使用 BFS 计算源和顶点之间的距离

Question

我正在尝试使用邻接表来计算从源顶点到其他顶点的距离。我正在使用队列来完成此操作，但是我将除源之外的每个顶点的距离设为 -1，但我不确定为什么会发生这种情况

#include <stdio.h>
#include <stdlib.h>
#include "input_error.h"
#define VertexToSearch 1

typedef struct edge {
    int vertexIndex;
    struct edge *edgePtr;
} edge;

typedef struct vertex {
    int vertexKey;
    struct edge *edgePtr;
    int visited;
    int distance;
} vertex;

typedef struct queue {
    struct vertex v;
    struct queue* next;
}queue;

int vertexCount = 0;
struct vertex graph[];
void load_file(char*);
void insertEdge(int, int, struct vertex[]);
void InsertVertex(int, struct vertex[]);
void printGraph();
void bfs();
void print_distances();
queue* enqueue(queue*,vertex );
vertex dequeue(queue*);

enum error program_error;
int count;

int main(int argc, char** argv) {
    load_file(argv[1]);
    printGraph();
    bfs();
    print_distances();
    return 0;
}

void load_file(char* filename) {

    int vertex1;
    int vertex2;
    FILE* file = fopen(filename, "r");

    if (file == NULL) {
        printf("%s did not open\n", filename);
        program_error = FILE_FAILED_TO_OPEN;
        exit(program_error);
    }

    fscanf(file, "%d", &count);
    graph[count];
    for (int i = 0; i < count; i++) {
        InsertVertex(i + 1, graph);
    }
    for (int i = 0; i < count; i++) {
        fscanf(file, "\n(%d,%d)", &vertex1, &vertex2);
        insertEdge(vertex1, vertex2, graph);
    }
    fclose(file);
}

void InsertVertex(int vertexKey, struct vertex graph[]) {
    graph[vertexCount].vertexKey = vertexKey;
    graph[vertexCount].edgePtr = NULL;
    graph[vertexCount].visited = 0;
    graph[vertexCount].distance = -1;
    vertexCount++;
}

void insertEdge(int vertex1, int vertex2, struct vertex graph[]) {
    struct edge *e, *e1, *e2;
    e = graph[vertex1 - 1].edgePtr;
    while (e && e->edgePtr) {
        e = e->edgePtr;
    }
    e1 = (struct edge *) malloc(sizeof (*e1));
    e1->vertexIndex = vertex2;
    e1->edgePtr = NULL;
    if (e)
        e->edgePtr = e1;
    else
        graph[vertex1 - 1].edgePtr = e1;

    e = graph[vertex2 - 1].edgePtr;
    while (e && e->edgePtr) {
        e = e->edgePtr;
    }
    e2 = (struct edge *) malloc(sizeof (*e2));
    e2->vertexIndex = vertex1;
    e2->edgePtr = NULL;
    if (e)
        e->edgePtr = e2;
    else
        graph[vertex2 - 1].edgePtr = e2;
}

void printGraph() {
    int i;
    struct edge *e;
    for (i = 0; i < vertexCount; i++) {
        printf("%d(%d)", i + 1, graph[i].vertexKey);
        e = graph[i].edgePtr;
        while (e) {
            printf("->%d", e->vertexIndex);
            e = e->edgePtr;
        }
        printf("\n");
    }
}

void bfs() {
    graph[0].distance = 0;
    queue* q = NULL;
   q = enqueue(q,graph[0]);
    while(q->next != NULL){
        vertex u = dequeue(q);
        while(u.edgePtr != NULL){
           if(graph[u.edgePtr->vertexIndex -1 ].distance == -1){
              graph[u.edgePtr->vertexIndex -1 ].distance = u.distance + 1;
              enqueue(q, graph[u.edgePtr->vertexIndex -1 ]);
           } 
           u.edgePtr = u.edgePtr->edgePtr;
        }
    }

}

void print_distances() {
    for (int i = 0; i < count; i++) {
        printf("%d %d\n", i + 1, graph[i].distance);
    }
}

queue* enqueue(queue* q,vertex v) {
    queue* new = malloc(sizeof (queue));
    new->next = NULL; 
    new->v = v;
    if (q == NULL) {
        q = malloc(sizeof(queue));
        q = new;
    } else {
        while (q->next != NULL) {
            q = q->next;
        }
        //add new node at the end
        q->next = new;

