis[u] = 1;        for(int i=head[u];i;i=edge[i].nx)        {            int v = edge[i].to;            LL w = edge[i].w;            if(d[v]>d[u]+w)            {                d[v] = d[u] + w;                q.push(node{v,d[v]});            }        }    }}int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);    ios::sync_with_stdio(0);    cin.tie(0);    int t;    t = read();    int cas = 1;    while(t--)    {        n = read(), m =read();        MS0(head);        cnt = 1;        z = n;        for(int i=1;i<=m;i++)        {            z++;            LL d;            int k,p;            scanf("%I64d%d",&d,&k);            for(int j=1;j<=k;j++)            {                scanf("%d",&p);                addedge(z,p,d);                addedge(p,z,d);            }        }        dijkstra(1,da);        dijkstra(n,db);        LL ans = inf_ll;        for(int i=1;i<=n;i++)        {            ans = min(ans,max(da[i],db[i]));        }        if(ans==inf_ll)printf("Case #%d: Evil John\n",cas++);        else        {            printf("Case #%d: %I64d\n",cas++,ans/2);            int flag = 0;            for(int i=1;i<=n;i++)            {                if(ans==max(da[i],db[i]))                {                    if(flag)printf(" ");                    flag = 1;                    printf("%d",i);                }            }            printf("\n");        }    }    return 0;}



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