最小—最大堆
//最小最大堆的定义,一颗完全二叉树，根节点为最小层，最小层和最大层交替出现，如果x为最小层的节点，那么他就是以x为根节点的二叉树
的最小节点，如果x为最大层的节点，那么他就是以x为根节点的二叉树的最大节点
//支持双端队列的实现（1：能够插入任意一个值 2：能够删除最大值 3：能够删除最小值）
//实现从节点1开始，0舍弃
/*
* 2009/06/03 By xylh
* */
#include
#include
#define MAXSIZE 1000
struct element {
int key;
};
element heap[MAXSIZE];
//判断节点所在是最大还是最小层，最小层返回true
bool level(int i)
{
double k = log(i)/log(2);
if((int)k%2 ==0) return true;
else return false;
}
//在最大层向上追溯
void max_verify(element heap[], int n, element item)
{
int i = n;
int parent = n/4;
while(parent) {
if(heap[parent].key < item.key) {
heap[i] = heap[parent];
i = parent;
parent = parent/4;
} else {
break;
}
}
heap[i] = item;
}
void min_verify(element heap[], int n, element item)
{
int i = n;
int parent = n/4;
while(parent) {
if(heap[parent].key > item.key) {
heap[i] = heap[parent];
i = parent;
parent = parent/4;
} else {
break;
}
}
heap[i] = item;
}
void insert(element heap[], int *n, element item)
{
(*n)++;
if(*n == MAXSIZE) {
printf("heap is full\n");
exit(1);
}
if(*n == 1) {
heap[*n].key = item.key;
return;
}
int parent = *n/2;
switch(level(parent)) {
case true:
if(heap[parent].key > item.key) {
heap[*n] = heap[parent];
min_verify(heap, parent, item);
} else {
max_verify(heap, *n, item);
}
break;
case false:
if(heap[parent].key < item.key) {
heap[*n] = heap[parent];
max_verify(heap, parent, item);
} else {
min_verify(heap, *n, item);
}
break;
}
}
//寻找子节点和后序节点中最小的节点
int min_grand_child(element heap[], int n, int i)
{
int min = 2*i;
int k[5] = {2*i+1, 4*i, 4*i+1, 4*i+2, 4*i+3};
for(int j=0; k[j]<=n&&j<=4; ++j) {
if(heap[k[j]].key < heap[min].key)
min = k[j];
}
return min;
}
element del_min(element heap[], int *n)
{
if(*n < 1) {
printf("heap is empty\n");
exit(1);
}
if(*n == 1) return heap[(*n)--];//case 1
element item = heap[(*n)--];
heap[0].key = heap[1].key;
int k, i, last = (*n)/2, parent;
for(i=1; i<=last; ) {
k = min_grand_child(heap, *n, i);
if(item.key <= heap[k].key) break;//case 2(a)
heap[i] = heap[k];
if(k <= 2*i+1) {//case 2(b)
i = k;
break;
}
parent = k/2;//case 2(c)
if(item.key > heap[parent].key) {
element temp = item;
item = heap[parent];
heap[parent] = temp;
}
i = k;
}
heap[i] = item;
return heap[0];
}
element del_max(element heap[], int *n)
{
}
int main()
{
int n = 0;
for(int i=1; i<=10; ++i) {
element item;
item.key = i;
insert(heap, &n, item);
}
del_min(heap, &n);
for(int i=1; i<=n; ++i) {
printf("%d ", heap[i].key);
}
printf("\n");
return 0;
}