Shortest path: Dijkstra,bellman,spfa,floyd implementation of the algorithm

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</pre><pre name= "code" class= "CPP" > #include <cstdio> #include <iostream> #include <cstring > #include <queue> #include <algorithm> #include <vector>using namespace Std;const int INF = 0x3f3f3f3f;//Infinity Const int MAXN = 20;//maximum number of vertices int n;//vertex number int edge[maxn][maxn];//adjacency matrix//dijkstra algorithm 3 array int s[maxn];/ /record whether vertices are in the collection int dist[maxn];//record path weights int path[maxn];//record path void Dijkstra (int v0)//Seek v0 to other points shortest path {int I, J, k;//loop variable fo        R (i=0; i<n; i++) {dist[i] = Edge[v0][i];        S[i] = 0;        if (i!=v0 && dist[i]<inf) path[i] = V0;    else Path[i] =-1; } S[v0] = 1;        Dist[v0] = 0;//Vertex v0 Add vertex set S for (i=0; i<n-1; i++)//from vertex v0 determine n-1 bar shortest path {int min = INF, u = v0;                Select the vertex with the shortest path in the current collection T U for (j=0; j<n; J + +) {if (!s[j] && dist[j]<min) {                U = j;            min = Dist[j]; }} S[u] = 1;//adds the vertex u to the set S. Indicates its shortest circuit.Dist and path array elements for (k=0; k<n; k++) {if (!s[k] && edge[u][k]<i) of the vertices in the T collection                    NF && Dist[u]+edge[u][k]<dist[k]) {dist[k] = Dist[u] + edge[u][k];                Path[k] = u;    }}}}int Main () {int i, j;//loop variable int u, V, start and end of w;//edge and weight scanf ("%d", &n);//read in vertex number n while (1)        {scanf ("%d%d%d", &u, &v, &w);        if (u==-1 && v==-1 && w==-1) break;                EDGE[U][V] = w;//building adjacency Matrix} for (i=0; i<n; i++) {for (j=0; j<n; J + +) {if (i==j)            EDGE[I][J] = 0;        else if (edge[i][j] = = 0) edge[i][j] = INF;        }} Dijkstra (0);//Find the shortest path of vertex 0 to other vertices int shortest[maxn];//The ordinal of each vertex on the output shortest path for (i=1; i<n; i++) { printf ("%d\t", Dist[i]);//output vertex 0 to vertex i shortest path length//The code below is used to output vertex 0 shortest path with vertex i memset (shortest, 0, sizeof (shorteST));        int k = 0;//k represents the subscript of the last element in the shorttest array shortest[k] = i;            while (path[Shortest[k]]!=0) {k++;            SHORTEST[K] = path[shortest[k-1]];        printf ("%d", k); } k++;        Shortest[k] = 0;        printf ("%d", k);        for (j=k; j>0; j--) printf ("%d--", Shortest[j]);    printf ("%d\n", shortest[0]); } return 0;}

Bellman:

#include <cstdio> #include <iostream> #include <cstring> #include <queue> #include < Algorithm> #include <vector>using namespace std;const int INF = 0x3f3f3f3f;const int maxn = 8;int EDGE[MAXN][MAXN]    ; int Dist[maxn];int path[maxn];int n;void Bellman (int v0) {int I, j, K, U;        for (i=0; i<n; i++) {dist[i] = Edge[v0][i];        if (i!=v0 && dist[i] < INF) Path[i] = V0;    else Path[i] =-1; } for (k=2, k<n; k++) {for (u=0; u<n; u++) {if (u!=v0) {f or (j=0; j<n; J + +) {if (Edge[j][u] < INF && Dist[j] + Edge[j][u] < di                        St[u]) {Dist[u] = Dist[j] + edge[j][u];                    Path[u] = j;    }}}}}}int main () {int i, J;    int U, V, W;    scanf ("%d", &n); while (1) {scanf ("%d%d%d", &u, &v, &w);         if (u==-1 && v==-1 && w==-1) break;    EDGE[U][V] = W;             } for (i=0; i<n; i++) {for (j=0; j<n; J + +) {if (i==j) edge[i][j] = 0;        else if (edge[i][j]==0) edge[i][j] = INF;    }} Bellman (0);    int SHORTEST[MAXN];        for (I=1; i<n; i++) {printf ("%d\t", Dist[i]);        memset (shortest, 0, sizeof (shortest));        int k = 0;        Shortest[k] = i;            while (path[shortest[k]]!=0) {k++;        SHORTEST[K] = path[shortest[k-1]];        } k++;        Shortest[k] = 0;        for (j=k; j>0; j--) printf ("%d--", Shortest[j]);    printf ("%d\n", shortest[0]); } return 0;}

SPFA:

