C++实现红黑树应用实例代码
红黑树的应用：
1、利用key_value对，快速查找，O(logn)
- socket与客户端id之间，形成映射关系(socket, id)
- 内存分配管理
- 一整块内存，不断分配小块
- 每分配一次，就加入到红黑树
- 释放的时候，在红黑树找到相应的块，然后去释放
2、利用红黑树中序遍历是顺序的特性
- 进程的调度
- 进程处于等待状态，每个进程都有等待的时间，在未来某个时刻会运行，将这些进程利用红黑树组织起来
- 在某个时刻，找到对应时刻的节点，然后中序遍历，就可以把该节点之前的节点全部运行到。
3、nginx定时器
为什么使用红黑树不使用哈希表？
- 极少情况下，需要key是有序的，如定时器
二叉排序树（bstree）
- 左子树 < 根 < 右子树
- 中序遍历结果是顺序的
- 极端情况下，如果顺序插入，结果就成了链表
- 为了解决这个问题，引入了红黑树
- 为了解决这个问题，引入了红黑树
红黑树性质
- 每个节点是红色的或黑色的
- 根节点是黑色的
- 叶子节点是黑色的
- 红色节点的两个子节点必须是黑色的
- 对每个节点，该节点到其子孙节点的所有路径上的包含相同数目的黑节点（黑高相同）
- 最短路径就是全黑
- 最长路径就是黑红相间
如何证明红黑树的正确性？
- 采用归纳法
左旋与右旋
- 改变三个方向，六根指针
红黑树的插入：
- 插入节点的时候，原先的树是满足红黑树性质的
- 插入节点的颜色是红色更容易满足红黑树的性质
- 插入的节点是红色，且其父节点也是红色的时候，需要调整
插入有三种情况：
- 叔父节点是红色
- 叔父节点是黑色，且祖父节点，父节点和插入节点不是一条直线
- 叔父节点是黑色，且祖父节点，父节点和插入节点是一条直线
平衡二叉树：
- 内部不是color，而是一个high记录高度，如果左右子树高度相差超过1，就需要调整。
红黑树的删除：
- 什么是删除节点? y-> y是z的后继节点
- 什么是轴心节点? x是y的右子树
- 如果x是红色，把x变成黑色
- 如果x是黑色，需要进行调整
删除y节点，是什么颜色的时候需要调整？
- 黑色需要调整，删除黑色破坏了黑高
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define RED 1
#define BLACK 2
typedef int KEY_TYPE;
typedef struct _rbtree_node {
unsigned char color;
struct _rbtree_node *right;
struct _rbtree_node *left;
struct _rbtree_node *parent;
KEY_TYPE key;
void *value;
} rbtree_node;
typedef struct _rbtree {
rbtree_node *root;
rbtree_node *nil;
} rbtree;
rbtree_node *rbtree_mini(rbtree *T, rbtree_node *x) {
while (x->left != T->nil) {
x = x->left;
}
return x;
}
rbtree_node *rbtree_maxi(rbtree *T, rbtree_node *x) {
while (x->right != T->nil) {
x = x->right;
}
return x;
}
rbtree_node *rbtree_successor(rbtree *T, rbtree_node *x) {
rbtree_node *y = x->parent;
if (x->right != T->nil) {
return rbtree_mini(T, x->right);
}
while ((y != T->nil) && (x == y->right)) {
x = y;
y = y->parent;
}
return y;
}
void rbtree_left_rotate(rbtree *T, rbtree_node *x) {
rbtree_node *y = x->right; // x --> y , y --> x, right --> left, left --> right
x->right = y->left; //1 1
if (y->left != T->nil) { //1 2
y->left->parent = x;
}
y->parent = x->parent; //1 3
if (x->parent == T->nil) { //1 4
T->root = y;
} else if (x == x->parent->left) {
x->parent->left = y;
} else {
x->parent->right = y;
}
y->left = x; //1 5
x->parent = y; //1 6
}
void rbtree_right_rotate(rbtree *T, rbtree_node *y) {
rbtree_node *x = y->left;
y->left = x->right;
if (x->right != T->nil) {
x->right->parent = y;
}
x->parent = y->parent;
if (y->parent == T->nil) {
T->root = x;
} else if (y == y->parent->right) {
y->parent->right = x;
} else {
y->parent->left = x;
}
x->right = y;
y->parent = x;
}
void rbtree_insert_fixup(rbtree *T, rbtree_node *z) {
while (z->parent->color == RED) { //z ---> RED
if (z->parent == z->parent->parent->left) {
rbtree_node *y = z->parent->parent->right;
if (y->color == RED) {
z->parent->color = BLACK;
y->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent; //z --> RED
} else {
if (z == z->parent->right) {
z = z->parent;
rbtree_left_rotate(T, z);
}
z->parent->color = BLACK;
z->parent->parent->color = RED;
rbtree_right_rotate(T, z->parent->parent);
}
}else {
rbtree_node *y = z->parent->parent->left;
if (y->color == RED) {
z->parent->color = BLACK;
y->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent; //z --> RED
} else {
if (z == z->parent->left) {
z = z->parent;
rbtree_right_rotate(T, z);
}
z->parent->color = BLACK;
z->parent->parent->color = RED;
rbtree_left_rotate(T, z->parent->parent);
}
}
}
T->root->color = BLACK;
}
void rbtree_insert(rbtree *T, rbtree_node *z) {
