pat dijkstra系列题目代码详解

1003：

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define int long long 
 4 #define IOS ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
 5 const int N=550;
 6 const int INF=0x3f3f3f3f;
 7 int g[N][N];
 8 bool vis[N];
 9 int dis[N];
10 int n,m;
11 int s,t;
12 int w[N];
13 int va[N];
14 int num[N];
15 void init()
16 {
17     for(int i=0;i<N;i++)
18     {
19         for(int j=0;j<N;j++)
20         {
21             g[i][j]=INF;
22         }
23     }
24 }
25 void dijkstra(int s)
26 {
27     memset(dis,INF,sizeof(dis));
28     dis[s]=0;
29     num[s]=1;
30     va[s]=w[s];
31     for(int i=0;i<n;i++)
32     {
33         int u=-1;
34         int Min=INF;
35         for(int j=0;j<n;j++)
36         {
37             if(!vis[j]&&dis[j]<Min)
38             {
39                 u=j;
40                 Min=dis[j];
41             }
42         }
43        // if(u==-1)
44            // return ;
45              vis[u]=true;
46         for(int v=0;v<n;v++)
47         {
48             if(!vis[v]&&g[u][v]!=INF)
49             {
50                 if(dis[u]+g[u][v]<dis[v])
51                 {      
52                     //vis[v]=true;
53                     dis[v]=dis[u]+g[u][v];
54                     num[v]=num[u];
55                     va[v]=va[u]+w[v];
56                 }
57             
58             else if(dis[u]+g[u][v]==dis[v])
59             {
60                 if(va[u]+w[v]>va[v])
61                 {
62                     va[v]=va[u]+w[v];
63                 }
64                 num[v]+=num[u];
65             }
66             }
67         }
68     }
69 }
70 signed main()
71 {
72     IOS;
73     init();
74     cin>>n>>m>>s>>t;
75     for(int i=0;i<n;i++)
76     {
77         cin>>w[i];
78     }
79     int st,f,d;
80     for(int i=0;i<m;i++)
81     {
82         cin>>st>>f>>d;
83         g[st][f]=g[f][st]=d;
84     }
85     dijkstra(s);
86     cout<<num[t]<<" "<<va[t];
87     return 0;
88 }

1030

dfs版本

  1 #include<bits/stdc++.h>
  2 using namespace std;
  3 #define int long long 
  4 #define IOS ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
  5 const int N=550;
  6 const int INF=0x3f3f3f3f;
  7 int n,m,s,d;
  8 int g[N][N];
  9 int dis[N];
 10 bool vis[N];
 11 int cost[N][N];
 12 int w[N];
 13 vector<int>pre[N];
 14 vector<int>tmp,path;
 15 int ans=INF;
 16 void init()
 17 {
 18     for(int i=0;i<N;i++)
 19     {
 20         for(int j=0;j<N;j++)
 21         {
 22             g[i][j]=INF;
 23             cost[i][j]=INF;
 24         }
 25     }
 26 }
 27 void dfs(int p)
 28 {
 29     if(p==s)
 30     {
 31         tmp.push_back(p);
 32         int value=0;
 33         for(int i=tmp.size()-1;i>0;i--)
 34         {
 35             int id1=tmp[i];
 36             int id2=tmp[i-1];
 37             value+=cost[id1][id2];
 38         }
 39         if(value<ans)
 40         {
 41             ans=value;
 42             path=tmp;
 43         }
 44         tmp.pop_back();
 45         return ;
 46     }
 47     tmp.push_back(p);
 48     for(int i=0;i<pre[p].size();i++)
 49     {
 50         dfs(pre[p][i]);
 51     }
 52     tmp.pop_back();
 53 }
 54 void dijkstra()
 55 {
 56     memset(dis,INF,sizeof(dis));
 57     dis[s]=0;
 58     w[s]=0;
 59     for(int i=0;i<n;i++)
 60     {
 61         int u=-1;
 62         int minn=INF;
 63         for(int j=0;j<n;j++)
 64         {
 65             if(!vis[j]&&dis[j]<minn)
 66             {
 67                 u=j;
 68                 minn=dis[j];
 69             }
 70         }
 71                if(u==-1)
 72                return ;
 73         vis[u]=true;
 74         for(int v=0;v<n;v++)
 75         {
 76             if(!vis[v]&&g[u][v]!=INF)
 77             {
 78                 if(dis[u]+g[u][v]<dis[v])
 79                 {
 80                     dis[v]=dis[u]+g[u][v];
 81                     pre[v].clear();
 82                     pre[v].push_back(u);
 83                 }
 84                 else if(dis[u]+g[u][v]==dis[v])
 85                 {
 86                      pre[v].push_back(u);
 87                 }
 88             }
 89         }
 90     }
 91 }
 92 signed main()
 93 {
 94     IOS;
 95     cin>>n>>m>>s>>d;
 96     init();
 97     int st,ed,d1,c1;
 98     for(int i=0;i<m;i++)
 99     {
100         cin>>st>>ed>>d1>>c1;
101         g[st][ed]=g[ed][st]=d1;
102         cost[st][ed]=cost[ed][st]=c1;
103     }
104     dijkstra();
105     dfs(d);
106     for(int i=path.size()-1;i>=0;i--)
107     {
108         cout<<path[i]<<" ";
109     }
110     cout<<dis[d]<<" "<<ans;
111     return 0;
112 }

