c - 修改 Dijkstra 代码打印路径

Question

我得到了这个使用邻接表的图的 Dijkstra 代码，但我无法修改它以显示最小路径。有什么帮助吗？我需要先行 vector 来计算每个顶点的介数和接近度。

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

struct AdjListNode
{
    int dest;
    int weight;
    struct AdjListNode* next;
};

struct AdjList
{
    struct AdjListNode *head;  // pointer to head node of list
};

struct Graph
{
    int V;
    struct AdjList* array;
};

struct AdjListNode* newAdjListNode(int dest, int weight)
{
    struct AdjListNode* newNode =
            (struct AdjListNode*) malloc(sizeof(struct AdjListNode));
    newNode->dest = dest;
    newNode->weight = weight;
    newNode->next = NULL;
    return newNode;
}

struct Graph* createGraph(int V)
{
    struct Graph* graph = (struct Graph*) malloc(sizeof(struct Graph));
    graph->V = V;

    // Create an array of adjacency lists.  Size of array will be V
    graph->array = (struct AdjList*) malloc(V * sizeof(struct AdjList));

     // Initialize each adjacency list as empty by making head as NULL
    for (int i = 0; i < V; ++i)
        graph->array[i].head = NULL;

    return graph;
}

void addEdge(struct Graph* graph, int src, int dest, int weight)
{
    // Add an edge from src to dest.  A new node is added to the adjacency
    // list of src.  The node is added at the begining
    struct AdjListNode* newNode = newAdjListNode(dest, weight);
    newNode->next = graph->array[src].head;
    graph->array[src].head = newNode;

    // Since graph is undirected, add an edge from dest to src also
    newNode = newAdjListNode(src, weight);
    newNode->next = graph->array[dest].head;
    graph->array[dest].head = newNode;
}

struct MinHeapNode
{
    int  v;
    int dist;
};

struct MinHeap
{
    int size;      // Number of heap nodes present currently
    int capacity;  // Capacity of min heap
    int *pos;     // This is needed for decreaseKey()
    struct MinHeapNode **array;
};

struct MinHeapNode* newMinHeapNode(int v, int dist)
{
    struct MinHeapNode* minHeapNode =
           (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    minHeapNode->v = v;
    minHeapNode->dist = dist;
    return minHeapNode;
}

struct MinHeap* createMinHeap(int capacity)
{
    struct MinHeap* minHeap =
         (struct MinHeap*) malloc(sizeof(struct MinHeap));
    minHeap->pos = (int *)malloc(capacity * sizeof(int));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array =
         (struct MinHeapNode**) malloc(capacity * sizeof(struct MinHeapNode*));
    return minHeap;
}

void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b)
{
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

void minHeapify(struct MinHeap* minHeap, int idx)
{
    int smallest, left, right;
    smallest = idx;
    left = 2 * idx + 1;
    right = 2 * idx + 2;

    if (left < minHeap->size &&
        minHeap->array[left]->dist < minHeap->array[smallest]->dist )
      smallest = left;

    if (right < minHeap->size &&
        minHeap->array[right]->dist < minHeap->array[smallest]->dist )
      smallest = right;

    if (smallest != idx)
    {
        MinHeapNode *smallestNode = minHeap->array[smallest];
        MinHeapNode *idxNode = minHeap->array[idx];

        minHeap->pos[smallestNode->v] = idx;
        minHeap->pos[idxNode->v] = smallest;

        swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);

        minHeapify(minHeap, smallest);
    }
}

int isEmpty(struct MinHeap* minHeap)
{
    return minHeap->size == 0;
}

struct MinHeapNode* extractMin(struct MinHeap* minHeap)
{
    if (isEmpty(minHeap))
        return NULL;

    struct MinHeapNode* root = minHeap->array[0];

    struct MinHeapNode* lastNode = minHeap->array[minHeap->size - 1];
    minHeap->array[0] = lastNode;

    minHeap->pos[root->v] = minHeap->size-1;
    minHeap->pos[lastNode->v] = 0;

    --minHeap->size;
    minHeapify(minHeap, 0);

    return root;
}

void decreaseKey(struct MinHeap* minHeap, int v, int dist)
{
    int i = minHeap->pos[v];

    minHeap->array[i]->dist = dist;

    while (i && minHeap->array[i]->dist < minHeap->array[(i - 1) / 2]->dist)
    {
        minHeap->pos[minHeap->array[i]->v] = (i-1)/2;
        minHeap->pos[minHeap->array[(i-1)/2]->v] = i;
        swapMinHeapNode(&minHeap->array[i],  &minHeap->array[(i - 1) / 2]);

        i = (i - 1) / 2;
    }
}

bool isInMinHeap(struct MinHeap *minHeap, int v)
{
   if (minHeap->pos[v] < minHeap->size)
     return true;
   return false;
}

void printArr(int dist[], int n)
{
    printf("Vertex   Distance from Source\n");
    for (int i = 0; i < n; ++i)
        printf("%d \t\t %d\n", i, dist[i]);
}

void dijkstra(struct Graph* graph, int src)
{
    int V = graph->V;// Get the number of vertices in graph
    int dist[V];      // dist values used to pick minimum weight edge in cut

    struct MinHeap* minHeap = createMinHeap(V);

    for (int v = 0; v < V; ++v)
    {
        dist[v] = INT_MAX;
        minHeap->array[v] = newMinHeapNode(v, dist[v]);
        minHeap->pos[v] = v;
    }

    minHeap->array[src] = newMinHeapNode(src, dist[src]);
    minHeap->pos[src]   = src;
    dist[src] = 0;
    decreaseKey(minHeap, src, dist[src]);

    minHeap->size = V;

    while (!isEmpty(minHeap))
    {
        struct MinHeapNode* minHeapNode = extractMin(minHeap);
        int u = minHeapNode->v; // Store the extracted vertex number

        struct AdjListNode* pCrawl = graph->array[u].head;
        while (pCrawl != NULL)
        {
            int v = pCrawl->dest;

            if (isInMinHeap(minHeap, v) && dist[u] != INT_MAX && 
                                          pCrawl->weight + dist[u] < dist[v])
            {
                dist[v] = dist[u] + pCrawl->weight;
                decreaseKey(minHeap, v, dist[v]);
            }
            pCrawl = pCrawl->next;
        }
    }
    printArr(dist, V);
}

Answer 1

保留一些额外信息，例如 parent指向发现的前一个节点的指针。

struct MinHeapNode
{
    int v;
    int dist;

    struct MinHeapNode *parent;
}

现在每当你做 extractMin()操作，你得到的地址，你可以将它存储在一些临时变量中，并将它分配给 minHeapNode->parent

 struct MinHeapNode *prev = NULL;
 while (!isEmpty(minHeap))
    {
        struct MinHeapNode* minHeapNode = extractMin(minHeap);

        // Storing the previous node's address
        minHeapNode->parent = prev;
        prev = minHeapNode;

        int u = minHeapNode->v; // Store the extracted vertex number

例如，如果您的节点按此顺序排列，1 2 3 4 5

然后你将能够得到如下表示: 1 <- 2 <- 3 <- 4 <- 5

现在在 while 循环结束时，您可以通过向后遍历打印数据，如下所示的函数可以工作。

void printPath (struct MinHeapNode *last)
{
    while (last != NULL)
    {
        printf ("%d -> ", last->v);

        last = last->parent;
    }

    printf ("NULL\n");
}

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