【SDOI 2010】 魔法猪学院

【题目链接】

            https://www.lydsy.com/JudgeOnline/problem.php?id=1975

【算法】

           A*求k短路

【代码】

           

#include<bits/stdc++.h>
using namespace std;
#define MAXN 5010
#define MAXM 200010
const double INF = 1e15;

int i,tot,n,m,u,v;
int head[MAXN],rhead[MAXN];
double dist[MAXN];
double w,val;

struct Edge
{
        int to;
        double w;
        int nxt;
} e[MAXM<<1];
struct info
{
        int s;
        double d;
        friend bool operator < (info a,info b)
        {
                return a.d + dist[a.s] > b.d + dist[b.s];
        }
} ;

inline void add(int u,int v,double w)
{
        tot++;
        e[tot] = (Edge){v,w,head[u]};
        head[u] = tot;
        tot++;
        e[tot] = (Edge){u,w,rhead[v]};
        rhead[v] = tot;    
}
inline void dijkstra(int s)
{
        int i,u,v;
        double w;
        priority_queue< pair<double,int> > q;
        static bool vis[MAXN];
        memset(vis,false,sizeof(vis));
        while (!q.empty()) q.pop();
        for (i = 1; i <= n; i++) dist[i] = INF;
        dist[s] = 0;
        q.push(make_pair(0,s));
        while (!q.empty())
        {
                u = q.top().second;
                q.pop();
                if (vis[u]) continue;
                vis[u] = true;
                for (i = rhead[u]; i; i = e[i].nxt)
                {
                        v = e[i].to;
                        w = e[i].w;
                        if (dist[u] + w < dist[v])
                        {
                                dist[v] = dist[u] + w;
                                q.push(make_pair(-dist[v],v));
                        }
                }
        }        
}
inline int Astar(int s,int t)
{
        int i,cnt = 0,v;
        double w,sum = 0;
        priority_queue< info > q;
        info cur;
        while (!q.empty()) q.pop();
        q.push((info){s,0});
        while (!q.empty())
        {
                cur = q.top();
                q.pop();
                if (cur.s == t)
                {
                        if (sum + cur.d <= val) 
                        {
                                sum += cur.d;
                                cnt++;
                        } else return cnt;
                }
                for (i = head[cur.s]; i; i = e[i].nxt)
                {
                         v = e[i].to;
                        w = e[i].w;
                        q.push((info){v,cur.d+w});
                }
        }
        return 0;
}

int main() 
{
        
        scanf("%d%d%lf",&n,&m,&val);
        for (i = 1; i <= m; i++)
        {
                scanf("%d%d%lf",&u,&v,&w);
                add(u,v,w);        
        }
        dijkstra(n);
        printf("%d
",Astar(1,n));
        
        return 0;
    
}