单源最短路模板 + hdu - 2544

Floyd

Floyd 本质上类似一种动态规划，dp [ i ] [ j ] = dp [ i ] [ k ] + dp[ k ] [ j ]。

 /**
  *  Night gathers, and now my watch begins.
  *  It shall not end until my death.
  *  I shall take no wife, hold no lands, father no children.
  *  I shall wear no crowns and win no glory.
  *  I shall live and die at my post.
  *  I am the sword in the darkness.
  *  I am the watcher on the walls.
  *  I am the fire that burns against the cold,
  *  the light that wakes the sleepers,
  *  the shield that guards the realms of men.
  *  I pledge my life and honor to the Night's Watch,
  *  for this night,
  *  and all the nights to come.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int Map[MAXN][MAXN];
 int n, m, q;
 int a, b, c;

 void Floyd () {
     ; k < n; k++)
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = min (Map[i][j], Map[i][k] + Map[k][j]);
 }

 int main() {
     while (cin >> n >> m >> q) {
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = INF;

         ; i <= m; i++) {
             cin >> a >> b >> c;
             Map[a][b] = Map[b][a] = min (Map[a][b], c);
         }
         Floyd();
         ; i <= q; i++) {
             cin >> a >> b;
             cout << Map[a][b] << endl;
         }
     }
     ;
 }

Floyd

 /**
  *  Night gathers, and now my watch begins.
  *  It shall not end until my death.
  *  I shall take no wife, hold no lands, father no children.
  *  I shall wear no crowns and win no glory.
  *  I shall live and die at my post.
  *  I am the sword in the darkness.
  *  I am the watcher on the walls.
  *  I am the fire that burns against the cold,
  *  the light that wakes the sleepers,
  *  the shield that guards the realms of men.
  *  I pledge my life and honor to the Night's Watch,
  *  for this night,
  *  and all the nights to come.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int Map[MAXN][MAXN];
 int n, m, q;
 int a, b, c;

 void Floyd () {
     ; k <= n; k++)
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = min (Map[i][j], Map[i][k] + Map[k][j]);
 }

 int main() {
     while (~scanf ("%d%d", &n, &m) && n || m) {
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = INF;

         ; i <= m; i++) {
             scanf ("%d%d%d", &a, &b, &c);
             Map[a][b] = Map[b][a] = min (Map[a][b], c);
         }
         Floyd();
         cout << Map[][n] << endl;

     }
     ;
 }

Dijkstra

从源点出发，首先寻找离源点最近的几个节点，now 储存现在离源点最近的节点的序号。

 /**
  *  Night gathers, and now my watch begins.
  *  It shall not end until my death.
  *  I shall take no wife, hold no lands, father no children.
  *  I shall wear no crowns and win no glory.
  *  I shall live and die at my post.
  *  I am the sword in the darkness.
  *  I am the watcher on the walls.
  *  I am the fire that burns against the cold,
  *  the light that wakes the sleepers,
  *  the shield that guards the realms of men.
  *  I pledge my life and honor to the Night's Watch,
  *  for this night,
  *  and all the nights to come.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int Map[MAXN][MAXN];
 int dis[MAXN];
 int vis[MAXN];
 int n, m, q;
 int a, b, c;

 void Dijkstra (int src) {
     mem (vis, );
     ; i <= n; i++)
         dis[i] = INF;
     dis[src] = ;
     ) {
         ;
         ; i <= n; i++)
              || dis[i] < dis[now]))
                 now = i;
         )
             break;
         vis[now] = ;
         ; i <= n; i++)
             dis[i] = min (dis[i], dis[now] + Map[now][i]);
         cout<<now<<endl;
         ; i <= n; i++)
             cout << dis[i] << ' ';
         cout << endl;
     }
 }

 int main() {
     while (cin >> n >> m >> q) {
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = INF;

         ; i <= m; i++) {
             cin >> a >> b >> c;
             Map[a][b] = Map[b][a] = min (Map[a][b], c);
         }
         Dijkstra ();
         ; i <= q; i++) {
             cin >> a >> b;
             cout << dis[i] << endl;
         }