dijkstra+dfs版本

  1 #include<bits/stdc++.h>
  2 using namespace std;
  3 #define int long long
  4 #define IOS ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
  5 const int N=510;
  6 const int INF=0x3f3f3f3f;
  7 int n,m,s,t;
  8 int g[N][N];
  9 int cost[N][N];
 10 int dis[N];
 11 int ans=INF;
 12 bool vis[N];
 13 vector<int>path,tmp;
 14 vector<int>pre[N];
 15 void init()
 16 {
 17     
 18     for(int i=0;i<N;i++)
 19     {
 20         for(int j=0;j<N;j++)
 21         {
 22             g[i][j]=INF;
 23             cost[i][j]=INF;
 24         }
 25     }
 26 }
 27 void dijkstra()
 28 {
 29     for(int i=0;i<N;i++)
 30     {
 31         dis[i]=INF;
 32     }
 33     dis[s]=0;
 34     for(int i=0;i<n;i++)
 35     {
 36         int u=-1;
 37         int minn=INF;
 38         for(int j=0;j<n;j++)
 39         {
 40             if(!vis[j]&&dis[j]<minn)
 41             {
 42                 u=j;
 43                 minn=dis[j];
 44             }
 45         }
 46         if(u==-1)
 47         return ;
 48         vis[u]=true;
 49         for(int v=0;v<n;v++)
 50         {
 51             if(!vis[v]&&g[u][v]!=INF)
 52             {
 53                 if(dis[u]+g[u][v]<dis[v])
 54                 {
 55                     dis[v]=dis[u]+g[u][v];
 56                     pre[v].clear();
 57                     pre[v].push_back(u);
 58                 }
 59                 else if(dis[u]+g[u][v]==dis[v])
 60                 {
 61                     //pre[v].push_back(u);
 62                     pre[v].push_back(u);
 63                     
 64                 }
 65             }
 66         }
 67     }
 68 }
 69 void dfs(int p)
 70 {
 71     if(p==s)
 72     {
 73         tmp.push_back(p);
 74         int value=0;
 75         for(int i=tmp.size()-1;i>0;i--)
 76         {
 77             int id1=tmp[i];
 78             int id2=tmp[i-1];
 79             value+=cost[id1][id2];
 80         }
 81         if(value<ans)
 82         {
 83             ans=value;
 84             path=tmp;
 85         }
 86         tmp.pop_back();
 87         return ;
 88     }
 89     tmp.push_back(p);
 90     for(int i=0;i<pre[p].size();i++)
 91     {
 92         dfs(pre[p][i]);
 93     }
 94     tmp.pop_back();
 95 }
 96 signed main()
 97 {
 98     IOS;
 99     init();
100     cin>>n>>m>>s>>t;
101     for(int i=0;i<m;i++)
102     {
103         int u,v,d,w;
104         cin>>u>>v>>d>>w;
105         g[u][v]=g[v][u]=d;
106         cost[u][v]=cost[v][u]=w;
107     }
108     dijkstra();
109     dfs(t);
110     for(int i=path.size()-1;i>=0;i--)
111     {
112         cout<<path[i]<<" ";
113     }
114     cout<<dis[t]<<" "<<ans;
115     return 0;
116 }

