单源最短路径算法

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Bellman-Ford算法

struct Node{    int distance;    int prev;};void PrintPath(Node* node, int source, int index){    if (node[index].index == source)    {        printf("%4d", source);        return;    }    PrintPath(node, source, node[index].prev);    printf("%4d", index);}int BellmanFord(int** matrix, int node_num, int source, int dest){    Node* node = new Node[node_num];    for (int i = 0; i < node_num; i++)    {        node[i].distance=100;        node[i].prev = -1;    }    node[source].distance = 0;    for (int t = 0; t < node_num; t++)    {        for (int i = 0; i < node_num; i++)        {            for (int k = 0; k < node_num; k++)            {                if (matrix[i][k] > -5 && matrix[i][k] + node[i].distance < node[k].distance)                {                    node[k].distance = matrix[i][k] + node[i].distance;                    node[k].prev = i;                }            }        }    }    for (int i = 0; i < node_num; i++)    {        for (int k = 0; k < node_num; k++)        {            if (matrix[i][k] > 0 && matrix[i][k] + node[i].distance < node[k].distance)            {                return false;            }        }    }    for (int i = 0; i < node_num; i++)    {        printf("distance from %d to %d is %d\n", source, i, node[i].distance);    }    PrintPath(node, source, dest);    return true;}int main(){    int num_node, num_vert;    int binary_vertex;    FILE* fp = fopen("input.txt", "r");    char buf[1024];    if (fscanf(fp, "%d %d %d\n", &num_node, &num_vert, &binary_vertex) != 3)    {        fprintf(stderr, "\nfscanf error: %s: %d\n", strerror(errno), errno);        exit(1);    }    int** matrix = new int*[num_node];    for (int i = 0; i < num_node; i++)    {        matrix[i] = new int[num_node];    }    for (int i = 0; i < num_node; i++)    {        for (int j = 0; j < num_node; j++)        {            matrix[i][j] = -100;        }    }    while (fgets(buf, 1024, fp) != NULL)    {        int begin, end;        int weight;        if (sscanf(buf, "%d %d %d\n", &begin, &end,&weight) != 3)        {            fprintf(stderr, "\nsscanf error: %s: %d\n", strerror(errno), errno);            exit(1);        }        if (binary_vertex == 1)        {            matrix[end][begin] = weight;        }        matrix[begin][end] = weight;    }    for (int i = 0; i < num_node; i++)    {        for (int j = 0; j < num_node; j++)        {            printf("%8d", matrix[i][j]);        }        printf("\n");    }    int source = 0;    int dest = 1;    int dis = BellmanFord(matrix, num_node, source, dest);    return 0;}

Dijkstra算法

struct Node{    int index;    int distance;    int prev;};struct Compare {    bool operator() (Node a, Node b)     {        if (a.distance > b.distance)        {            return true;        }        else        {            return false;        }    }};void PrintPath(Node* node, int source, int index){    if (node[index].index == source)    {        printf("%4d", source);        return;    }    PrintPath(node, source, node[index].prev);    printf("%4d", index);}int Dijkstra(int** matrix, int node_num, int source, int dest){    Node* node = new Node[node_num];    for (int i = 0; i < node_num; i++)    {        node[i].index = i;        node[i].distance = 100;        node[i].prev = -1;    }    node[source].distance = 0;    priority_queue<Node,vector<Node>,Compare > que;    que.push(node[source]);    while (!que.empty())    {        Node cur = que.top();        que.pop();        for (int i = 0; i < node_num; i++)        {            if (matrix[cur.index][i] >= 0 && matrix[cur.index][i] + cur.distance < node[i].distance)            {                node[i].distance = matrix[cur.index][i] + cur.distance;                node[i].prev = cur.index;                que.push(node[i]);            }        }    }    for (int i = 0; i < node_num; i++)    {        printf("distance from %d to %d is %d\n", source, i, node[i].distance);    }    PrintPath(node,source,dest);    return node[dest].distance;}int main(){    int num_node, num_vert;    int binary_vertex;    FILE* fp = fopen("input.txt", "r");    char buf[1024];    if (fscanf(fp, "%d %d %d\n", &num_node, &num_vert, &binary_vertex) != 3)    {        fprintf(stderr, "\nfscanf error: %s: %d\n", strerror(errno), errno);        exit(1);    }    int** matrix = new int*[num_node];    for (int i = 0; i < num_node; i++)    {        matrix[i] = new int[num_node];    }    for (int i = 0; i < num_node; i++)    {        for (int j = 0; j < num_node; j++)        {            matrix[i][j] = -1;        }    }    while (fgets(buf, 1024, fp) != NULL)    {        int begin, end;        int weight;        if (sscanf(buf, "%d %d %d\n", &begin, &end,&weight) != 3)        {            fprintf(stderr, "\nsscanf error: %s: %d\n", strerror(errno), errno);            exit(1);        }        if (binary_vertex == 1)        {            matrix[end][begin] = weight;        }        matrix[begin][end] = weight;    }    for (int i = 0; i < num_node; i++)    {        for (int j = 0; j < num_node; j++)        {            printf("%8d", matrix[i][j]);        }        printf("\n");    }    int source = 0;    int dest = 2;    int dis = Dijkstra(matrix, num_node, source, dest);    return 0;}

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