提取最小元素后的最小堆问题

Question

我正在做一个最小堆的实现，并且对这个概念还是个新手。

以此作为参考：

https://www.geeksforgeeks.org/building-heap-from-array/

https://algorithmtutor.com/Data-Structures/Tree/Binary-Heaps/

我修改了代码，并提出：

(这是我遇到问题的代码，所有其他代码都与我的问题无关，至少我是这样认为的)

#define LCHILD(x) (2 * (x)) + 1
#define RCHILD(x) (2 * (x)) + 2
#define PARENT(x) ((x) - 1) / 2

typedef struct {
    int key;
    Event *element; // Assume NULL for this example
} Node;

void swap(Node **x, Node **y) {
    Node *temp = *x;
    *x = *y;
    *y = temp;
}

void heapify(void *pq, int n, int i) {
    Node **node = (Node**) pq;

    int smallest = i; // Initialize smallest as root 
    int left = LCHILD(i);
    int right = RCHILD(i); // right = 2*i + 2 
  
    if (left < n && (node[left])->key < (node[smallest ])->key) 
        smallest = left; 
  
    if (right < n && (node[right])->key < (node[smallest ])->key) 
        smallest = right; 
  
    if (smallest != i) { 
        swap(&node[i], &node[smallest ]); 
        heapify(node, n, smallest ); 
    } 
}

int extractKey(void *pq, int *n) {
    Node **node = (Node**) pq;

    int minElement = (node[0])->key;

    node[0] = node[*n - 1];
    *n = *n - 1;

    heapify(pq, *n, 0);
    return minElement;
}

void insert(void *pq, int key, void *element, int *n) {
    Node **node = (Node**) pq;

    node[*n]->key = key;
    node[*n]->element = element;
    *n = *n + 1;

    int i = *n - 1;
    while ( (i != 0) && (node[PARENT(i)]->key > node[i]->key) ) {
        swap(&node[PARENT(i)], &node[i]);
        i = PARENT(i);
    }
}

int main() { 

    Node **pq = malloc (100 * sizeof(Node*));
    int i;
    for(i = 0; i < 100; i++) {
        pq[i] = malloc(sizeof(Node));
        pq[i]->element = malloc(sizeof(Event));
    }
  
    int n = 0; // heap size
  
    insert(pq, 0, NULL, &n);
    printHeap(pq, n); 
    
    insert(pq, 5, NULL, &n);
    printHeap(pq, n); 
    
    insert(pq, 1, NULL, &n);
    printHeap(pq, n); 
    
    insert(pq, 50, NULL, &n);
    printHeap(pq, n); 

    extractKey(pq, &n);
    printHeap(pq, n); 
    
    insert(pq, 10, NULL, &n);
    printHeap(pq, n); 

    return 0;
}

输出：

Array representation of heap is:
0 
Array representation of heap is:
0 5 
Array representation of heap is:
0 5 1 
Array representation of heap is:
0 5 1 50 
Array representation of heap is:
1 5 50 
Array representation of heap is:
1 5 10 10 // What happened here?

只有当我提取最小节点，然后添加一个新节点时，才会发生这种情况。如果我不提取节点，那么它工作得很好。我是不是漏掉了什么？

编辑1

：这是我正在使用的打印函数。我忘了在最初的帖子中添加它

(它是在这里找到的版本的修改版本：

https://algorithmtutor.com/Data-Structures/Tree/Binary-Heaps/))

void printHeap(void *pq, int n) {
    Node **node = (Node**) pq;

    printf("Array representation of heap is:\n");
  
    for (int i = 0; i < n; ++i) { 
        printf("%d ", node[i]->key);
    }
     printf("\n");
}

编辑2：我又做了一些测试。这是我得到的：

插入了一些print语句：

void insert(void *pq, int key, void *element, int *n) {
    Node **node = (Node**) pq;
    if(*n > 0) {
       printf("node[%d] = %d\n", *n-1, node[*n-1]->key);
    }

    node[*n]->key = key;
    printf("node[%d] = %d\n", *n, node[*n]->key);
    if(*n > 0) {
       printf("node[%d] = %d\n", *n-1, node[*n-1]->key);
    }
    node[*n]->element = element;
    *n = *n + 1;

    // move up until the heap property satisfies
    int i = *n - 1;
    while ( (i != 0) && (node[PARENT(i)]->key > node[i]->key) ) {
        swap(&node[PARENT(i)], &node[i]);
        i = PARENT(i);
    }
}

输出：

node[0] = 0
Array representation of heap is:
0 
node[0] = 0
node[1] = 5
node[0] = 0
Array representation of heap is:
0 5 
node[1] = 5
node[2] = 1
node[1] = 5
Array representation of heap is:
0 5 1 
node[2] = 1
node[3] = 50
node[2] = 1
Array representation of heap is:
0 5 1 50 
Array representation of heap is:
1 5 50 
node[2] = 50
node[3] = 10
node[2] = 10 // Huh? it should be 50
Array representation of heap is:
1 5 10 10

Answer 1

问题是行 node[0] = node[*n - 1];在提取密钥中。那就是将您的两个节点指针设置为相同的值，因此您不再有 100 个唯一的节点指针。（因此，它也会泄漏内存。）将行更改为 swap(&node[0], &node[*n - 1]);应该可以解决问题。