    }
    return q;
}

vertex dequeue(queue* q) {
    vertex v;
    queue* tempPtr;
    tempPtr = q; //makes temp the address of the node to be deleted
    v = tempPtr->v;
    q = q->next; //sets the new head as the address of the next node

    return v;
} 

Answer 1

我想通了，基本上我的队列实现很糟糕，出队没有清除队列，而且这个while(q->next != NULL)不正确应该是while(q != NULL)下面是这个程序的正确实现

#include <stdio.h>
#include <stdlib.h>
#include "input_error.h"
#define VertexToSearch 1

typedef struct edge {
    int vertexIndex;
    struct edge *edgePtr;
} edge;

typedef struct vertex {
    int vertexKey;
    struct edge *edgePtr;
    int visited;
    int distance;
} vertex;

typedef struct queue {
    struct vertex v;
    struct queue* next;
}queue;

int vertexCount = 0;
struct vertex graph[];
queue* q = NULL;
void load_file(char*);
void insertEdge(int, int, struct vertex[]);
void InsertVertex(int, struct vertex[]);
void printGraph();
void bfs();
void print_distances();
void enqueue(vertex);
vertex dequeue();

enum error program_error;
int count;

int main(int argc, char** argv) {
    load_file(argv[1]);
    printGraph();
    bfs();
    print_distances();
    return 0;
}

void load_file(char* filename) {

    int vertex1;
    int vertex2;
    FILE* file = fopen(filename, "r");

    if (file == NULL) {
        printf("%s did not open\n", filename);
        program_error = FILE_FAILED_TO_OPEN;
        exit(program_error);
    }

    fscanf(file, "%d", &count);
    graph[count];
    for (int i = 0; i < count; i++) {
        InsertVertex(i + 1, graph);
    }
    for (int i = 0; i < count; i++) {
        fscanf(file, "\n(%d,%d)", &vertex1, &vertex2);
        insertEdge(vertex1, vertex2, graph);
    }
    fclose(file);
}

void InsertVertex(int vertexKey, struct vertex graph[]) {
    graph[vertexCount].vertexKey = vertexKey;
    graph[vertexCount].edgePtr = NULL;
    graph[vertexCount].visited = 0;
    graph[vertexCount].distance = -1;
    vertexCount++;
}

void insertEdge(int vertex1, int vertex2, struct vertex graph[]) {
    struct edge *e, *e1, *e2;
    e = graph[vertex1 - 1].edgePtr;
    while (e && e->edgePtr) {
        e = e->edgePtr;
    }
    e1 = (struct edge *) malloc(sizeof (*e1));
    e1->vertexIndex = vertex2;
    e1->edgePtr = NULL;
    if (e)
        e->edgePtr = e1;
    else
        graph[vertex1 - 1].edgePtr = e1;

    e = graph[vertex2 - 1].edgePtr;
    while (e && e->edgePtr) {
        e = e->edgePtr;
    }
    e2 = (struct edge *) malloc(sizeof (*e2));
    e2->vertexIndex = vertex1;
    e2->edgePtr = NULL;
    if (e)
        e->edgePtr = e2;
    else
        graph[vertex2 - 1].edgePtr = e2;
}

void printGraph() {
    int i;
    struct edge *e;
    for (i = 0; i < vertexCount; i++) {
        printf("%d(%d)", i + 1, graph[i].vertexKey);
        e = graph[i].edgePtr;
        while (e) {
            printf("->%d", e->vertexIndex);
            e = e->edgePtr;
        }
        printf("\n");
    }
}

void bfs() {
    graph[0].distance = 0;
   enqueue(graph[0]);
    while(q != NULL){
        vertex u = dequeue();
        while(u.edgePtr != NULL){
       if(graph[u.edgePtr->vertexIndex - 1].distance == -1){
          graph[u.edgePtr->vertexIndex - 1].distance = u.distance + 1;
          enqueue(graph[u.edgePtr->vertexIndex - 1]);
       } 
           u.edgePtr = u.edgePtr->edgePtr;
        }
    }

