提取最小元素后的最小堆问题

如何解决提取最小元素后的最小堆问题

我正在研究最小堆实现，并且对这个概念非常陌生。

以此为参考：
https://www.geeksforgeeks.org/building-heap-from-array/
https://algorithmtutor.com/Data-Structures/Tree/Binary-Heaps/

我修改了代码并想出了：

（这是我遇到问题的代码，所有其他代码都与我的问题无关，至少我认为是这样）

#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,NULL,&n);
    printHeap(pq,n); 
    
    insert(pq,5,1,50,n); 

    extractKey(pq,10,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?

这只发生在我提取最小节点然后添加一个新节点时。如果我不提取节点，那么它工作得很好。我错过了什么吗？

EDIT 1：这是我正在使用的打印功能。忘记在初始帖子中添加它

（这是从这里找到的修改版本：
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");
}

EDIT 2：我进行了更多测试。这是我得到的：

插入了一些打印语句：

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

解决方法

问题在于 node[0] = node[*n - 1]; 中的行 extractKey。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。