【ACM-ICPC 2018 沈阳赛区网络预赛】D. Made In Heaven ---- 第K短路（A*算法）

做法：

A*算法（最佳搜索算法，基于启发式）（人工智能课上也学习了）
讲解：
求图的第K短路（A*算法与最短路的应用）
A* && 第k短路详解（详尽）
说一下注意的地方：
用逆向建图，用dijkstra跑一边是为了求出g(i)，因为g(i)为结点i到终点的实际距离。所以我们逆向跑一边，就得到了终点到各个点i的距离，就得了g(i)。
存个板子~

AC代码： 基于邻接表

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <string>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <stack>
using namespace std;

#define IO          ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)
#define pb(x)       push_back(x)
#define sz(x)       (int)(x).size()
#define sc(x)       scanf("%d",&x)
#define abs(x)      ((x)<0 ? -(x) : x)
#define all(x)      x.begin(),x.end()
#define mk(x,y)     make_pair(x,y)
#define fin         freopen("in.txt","r",stdin)
#define fout        freopen("out.txt","w",stdout)

typedef long long ll;
typedef pair<int,int> P;
const int mod = 1e9+7;
const double PI = 4*atan(1.0);
const int maxm = 1e8+5;
const int maxn = 1e3+10;
const int INF = 0x3f3f3f3f;
const ll LINF = 1ll<<62;

struct node
{
    int to,w;
    node(int to,int w){
        this->to = to;
        this->w = w;
    }
};
vector<node> edge[maxn],_edge[maxn];

struct anode
{
    int h,g,id;
    anode(int h,int g,int id){
        this->h = h;
        this->g = g;
        this->id = id;
    }
    bool operator < (anode y)const{
        return h+g > y.h+y.g;
    }
};
int n,m,s,t,k,q;
int dist[maxn];

void addedge(int u,int v,int w)
{
    edge[u].push_back(node(v,w));
    _edge[v].push_back(node(u,w));
}
void dij(int s)
{
    priority_queue<P,vector<P>,greater<P> >q;
    // memset(dist,INF,sizeof(dist));
    fill(dist,dist+n+1,INF);
    dist[s] = 0;
    q.push(P(0,s));
    while(!q.empty())
    {
        P p = q.top();q.pop();
        int v = p.second;
        if(dist[v] < p.first) continue;
        for(int i=0;i<(int)_edge[v].size();i++)
        {
            node e = _edge[v][i];
            if(dist[e.to] > dist[v]+e.w)
            {
                dist[e.to] = dist[v]+e.w;
                q.push(P(dist[e.to],e.to));
            }
        }
    }
}
int Astar(int s,int t)
{
    if(dist[s]==INF) return -1;//判断有无最短路
    priority_queue<anode> qa;
    qa.push(anode(0,dist[s],s));
    int cnt = 0;
    while(!qa.empty())
    {
        anode u = qa.top();qa.pop();
        if(u.id == t) ++cnt;
        if(cnt>=k) return u.h;
        if(cnt<k && u.h>q) return -1; //剪枝
        for(int i=0;i<(int)edge[u.id].size();i++)
        {
            node v = edge[u.id][i];
            qa.push(anode(u.h+v.w,dist[v.to],v.to));
        }
    }
    return -1;
}
int main()
{
    // fin;
    // IO;
    while(~scanf("%d %d",&n,&m))
    {
        for(int i=0;i<=n;i++){
            edge[i].clear();
            _edge[i].clear();
        }
        sc(s);sc(t);sc(k);sc(q);
        for(int i=1;i<=m;i++)
        {
            int u,v,w;
            sc(u);sc(v);sc(w);
            addedge(u,v,w);
        }
        //if(s == t) k++;
        dij(t);
        int ans = Astar(s,t); 
        if(ans<=q && ans!=-1) printf("yareyaredawa\n");
        else printf("Whitesnake!\n");
    }
    return 0;
}

AC代码： 基于链式前向星

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <string>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <stack>
using namespace std;

#define IO          ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)
#define pb(x)       push_back(x)
#define sz(x)       (int)(x).size()
#define sc(x)       scanf("%d",&x)
#define abs(x)      ((x)<0 ? -(x) : x)
#define all(x)      x.begin(),x.end()
#define mk(x,y)     make_pair(x,y)
#define fin         freopen("in.txt","r",stdin)
#define fout        freopen("out.txt","w",stdout)

typedef long long ll;
typedef pair<int,int> P;
const int mod = 1e9+7;
const int maxm = 1e8+5;
const int maxn = 1e4+10;
const int INF = 0x3f3f3f3f;
const ll LINF = 1ll<<62;

struct node
{
    int to,nex;
    int w;
};
node edge[maxn],_edge[maxn];
//vector<node> edge[maxn],_edge[maxn];

struct anode
{
    int h,g,id;
    anode(int h,int g,int id){
        this->h = h;
        this->g = g;
        this->id = id;
    }
    bool operator < (anode y)const{
        return h+g > y.h+y.g;
    }
};
int n,m,s,t,k,q;
int dist[maxn];
int head[maxn],_head[maxn];

void addedge(int u,int v,int w,int i)
{
    edge[i].to = v;
    edge[i].w = w;
    edge[i].nex = head[u];
    head[u] = i;

    _edge[i].to = u;
    _edge[i].w = w;
    _edge[i].nex = _head[v];
    _head[v] = i;
}
void dij(int s)
{
    priority_queue<P,vector<P>,greater<P> >q;
    fill(dist,dist+n+1,INF);
    dist[s] = 0;
    q.push(P(0,s));
    while(!q.empty())
    {
        P p = q.top();q.pop();
        int u = p.second;
        if(dist[u] < p.first) continue;
        for(int i=_head[u];~i;i = _edge[i].nex)
        {
            int v = _edge[i].to;
            if(dist[v] > dist[u]+_edge[i].w)
            {
                dist[v] = dist[u]+edge[i].w;
                q.push(P(dist[v],v));
            }
        }
    }
}
int Astar(int s,int t)
{
    if(dist[s]==INF) return -1;//判断有无最短路
    priority_queue<anode> qa;
    qa.push(anode(0,dist[s],s));
    int cnt = 0;
    while(!qa.empty())
    {
        anode u = qa.top();qa.pop();
        if(u.id == t) ++cnt;
        if(cnt>=k) return u.h;
        if(cnt<k && u.h>q) return -1; //剪枝
        for(int i=head[u.id];~i;i = edge[i].nex)
        {
            int v = edge[i].to;
            qa.push(anode(u.h+edge[i].w,dist[v],v));
        }
    }
    return -1;
}
int main()
{
//     fin;
    // IO;
    while(~scanf("%d %d",&n,&m))
    {
        memset(head,-1,sizeof(head));
        memset(_head,-1,sizeof(_head));
        sc(s);sc(t);sc(k);sc(q);
        for(int i=1;i<=m;i++)
        {
            int u,v,w;
            sc(u);sc(v);sc(w);
            addedge(u,v,w,i);
        }
        //if(s == t) k++;
        dij(t);
        int ans = Astar(s,t);
        if(ans<=q && ans!=-1) printf("yareyaredawa\n");
        else printf("Whitesnake!\n");
    }
    return 0;
}

【ACM-ICPC 2018 沈阳赛区网络预赛】D. Made In Heaven ---- 第K短路（A*算法）

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