     }
     ;
 }

Dijkstra

 /**
  *  Night gathers, and now my watch begins.
  *  It shall not end until my death.
  *  I shall take no wife, hold no lands, father no children.
  *  I shall wear no crowns and win no glory.
  *  I shall live and die at my post.
  *  I am the sword in the darkness.
  *  I am the watcher on the walls.
  *  I am the fire that burns against the cold,
  *  the light that wakes the sleepers,
  *  the shield that guards the realms of men.
  *  I pledge my life and honor to the Night's Watch,
  *  for this night,
  *  and all the nights to come.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 int Map[MAXN][MAXN];
 int dis[MAXN];
 int vis[MAXN];
 int n, m, q;
 int a, b, c;

 void Dijkstra (int src) {
     mem (vis, );
     ; i <= n; i++)
         dis[i] = INF;
     dis[src] = ;
     ) {
         ;
         ; i <= n; i++)
              || dis[i] < dis[now]))
                 now = i;
         )
             break;
         vis[now] = ;
         ; i <= n; i++)
             dis[i] = min (dis[i], dis[now] + Map[now][i]);
         cout<<now<<endl;
         ; i <= n; i++)
             cout << dis[i] << ' ';
         cout << endl;
     }
 }

 int main() {
     while (cin >> n >> m >> q) {
         ; i <= n; i++)
             ; j <= n; j++)
                 Map[i][j] = INF;

         ; i <= m; i++) {
             cin >> a >> b >> c;
             Map[a][b] = Map[b][a] = min (Map[a][b], c);
         }
         Dijkstra ();
         ; i <= q; i++) {
             cin >> a >> b;
             cout << dis[i] << endl;
         }

     }
     ;
 }

SPFA

将每次被松弛了的节点入队，直到队列为空，得到的就是源点到各节点的最短路。

 /**
  *  Night gathers, and now my watch begins.
  *  It shall not end until my death.
  *  I shall take no wife, hold no lands, father no children.
  *  I shall wear no crowns and win no glory.
  *  I shall live and die at my post.
  *  I am the sword in the darkness.
  *  I am the watcher on the walls.
  *  I am the fire that burns against the cold,
  *  the light that wakes the sleepers,
  *  the shield that guards the realms of men.
  *  I pledge my life and honor to the Night's Watch,
  *  for this night,
  *  and all the nights to come.
  */

 #include<bits/stdc++.h>
 #define lson i<<2
 #define rson i<<2|1
 #define LS l,mid,lson
 #define RS mid+1,r,rson
 #define mem(a,x) memset(a,x,sizeof(a))
 #define gcd(a,b) __gcd(a,b)
 #define ll long long
 #define ull unsigned long long
 #define lowbit(x) (x&-x)
 #define enld endl
 #define mian main
 #define itn int
 #define prinft printf

 const double PI = acos (-1.0);
 const int INF = 0x3f3f3f3f;
 ;
 ;
 ;
 ;

 using namespace std;

 //邻接表实现
 struct node {
     int to, cost;
     node (int a, int b) {
         to = a, cost = b;
     }
 };
 vector<node> edge[MAXN];

 int vis[MAXN];      //可以用map
 int dis[MAXN];
 int n, m;
 int a, b, c;
 queue<int> q;

 void spfa (int src) {
     mem (vis, );
     vis[src] = ;
     dis[src] = ;
     q.push (src);
     while (!q.empty()) {
         int now = q.front();
         q.pop();
         vis[now] = ;
         ; i < edge[now].size(); ++i) {
             if (dis[now] + edge[now][i].cost > dis[edge[now][i].to])
                 continue;
             dis[edge[now][i].to] = dis[now] + edge[now][i].cost;        //更新
             if (!vis[edge[now][i].to]) {                                //入队
                 q.push (edge[now][i].to);
                 vis[edge[now][i].to] = ;
             }
         }
     }
 }

 int main() {
     while (cin >> n >> m && (n || m)) {
         while (!q.empty())
             q.pop();
         ; i <= n; i++)
             dis[i] = INF;
         ; i <= n; i++)
             edge[i].clear();

         ; i <= m; i++) {
             cin >> a >> b >> c;
             edge[a].push_back (node (b, c)), edge[b].push_back (node (a, c));
         }
         spfa ();
         cout << dis[n] << endl;
     }
     ;
 }

hdu 2544 SPFA