#include <cstdio> #include <cstring> #include <queue> #define INF 1000000/Infinity # MAXN 10using Name    Space std;struct arcnode{int to;    int weight; struct Arcnode *next;};  Queue<int> Q;   The node in the queue is the vertex ordinal int n;  Number of vertices arcnode* LIST[MAXN];  Edge-Linked table header pointer for each vertex int INQ[MAXN];  Whether each vertex is a flag in the queue int DIST[MAXN]; int PATH[MAXN];  void spfa (int src) {int i, u;    U arcnode* temp for the queue overhead point ordinal;        for (i=0; i<n; i++)//Initialize {dist[i] = INF;        Path[i] = src;    Inq[i] = 0;    } DIST[SRC] = 0;    PATH[SRC] = src;    inq[src]++;    Q.push (SRC); while (!        Q.empty ()) {u = Q.front ();        Q.pop ();        inq[u]--;        temp = List[u];            while (temp!=null) {int v = temp->to;                if (Dist[v] > Dist[u] + temp->weight) {Dist[v] = Dist[u] + temp->weight;                PATH[V] = u;  if (!inq[v]) {Q.push (v);                  inq[v]++;        }} temp = temp->next;  }}}int Main () {int i, J;  loop variable int u, V, W;  The start and end point of the edge and the weight value scanf ("%d", &n);    Reads the number of vertices n memset (list, 0, sizeof (list));    arcnode* temp;  while (1) {scanf ("%d%d%d", &u, &v, &w);//start and end of read-in Edge if (u==-1 && v==-1 &&        W==-1) break;        temp = new Arcnode;        Construct adjacency Table temp->to = v;        Temp->weight = W;        Temp->next = NULL;        if (list[u]==null) list[u] = temp;            else {temp->next = List[u];        List[u] = temp; }} SPFA (0);        Find the shortest path to vertex 0 to other vertices for (j=0; j<n; j + +)//release the storage space occupied by each edge node on the edge list {temp = List[j];            while (Temp!=null) {List[j] = temp->next;            Delete temp;        temp = List[j];  }} int SHORTEST[MAXN];    The ordinal number of each vertex is stored for the output of each vertex on the shortest path for (i=1; i<n; i++) {    printf ("%d\t", Dist[i]);        The shortest path length of the output vertex 0 to vertex I//The code below is used to output the shortest path of vertex 0 to vertex i memset (shortest, 0, sizeof (shortest));  int k = 0;        K represents the subscript of the last element in the shortest array shortest[k] = i;            while (path[shortest[k]! = 0) {k++;        Shortest[k] = path[shortest[k-1]];        } k++;        Shortest[k] = 0;        for (j=k; j>0; j--) printf ("%d→", Shortest[j]);    printf ("%d\n", shortest[0]); } return 0;}

Floyd:

#include <cstdio> #include <iostream> #include <cstring> #include <queue> #include <   Algorithm> #include <vector>using namespace std; #define INF 1000000/Infinity # define MAXN 8int N;  Number of vertices int EDGE[MAXN][MAXN];    adjacency matrix int A[MAXN][MAXN];  int PATH[MAXN][MAXN];    void Floyd ()//assuming that the adjacency matrix and the number of vertices of the graph have been read in {int i, j, K;            For (i=0, i<n; i++) {for (j=0; j<n; J + +) {A[i][j] = edge[i][j];//to a[[] initialization if (i!=j && a[i][j]<inf) path[i][j] = i; I to J have path else path[i][j] =-1;    From I to J no direct path}}//from a (-1) to a (0), a (1), ..., a (n-1), or understood to be V0,v1,..., V (n-1) as the middle vertex for (k=0; k<n; k++) {for (i=0, i<n; i++) {for (j=0; j<n; J + +) {if (K==i | | k==j                ) continue;                    if (A[i][k] + a[k][j] < A[i][j]) {a[i][j] = A[i][k] + a[k][j];          PATH[I][J] = Path[k][j];      }}}}}int main () {int i, J;  loop variable int u, V, W;  The start and end point of the edge and the weight value scanf ("%d", &n);    Reads the number of vertices n for (i=0; i<n; i++)//sets the initial value of each element in the adjacency matrix to inf {for (j=0; j<n; j + +) edge[i][j] = inf;    } for (i=0; i<n; i++)//sets the value of the element on the diagonal of the adjacency matrix to 0 {edge[i][i] = 0; while (1) {scanf ("%d%d%d", &u, &v, &w);//The Start and end of the read-in Edge if (u==-1 && V==-1 &        & W==-1) break; EDGE[U][V] = W; Constructs adjacency matrix} Floyd (); Find the shortest path between the vertices int SHORTEST[MAXN]; The ordinal of each vertex is stored in the output of each vertex of the shortest path for (i=0; i<n; i++) {for (j=0; j<n; J + +) {if (I==J) CO Ntinue;  Skip printf ("%d=>%d\t%d\t", I, J, A[i][j]);            The shortest path length of the output vertex I to the vertex J//The code below is used to output the shortest path of vertex 0 to vertex i memset (shortest, 0, sizeof (shortest)); int k = 0;            K represents the subscript of the last element in the shortest array shortest[k] = j;       while (path[i][shortest[k]! = i) {         k++;            Shortest[k] = path[i][shortest[k-1]];            } k++;            Shortest[k] = i;            for (int t=k; t>0; t--) printf ("%d→", shortest[t]);        printf ("%d\n", shortest[0]); }} return 0;}

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Shortest path: Dijkstra,bellman,spfa,floyd implementation of the algorithm