uva 10740 Not the Best （最短路 A*算法）

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uva 10740 Not the Best

题目大意：求第K短路。

解题思路：A*算法。这题数据量比较小，也可以暴力。

A*算法

#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <cstdlib>#include <queue>using namespace std;typedef long long ll;const int N = 105;const int INF = 0x3f3f3f3f;int n, m;int s, t, K;int h[N]; bool vis[N];struct Node {    int to, dis;};int gra[N][N], gra2[N][N];bool operator < (const Node& a, const Node& b) {    return (a.dis + h[a.to] > b.dis + h[b.to]);}void init() {    memset(vis, 0, sizeof(vis));    for(int i = 0; i <= n + 1; i++) h[i] = INF;    h[t] = 0;    for(int i = 1; i <= n; i++) {        int x, m = INF;        for(int j = 1; j <= n; j++) {            if(!vis[j] && m > h[j]) {                m = h[j];                   x = j;            }        }        vis[x] = true;        for (int j = 1; j <= n; j++) {            if (!vis[j] && gra2[x][j] + h[x] < h[j]) {                h[j] = gra2[x][j] + h[x];            }           }    }}int Astar() {    priority_queue<Node> Q;    init();    if (s == t) K++;    if (h[s] == INF) return -1;    int ans = -1, count = 0;    Node p;    p.to = s;    p.dis = 0;    Q.push(p);    while(!Q.empty()) {        p = Q.top(); Q.pop();        if (p.to == t) count++;        if (count == K) {            ans = p.dis;                break;        }        for (int i = 1; i <= n; i++) {            if (gra[p.to][i] != INF) {                Q.push((Node){i, p.dis + gra[p.to][i]});                }           }    }    return ans;}void input() {    for (int i = 0; i <= n; i++) {        for (int j = 0; j <= n; j++) {            gra[i][j] = INF;                gra2[i][j] = INF;        }    }    scanf("%d %d %d", &s, &t, &K);    int u, v, d;    for (int i = 0; i < m; i++) {        scanf("%d %d %d", &u, &v, &d);        gra[u][v] = min(gra[u][v], d);        gra2[v][u] = min(gra2[v][u], d);    }}int main() {    while (scanf("%d %d", &n, &m) == 2) {        if (n == 0 && m == 0) break;        input();            printf("%d\n", Astar());    }    return 0;}

暴力

#include<cstdio>  #include<algorithm>  #include<vector>  #include<cstring>  #include<stack>  #include<iostream>  #include<queue>  using namespace std;  const int N = 105;  int n, m;  int s, t, k;  struct Edge{      int to, dis;  };  vector<Edge> G[N];  int vis[N];  int BFS(){      int ans = -1;    priority_queue<pair<int, int> > q;      memset(vis, 0, sizeof vis);      q.push(make_pair(0, s));      while(!q.empty()){          pair<int, int> p = q.top();          q.pop();          int dist = -p.first;          int pos = p.second;          if(vis[pos] > k) continue;          vis[pos]++;          if(pos == t && vis[pos] == k){              ans = dist;              break;        }          for(int i = 0;i < G[pos].size();i++){              int to = G[pos][i].to;              int dis = G[pos][i].dis;              q.push(make_pair(-(dis + dist), to));          }      }      return ans;}  int main(){      while(scanf("%d%d", &n, &m)){          if(n == 0 && m == 0) break;          scanf("%d%d%d", &s, &t, &k);          for(int i = 0; i <= n; i++) G[i].clear();          for (int i = 0; i < m; i++) {            int u, v, d;              scanf("%d%d%d", &u, &v, &d);              G[u].push_back((Edge){v, d});          }          printf("%d\n", BFS());      }      return 0;  }

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