SGU 301 Boring. Hot. Summer...（最短路+区间覆盖）

题目链接：http://acm.sgu.ru/problem.php?contest=0&problem=301

题意：给出一个无向图，起点s和终点t。一个人从s到t，已知他走的是最短路。问这个人到达点i时，有可能在那些点上?(1<=i<=n)

思路：先从s和tSPFA一次，可以得到所有的关键路径。然后就是枚举每个路径覆盖了哪些点。

#include <iostream>

#include <cstdio>

#include <string.h>

#include <algorithm>

#include <cmath>

#include <vector>

#include <queue>

#include <set>

#include <string>



#define max(x,y) ((x)>(y)?(x):(y))

#define min(x,y) ((x)<(y)?(x):(y))

#define abs(x) ((x)>=0?(x):-(x))

#define i64 long long

#define u32 unsigned int

#define u64 unsigned long long

#define clr(x,y) memset(x,y,sizeof(x))

#define CLR(x) x.clear()

#define ph(x) push(x)

#define pb(x) push_back(x)

#define Len(x) x.length()

#define SZ(x) x.size()

#define PI acos(-1.0)

#define sqr(x) ((x)*(x))

#define MP(x,y) make_pair(x,y)



#define FOR0(i,x) for(i=0;i<x;i++)

#define FOR1(i,x) for(i=1;i<=x;i++)

#define FOR(i,a,b) for(i=a;i<=b;i++)

#define DOW0(i,x) for(i=x;i>=0;i--)

#define DOW1(i,x) for(i=x;i>=1;i--)

#define DOW(i,a,b) for(i=a;i>=b;i--)

using namespace std;





void RD(int &x){scanf("%d",&x);}

void RD(i64 &x){scanf("%lld",&x);}

void RD(u64 &x){scanf("%llu",&x);}

void RD(u32 &x){scanf("%u",&x);}

void RD(double &x){scanf("%lf",&x);}

void RD(int &x,int &y){scanf("%d%d",&x,&y);}

void RD(i64 &x,i64 &y){scanf("%lld%lld",&x,&y);}

void RD(u64 &x,u64 &y){scanf("%llu%llu",&x,&y);}

void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}

void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}

void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}

void RD(i64 &x,i64 &y,i64 &z){scanf("%lld%lld%lld",&x,&y,&z);}

void RD(u64 &x,u64 &y,u64 &z){scanf("%llu%llu%llu",&x,&y,&z);}

void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}

void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}

void RD(char &x){x=getchar();}

void RD(char *s){scanf("%s",s);}

void RD(string &s){cin>>s;}



void PR(int x) {printf("%d\n",x);}

void PR(i64 x) {printf("%lld\n",x);}

void PR(u64 x) {printf("%llu\n",x);}

void PR(u32 x) {printf("%u\n",x);}

void PR(double x) {printf("%lf\n",x);}

void PR(char x) {printf("%c\n",x);}

void PR(char *x) {printf("%s\n",x);}

void PR(string x) {cout<<x<<endl;}



class node

{

public:

    int u,v,dis;



    void get()

    {

        RD(u,v,dis);

    }

};



const int INF=1<<29;

const int N=2005;

const int M=200005;

int n,m,s,t,dis[N],dis1[N];

node a[M];

vector<int> G[N],p;



void SPFA(int s,int dis[])

{

    queue<int> Q;

    int i,j,k,t,d,inQ[N]={0};

    FOR1(i,n) dis[i]=INF;

    dis[s]=0;

    Q.push(s);

    while(!Q.empty())

    {

        k=Q.front();

        Q.pop();

        inQ[k]=0;



        FOR0(i,SZ(G[k]))

        {

            j=G[k][i];

            t=a[j].u+a[j].v-k;

            d=a[j].dis;

            if(dis[t]>dis[k]+d)

            {

                dis[t]=dis[k]+d;

                if(!inQ[t]) inQ[t]=1,Q.push(t);

            }

        }

    }

}



int cmp(int x,int y)

{

    return dis[x]<dis[y];

}



vector<pair<int,int> > V;



int main()

{

    RD(n,s,t);

    RD(m);

    int i,j,k,u,v,d;

    FOR1(i,m) a[i].get(),G[a[i].u].pb(i),G[a[i].v].pb(i);

    SPFA(s,dis);

    SPFA(t,dis1);

    int minDis=dis[t];

    FOR1(i,n) if(dis[i]+dis1[i]==minDis) p.pb(i);

    sort(p.begin(),p.end(),cmp);

    FOR1(i,m)

    {

        u=a[i].u;

        v=a[i].v;

        d=a[i].dis;

        if(dis[u]>dis[v]) swap(u,v);

        if(dis[u]+d==dis[v]&&dis[v]+dis1[v]==minDis)

        {

            V.pb(MP(dis[u]+1,1));

            V.pb(MP(dis[v],-1));

        }

    }

    sort(V.begin(),V.end());

    int ans[N]={0},cur=0,sum=0;

    for(i=0;i<SZ(p);)

    {

        while(cur<SZ(V)&&V[cur].first<=dis[p[i]])

        {

            sum+=V[cur++].second;

        }

        for(j=i;j<SZ(p)&&dis[p[j]]==dis[p[i]];j++)

        {

            ans[p[i]]++;

        }

        ans[p[i]]+=sum;

        for(k=i;k<j;k++) ans[p[k]]=ans[p[i]];

        i=j;

    }

    FOR1(i,n) printf("%d ",ans[i]);puts("");

	return 0;

}