rbtree_node *y = T->nil;
rbtree_node *x = T->root;
while (x != T->nil) {
y = x;
if (z->key < x->key) {
x = x->left;
} else if (z->key > x->key) {
x = x->right;
} else { //Exist
return ;
}
}
z->parent = y;
if (y == T->nil) {
T->root = z;
} else if (z->key < y->key) {
y->left = z;
} else {
y->right = z;
}
z->left = T->nil;
z->right = T->nil;
z->color = RED;
rbtree_insert_fixup(T, z);
}
void rbtree_delete_fixup(rbtree *T, rbtree_node *x) {
while ((x != T->root) && (x->color == BLACK)) {
if (x == x->parent->left) {
rbtree_node *w= x->parent->right;
if (w->color == RED) {
w->color = BLACK;
x->parent->color = RED;
rbtree_left_rotate(T, x->parent);
w = x->parent->right;
}
if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
w->color = RED;
x = x->parent;
} else {
if (w->right->color == BLACK) {
w->left->color = BLACK;
w->color = RED;
rbtree_right_rotate(T, w);
w = x->parent->right;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->right->color = BLACK;
rbtree_left_rotate(T, x->parent);
x = T->root;
}
} else {
rbtree_node *w = x->parent->left;
if (w->color == RED) {
w->color = BLACK;
x->parent->color = RED;
rbtree_right_rotate(T, x->parent);
w = x->parent->left;
}
if ((w->left->color == BLACK) && (w->right->color == BLACK)) {
w->color = RED;
x = x->parent;
} else {
if (w->left->color == BLACK) {
w->right->color = BLACK;
w->color = RED;
rbtree_left_rotate(T, w);
w = x->parent->left;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->left->color = BLACK;
rbtree_right_rotate(T, x->parent);
x = T->root;
}
}
}
x->color = BLACK;
}
rbtree_node *rbtree_delete(rbtree *T, rbtree_node *z) {
rbtree_node *y = T->nil;
rbtree_node *x = T->nil;
if ((z->left == T->nil) || (z->right == T->nil)) {
y = z;
} else {
y = rbtree_successor(T, z);
}
if (y->left != T->nil) {
x = y->left;
} else if (y->right != T->nil) {
x = y->right;
}
x->parent = y->parent;
if (y->parent == T->nil) {
T->root = x;
} else if (y == y->parent->left) {
y->parent->left = x;
} else {
y->parent->right = x;
}
if (y != z) {
z->key = y->key;
z->value = y->value;
}
if (y->color == BLACK) {
rbtree_delete_fixup(T, x);
}
return y;
}
rbtree_node *rbtree_search(rbtree *T, KEY_TYPE key) {
rbtree_node *node = T->root;
while (node != T->nil) {
if (key < node->key) {
node = node->left;
} else if (key > node->key) {
node = node->right;
} else {
return node;
}
}
return T->nil;
}
void rbtree_traversal(rbtree *T, rbtree_node *node) {
if (node != T->nil) {
rbtree_traversal(T, node->left);
printf("key:%d, color:%d\n", node->key, node->color);
rbtree_traversal(T, node->right);
}
}
int main() {
int keyArray[20] = {24,25,13,35,23, 26,67,47,38,98, 20,19,17,49,12, 21,9,18,14,15};
rbtree *T = (rbtree *)malloc(sizeof(rbtree));
if (T == NULL) {
printf("malloc failed\n");
return -1;
}
T->nil = (rbtree_node*)malloc(sizeof(rbtree_node));
T->nil->color = BLACK;
T->root = T->nil;
rbtree_node *node = T->nil;
int i = 0;
for (i = 0;i < 20;i ++) {
node = (rbtree_node*)malloc(sizeof(rbtree_node));
node->key = keyArray[i];
node->value = NULL;
rbtree_insert(T, node);
}
rbtree_traversal(T, T->root);
printf("----------------------------------------\n");
for (i = 0;i < 20;i ++) {
rbtree_node *node = rbtree_search(T, keyArray[i]);
rbtree_node *cur = rbtree_delete(T, node);
free(cur);
rbtree_traversal(T, T->root);
printf("----------------------------------------\n");
}
}
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