最短路算法 —— Dijkstra算法

  1 #include <iostream>
  2 #include <algorithm>
  3 #include <cstring>
  4 #include <deque>
  5 #include <cstdio>
  6 #include <vector>
  7 #include <queue>
  8 #include <cmath>
  9 #define INF 0x3f3f3f3f
 10 using namespace std;
 11 
 12 //邻接矩阵
 13 
 14 const int MAXN = 110;
 15 int dis[MAXN];
 16 int e[MAXN][MAXN];
 17 bool vis[MAXN];
 18 int N, M;
 19 
 20 void dij()
 21 {
 22     int p, mis;
 23     for(int i = 1; i <= N; i++)
 24         dis[i] = e[1][i];
 25 
 26 
 27     vis[1] = true;
 28     dis[1] = 0;
 29     for(int i = 1; i < N; i++)
 30     {
 31         mis = INF;
 32         for(int j = 1; j <= N; j++)
 33         {
 34             if(!vis[j] && dis[j] < mis)
 35             {
 36                 mis = dis[j];
 37                 p = j;
 38             }
 39         }
 40         vis[p] = true;
 41 
 42         for(int k = 1; k <= N; k++)
 43         {
 44             if(dis[k] > dis[p] + e[p][k] && !vis[k])
 45                 dis[k] = dis[p] + e[p][k];
 46         }
 47     }
 48 }
 49 
 50 void init()
 51 {
 52     for(int i  = 1; i <= N; i++)
 53         for(int j = 1; j <= N; j++)
 54             if(i == j) e[i][j] = 0;
 55             else e[i][j] = INF;
 56     memset(vis, false, sizeof(vis));
 57 }
 58 int main()
 59 {
 60     int a, b, c;
 61     while(~scanf("%d%d", &N, &M))
 62     {
 63         if(N == 0 && M == 0) break;
 64         init();
 65         while(M--)
 66         {
 67             scanf("%d%d%d", &a, &b, &c);
 68             e[a][b] = c;
 69             e[b][a] = c;
 70         }
 71 
 72         dij();
 73         printf("%d\n", dis[N]);
 74     }
 75 
 76     return 0;
 77 }
 78 
 79 
 80 
 81 //vector 动态邻接表 + 优先队列
 82 
 83 const int MAXN = 1e3 + 50;
 84 struct edge
 85 {
 86     int to, cost;
 87     edge(int vo = 0, int vt = 0):
 88         to(vo),cost(vt){}
 89 };
 90 
 91 vector<edge>G[MAXN];
 92 typedef pair<int, int>P;
 93 int dis[MAXN];
 94 int N, M;
 95 
 96 void init()
 97 {
 98     for(int i = 1; i <= N; i++)
 99     {
100         G[i].clear();
101         dis[i] = INF;
102     }
103 
104 }
105 void Dijkstra(int s)
106 {
107     int u, v;
108     priority_queue<P, vector<P>, greater<P> > que;
109     que.push(P(0, s));
110     dis[s] = 0;
111 
112     while(!que.empty())
113     {
114         P p = que.top(); que.pop();
115 
116         int u = p.second;
117         if(dis[u] < p.first) continue;
118 
119         for(int i = 0; i < G[u].size(); i++)
120         {
121             edge v = G[u][i];
122             if(dis[v.to] > dis[u] + v.cost)
123             {
124                 dis[v.to] = dis[u] + v.cost;
125                 que.push(P(dis[v.to], v.to));
126             }
127         }
128     }
129 }
130 
131 int main()
132 {
133     int u, v, c;
134     scanf("%d%d", &N, &M);
135     init();
136     while(M--)
137     {
138         scanf("%d%d", &u, &v, &c);
139         G[u].push_back(edge(v, c));
140         //G[v].push(edge(u, c));  建无向图
141     }
142 
143     //see see
144     /*
145     for(int i = 1; i <= N; i++)
146     {
147         for(int j = 0; j < G[i].size(); j++)
148             printf("%d ", G[i][j].to);
149         puts("");
150     }
151     */
152 
153     Dijkstra(1);
154     for(int i = 1; i <= N; i++)
155         printf("%d ", dis[i]);
156     puts("");
157 
158     return 0;
159 }
160 
161 
162 
163 
164 ///静态邻接表 + 优先队列优化
165 
166 const int MAXN = 1e3 + 50;
167 typedef pair<int, int> HeapNode;
168 struct edge
169 {
170     int v, nxt, w;
171 }G[MAXN*100];
172 int head[MAXN], dis[MAXN];
173 int N, M, cnt;
174 
175 inline void init()
176 {
177     for(int i = 0; i <= N; i++)
178         head[i] = -1, dis[i] = INF;
179     cnt = 0;
180 }
181 
182 inline void add(int from, int to, int we)
183 {
184     G[cnt].w = we;
185     G[cnt].v = to;
186     G[cnt].nxt = head[from];
187     head[from] = cnt++;
188 }
189 
190 void dij()
191 {
192     priority_queue<HeapNode, vector<HeapNode>, greater<HeapNode> > heap;
193     dis[1] = 0;
194     heap.push(make_pair(0, 1));
195     while(!heap.empty())
196     {
197         pair<int, int>T = heap.top();
198         heap.pop();
199 
200         if(T.first != dis[T.second]) continue;
201 
202         for(int i = head[T.second]; i != -1; i = G[i].nxt)
203         {
204             int v = G[i].v;
205             if(dis[v] > dis[T.second] + G[i].w)
206             {
207                 dis[v] = dis[T.second] + G[i].w;
208                 heap.push(make_pair(dis[v], v));
209             }
210         }
211     }
212 }
213 
214 int main()
215 {
216     int a, b, c;
217     while(~scanf("%d%d", &N, &M))
218     {
219         if(N == 0 && M == 0) break;
220         init();
221         while(M--)
222         {
223             scanf("%d%d%d", &a, &b, &c);
224             add(a, b, c);
225             add(b, a, c);
226         }
227 
228         dij();
229         printf("%d\n", dis[N]);
230     }
231 
232     return 0;
233 }