1087：

 1 #include <iostream>
 2 #include <map>
 3 #include <vector>
 4 #include <algorithm>
 5 using namespace std;
 6 int n, k;
 7 const int inf = 999999999;
 8 int e[205][205], weight[205], dis[205];
 9 bool visit[205];
10 vector<int> pre[205], temppath, path;
11 map<string, int> m;
12 map<int, string> m2;
13 int maxvalue = 0, mindepth, cntpath = 0;
14 double maxavg;
15 void dfs(int v) {
16     temppath.push_back(v);
17     if(v == 1) {
18         int value = 0;
19         for(int i = 0; i < temppath.size(); i++) {
20             value += weight[temppath[i]];
21         }
22         double tempavg = 1.0 * value / (temppath.size() - 1);
23         if(value > maxvalue) {
24             maxvalue = value;
25             maxavg = tempavg;
26             path = temppath;
27         } else if(value == maxvalue && tempavg > maxavg) {
28             maxavg = tempavg;
29             path = temppath;
30         }
31         temppath.pop_back();
32         cntpath++;
33         return ;
34     }
35    /* for(int i = 0; i < pre[v].size(); i++) {
36         dfs(pre[v][i]);
37     }*/
38     for(int i=pre[v].size()-1;i>=0;i--)
39     {
40         dfs(pre[v][i]);
41     }
42     temppath.pop_back();
43 }
44 int main() {
45     fill(e[0], e[0] + 205 * 205, inf);
46     fill(dis, dis + 205, inf);
47     scanf("%d %d", &n, &k);
48     string s;
49     cin >> s;
50     m[s] = 1;
51     m2[1] = s;
52     for(int i = 1; i < n; i++) {
53         cin >> s >> weight[i+1];
54         m[s] = i+1;
55         m2[i+1] = s;
56     }
57     string sa, sb;
58     int temp;
59     for(int i = 0; i < k; i++) {
60         cin >> sa >> sb >> temp;
61         e[m[sa]][m[sb]] = temp;
62         e[m[sb]][m[sa]] = temp;
63     }
64     dis[1] = 0;
65     for(int i = 0; i < n; i++) {
66         int u = -1, minn = inf;
67         for(int j = 1; j <= n; j++) {
68             if(visit[j] == false && dis[j] < minn) {
69                 u = j;
70                 minn = dis[j];
71             }
72         }
73         if(u == -1) break;
74         visit[u] = true;
75         for(int v = 1; v <= n; v++) {
76             if(visit[v] == false && e[u][v] != inf) {
77                 if(dis[u] + e[u][v] < dis[v]) {
78                     dis[v] = dis[u] + e[u][v];
79                     pre[v].clear();
80                     pre[v].push_back(u);
81                 } else if(dis[v] == dis[u] + e[u][v]) {
82                     pre[v].push_back(u);
83                 }
84             }
85         }
86     }
87     int rom = m["ROM"];
88     dfs(rom);
89     printf("%d %d %d %d\n", cntpath, dis[rom], maxvalue, (int)maxavg);
90     for(int i = path.size() - 1; i >= 1; i--) {
91         cout << m2[path[i]] << "->";
92     }
93     cout << "ROM";
94     return 0;
95 }

1072：

 1 #include<iostream>
 2 #include<string>
 3 #include<vector>
 4 #include<algorithm>
 5 #define INF (~(0x1<<31))
 6 using namespace std;
 7 int gra[1100][1100];
 8 int n, m, k, ds, mind = 0,minnode = -1;
 9 double average = INF;
10 vector<int> distd;
11 int toint(string s) {
12     int ans=0;
13     if(s[0]=='G')
14     {
15         for(int i=1;i<s.length();i++)
16         {
17             ans=ans*10+(s[i]-'0');
18         }
19         ans=ans+n;
20     }
21     else
22     {
23         for(int i=0;i<s.length();i++)
24         {
25             ans=ans*10+(s[i]-'0');
26         }
27     }
28     return ans;
29 }
30 void dijsktra(int v) {
31     vector<bool> visit(1100);
32     vector<int> dist(1100, INF);
33     dist[v] = 0;
34     for (int i = 0; i < n + m; i++) {//执行n+m次
35         int min = INF, u = -1;
36         for (int j = 1; j <= n + m; j++) {
37             if (!visit[j] && dist[j] < min) {
38                 u = j;
39                 min = dist[j];
40             }
41         }
42         if (u == -1) break;
43         visit[u] = true;
44         for (int j = 1; j <= n + m; j++) {//更新
45             if (!visit[j] && gra[u][j] != INF) {
46                 if (dist[u] + gra[u][j] < dist[j]) 
47                    dist[j] = dist[u] + gra[u][j];
48             }
49         }
50     }
51     int min = INF;
52     double sum = 0;
53     for (int i = 1; i <= n; i++) {//找最小节点
54         if (dist[i] < min) {
55             min = dist[i];
56             sum += 1.0*dist[i];
57         }
58         if (dist[i] > ds) return;//说明该加油站不能覆盖所有住户
59     }
60     if ((min > mind) || (min == mind && sum/n < average)) {
61         mind = min;
62         minnode = v;
63         average = sum / n;
64         distd = dist;
65     }
66     return;
67 }
68 int main() {
69     scanf("%d %d %d %d", &n, &m, &k, &ds);
70     fill(gra[0] , gra[0] + 1100 * 1100, INF);
71     for (int i = 0; i < k; i++) {
72         string s1,s2;
73         int d;
74         cin >> s1 >> s2 >> d;
75         int a = toint(s1);
76         int b = toint(s2);
77         gra[a][b] = gra[b][a] = d;
78     }
79     for (int i = n + 1; i <= n + m; i++) //从G1出发找最短路径
80         dijsktra(i);
81     if (minnode == -1) {
82         cout << "No Solution";
83         return 0;
84     }
85     cout << "G" << minnode - n << endl;
86     int sum = 0;
87     for (int i = 1; i <= n; i++)
88         sum += distd[i];
89     printf("%.1f %.1f", (double)mind,(double)sum/n);
90     return 0;
91 }

 

posted @ 2022-11-24 16:17  江上舟摇  阅读(13)  评论(0)  编辑  收藏  举报