分析与思考
数组是完全二叉树的存储结构,完全二叉树是数组的逻辑结构,这样我们就可以使用树形结构来解决线性问题。
堆
- 大顶堆(用于升序排序,根节点大于等于两个子节点)
- 小顶堆(用于降序排序,根节点小于等于两个子节点)
堆的插入与删除:尾部插入,头部弹出(联想到了队列)
不同编程语言在实现优先队列时底层90%是由堆构成的。
通过代码本身来提高编程能力是错误的,应注重思维逻辑结构的提升
数据结构 = 结构定义 + 结构操作
演示代码:
堆
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <time.h>
typedef struct Heap {
int *data;
int n, size;
} Heap;
Heap *init(int n);
void clear(Heap *);
void push(Heap *, int);
void pop(Heap *);
void output(Heap *);
int main(){
srand(time(0));
Heap *p = init(21);
for (int i = 0; i < 20; ++i) {
int value = rand() % 100;
printf("insert %d to heap\n", value);
push(p, value);
output(p);
}
for (int i = 0; i < 20; ++i) {
pop(p);
output(p);
}
clear(p);
return 0;
}
Heap * init(int n) {
Heap *p = (Heap *)malloc(sizeof(Heap));
p->data = (int *)malloc(sizeof(int) * n);
memset(p->data, 0 , sizeof(p->data));
p->size = n;
p->n = 0;
return p;
}
void clear(Heap *h) {
if (h == NULL) return;
free(h->data);
free(h);
return;
}
void push(Heap *h, int value) {
if (h->n == h->size) return;
h->n += 1;
h->data[h->n] = value;
int i = h->n;
while (i > 1) {
if (h->data[i] <= h->data[i / 2]) break;
h->data[i] ^= h->data[i / 2];
h->data[i / 2] ^= h->data[i];
h->data[i] ^= h->data[i / 2];
i /= 2;
}
return ;
}
void pop(Heap *h) {
if (h->n <= 1) {
h->n = 0;
return;
}
h->data[1] ^= h->data[h->n];
h->data[h->n] ^= h->data[1];
h->data[1] ^= h->data[h->n];
h->n -= 1;
int ind = 1;
while (ind * 2 <= h->n) {
int swap_ind = ind * 2;
if (h->data[ind * 2] > h->data[swap_ind]) swap_ind = ind * 2;
if (ind * 2 + 1 <= h->n && h->data[ind * 2 + 1] > h->data[swap_ind])
swap_ind = ind * 2 + 1;
if (swap_ind == ind) break;
h->data[ind] ^= h->data[swap_ind];
h->data[swap_ind] ^= h->data[ind];
h->data[ind] ^= h->data[swap_ind];
ind = swap_ind;
}
return;
}
void output(Heap *h) {
printf("Heap = [");
for (int i = 1; i < h->size; ++i) {
printf("%d, ", h->data[i]);
}
printf("]\n");
return;
}