}

void print_distances() {
    for (int i = 0; i < count; i++) {
        printf("%d %d\n", i + 1, graph[i].distance);
    }
}

void enqueue(vertex v) {
    queue* new = malloc(sizeof (queue));
    new->next = NULL; 
    new->v = v;
    if (q == NULL) {
        q = malloc(sizeof(queue));
        q = new;
    } else {
        while (q->next != NULL) {
            q = q->next;
        }
        //add new node at the end
        q->next = new;

    }
}

vertex dequeue() {
    vertex v;
    queue* tempPtr;
    tempPtr = q; //makes temp the address of the node to be deleted
    v = tempPtr->v;
    q = q->next; //sets the new head as the address of the next node
    return v;
}

Answer 2

在insertVertex(...) 中，您调用graph[vertexCount].distance = -1;。

您的代码很可能没有正确更改距离。据我所知，您将u.edgePtr->vertexIndex 设置为连接的第二个顶点的索引- 1（在insertEdge(...) 中）。这意味着您可能正在从人类可读的索引 (1, 2, ... n) 转换为机器可读的索引 (0, 1, ... n-1)

在bfs() 中，您不需要再次执行此操作！我找不到任何理由设置graph[u.edgePtr->vertexIndex - 1].distance，但我可能弄错了。我已经重做了你的 while 循环。试试把这个放到bfs():

while(u.edgePtr != NULL){
       if(graph[u.edgePtr->vertexIndex].distance == -1){
          graph[u.edgePtr->vertexIndex].distance = u.distance + 1;
          enqueue(q, graph[u.edgePtr->vertexIndex]);
       } 

我不确定为什么 none 您的距离会发生变化，因为您的代码应该仍然会影响 index-1 的距离就好了。尝试上面的修复，让我知道这是否足以捕获错误，或者是否可能存在另一个错误。

Answer 3

你有大致的想法。这里有一些简化代码的方法

• 使用固定大小的基于数组的队列。尺寸 256 是理想的，因为 无符号整数索引将自动翻转。权衡： 简单的代码，但在任何给定的队列中不超过 255 个项目 时间。
• 使用边数组。权衡：易于实现边缘阵列， 但需要 O(E) 搜索来找到源自任何 给定顶点。
• 使用距离来跟踪节点是否已被访问。一种 负距离表示该顶点尚未被访问。 权衡：对我来说似乎是双赢的，更简单的代码，更少的空间，没有 额外的时间。
• 使用顶点 ID 在顶点数组中定位一个顶点。权衡： 防止格式错误的边缘使您的程序崩溃，但需要 O(V) 搜索找到顶点。

这是简化的代码。我将其作为练习留给读者根据需要优化代码以提高速度和/或删除队列限制。

#include <stdio.h>
#include <stdint.h>

struct Vertex
{
    int id;
    int distance;
};

struct Queue
{
    uint8_t head;
    uint8_t tail;
    void *data[256];
};

int main( void )
{
    int edge[][2] = { {2,3}, {1,4}, {1,3}, {3,4}, {4,5}, {0,0} };
    struct Vertex vertex[] = { {1,0}, {2,-1}, {3,-1}, {4,-1}, {5,-1}, {0,0} };
    struct Queue q = { 0, 0 };

    q.data[q.head++] = &vertex[0];
    while ( q.tail != q.head )
    {
        struct Vertex *src = q.data[q.tail++];
        for ( int i = 0; edge[i][0] > 0; i++ )
            for ( int j = 0; j < 2; j++ )
                if ( edge[i][j] == src->id )
                {
                    int destID = edge[i][(j+1)%2];
                    struct Vertex *dest;
                    for ( dest = vertex; dest->id > 0; dest++ )
                        if ( dest->id == destID )
                            break;

                    if ( dest->distance < 0 )
                    {
                        dest->distance = src->distance + 1;
                        q.data[q.head++] = dest;
                    }
                }
    }

    for ( int i = 0; vertex[i].id > 0; i++ )
        printf( "Vertex %d is at distance %d\n", vertex[i].id, vertex[i].distance );
}