K短路模板题目, A*, POJ2449

最新推荐文章于 2020-08-01 22:44:06 发布

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最新推荐文章于 2020-08-01 22:44:06 发布

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分类专栏：图的生成树以及最短路

本文链接：https://blog.youkuaiyun.com/qq_30446721/article/details/52800208

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本文介绍了一种结合反向边构造启发式函数的方法，并将其应用于A*搜索算法中，通过SPFA算法预处理得到节点间的最短路径估价，以解决特定类型的最短路径问题。

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#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<queue>
#define INF 0x7fffffff
#define rep(i,a,b) for(int i=a; i<=b; ++i)
#define Nodes(i,h,bgn,nxt) for(int i=bgn[h]; i!=-1; i=nxt[i])
#define M 200000 + 1000
using namespace std;
int e = 0;
int e1 = 0;
int k;
int s;
int t;
int d[M];
int p[M];
struct f
{
   int  v, h, g;
   bool operator <(const f a)const
   { if(a.h == h) return a.g < g; return a.h < h; }
};
struct node
{
   int x;
};
int bgn[M], nxt[M], to[M], w[M];
int bgn1[M], nxt1[M], to1[M], w1[M];
int n, m;
inline void add(int x,int y,int z){to[e] = y; nxt[e] = bgn[x]; bgn[x] = e; w[e] = z; ++e;}
inline void fadd(int x,int y,int z){to1[e1] = y; nxt1[e1] = bgn1[x]; bgn1[x] = e1; w1[e1]=z; ++e1;}
void Spfa()
{
   queue<node> q;
   for(int i=1; i<=n; ++i) d[i] = INF;
   for(int i=1; i<=n; ++i) p[i] = 0;
   p[t] = 1;
   d[t]  = 0;
   q.push((node){t});
   while(!q.empty())
   {
      int h = q.front().x; q.pop();
      p[h] = 0;
      Nodes(i,h,bgn1,nxt1)
      {
         int y = to1[i];
         if(d[h] + w1[i] < d[y]) 
         {
         	d[y] = d[h] + w1[i];
         	if(!p[y]) q.push((node){y}), p[y] = 1;
         }
      }
   }
}

int A_star()
{
    priority_queue<f> q;
    if(s == t) k++;
    int cnt = 0;
    if(d[s] == INF) return -1;
    struct f fir;
    fir.v = s; fir.g = 0; fir.h = fir.g + d[s];
    q.push(fir);
    while(!q.empty())
    {
       int h = q.top().v;
       int key = q.top().g;
       q.pop();
       if(h == t)
       {
          cnt++;
          if(cnt == k) return key;
       }
       Nodes(i,h,bgn,nxt)
       {
          int y = to[i];
          struct f end;
          end. g = key + w[i];
          end. h = end.g + d[y];
          end. v = y;
          q.push(end);
       }
    }
    return -1;
}

int main()
{
   while(scanf("%d%d",&n,&m) != EOF)
   {
      int x, y, z;
      memset(bgn, -1, sizeof(bgn));
      memset(bgn1, -1, sizeof(bgn1));
      e = e1 = 0;
      while(m--) 
      {
         scanf("%d%d%d",&x,&y,&z);
         add(x,y,z), fadd(y,x,z);
      }
      scanf("%d%d%d",&s,&t,&k);
      Spfa();
      cout<<A_star()<<endl;
   }
}

用反向边去构造h函数，直接加入A*搜索，只不过特别难调