红黑树与平衡二叉树_腾讯面试-红黑树(c/c++版本)

/*
  Red Black Trees
  (C) 1999  Andrea Arcangeli <andrea@suse.de>
 
  This program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation; either version 2 of the License, or
  (at your option) any later version.
 
  This program is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
  linux/include/linux/rbtree.h
 
  To use rbtrees you'll have to implement your own insert and search cores.
  This will avoid us to use callbacks and to drop drammatically performances.
  I know it's not the cleaner way,  but in C (not in C++) to get
  performances and genericity...
 
  Some example of insert and search follows here. The search is a plain
  normal search over an ordered tree. The insert instead must be implemented
  in two steps: First, the code must insert the element in order as a red leaf
  in the tree, and then the support library function rb_insert_color() must
  be called. Such function will do the not trivial work to rebalance the
  rbtree, if necessary.
 
-----------------------------------------------------------------------
static inline struct page * rb_search_page_cache(struct inode * inode,
                         unsigned long offset)
{
    struct rb_node * n = inode->i_rb_page_cache.rb_node;
    struct page * page;
 
    while (n)
    {
        page = rb_entry(n, struct page, rb_page_cache);
 
        if (offset < page->offset)
            n = n->rb_left;
        else if (offset > page->offset)
            n = n->rb_right;
        else
            return page;
    }
    return NULL;
}
 
static inline struct page * __rb_insert_page_cache(struct inode * inode,
                           unsigned long offset,
                           struct rb_node * node)
{
    struct rb_node ** p = &inode->i_rb_page_cache.rb_node;
    struct rb_node * parent = NULL;
    struct page * page;
 
    while (*p)
    {
        parent = *p;
        page = rb_entry(parent, struct page, rb_page_cache);
 
        if (offset < page->offset)
            p = &(*p)->rb_left;
        else if (offset > page->offset)
            p = &(*p)->rb_right;
        else
            return page;
    }
 
    rb_link_node(node, parent, p);
 
    return NULL;
}
 
static inline struct page * rb_insert_page_cache(struct inode * inode,
                         unsigned long offset,
                         struct rb_node * node)
{
    struct page * ret;
    if ((ret = __rb_insert_page_cache(inode, offset, node)))
        goto out;
    rb_insert_color(node, &inode->i_rb_page_cache);
 out:
    return ret;
}
-----------------------------------------------------------------------
*/
 
#ifndef    _SLINUX_RBTREE_H
#define    _SLINUX_RBTREE_H
 
#include <stdio.h>
//#include <linux/kernel.h>
//#include <linux/stddef.h>
 
struct rb_node
{
    unsigned long  rb_parent_color;
#define    RB_RED        0
#define    RB_BLACK    1
    struct rb_node *rb_right;
    struct rb_node *rb_left;
} /*  __attribute__((aligned(sizeof(long))))*/;
    /* The alignment might seem pointless, but allegedly CRIS needs it */
 
struct rb_root
{
    struct rb_node *rb_node;
};
 
 
#define rb_parent(r)   ((struct rb_node *)((r)->rb_parent_color & ~3))
#define rb_color(r)   ((r)->rb_parent_color & 1)
#define rb_is_red(r)   (!rb_color(r))
#define rb_is_black(r) rb_color(r)
#define rb_set_red(r)  do { (r)->rb_parent_color &= ~1; } while (0)
#define rb_set_black(r)  do { (r)->rb_parent_color |= 1; } while (0)
 
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
    rb->rb_parent_color = (rb->rb_parent_color & 3) | (unsigned long)p;
}
static inline void rb_set_color(struct rb_node *rb, int color)
{
    rb->rb_parent_color = (rb->rb_parent_color & ~1) | color;
}
 
#define offsetof(TYPE, MEMBER) ((size_t) &((TYPE *)0)->MEMBER)
 
#define container_of(ptr, type, member) ({          
    const typeof( ((type *)0)->member ) *__mptr = (ptr);    
    (type *)( (char *)__mptr - offsetof(type,member) );})
 
#define RB_ROOT    (struct rb_root) { NULL, }
#define    rb_entry(ptr, type, member) container_of(ptr, type, member)
 
#define RB_EMPTY_ROOT(root)    ((root)->rb_node == NULL)
#define RB_EMPTY_NODE(node)    (rb_parent(node) == node)
#define RB_CLEAR_NODE(node)    (rb_set_parent(node, node))
 
static inline void rb_init_node(struct rb_node *rb)
{
    rb->rb_parent_color = 0;
    rb->rb_right = NULL;
    rb->rb_left = NULL;
    RB_CLEAR_NODE(rb);
}
 
extern void rb_insert_color(struct rb_node *, struct rb_root *);
extern void rb_erase(struct rb_node *, struct rb_root *);
 
typedef void (*rb_augment_f)(struct rb_node *node, void *data);
 
extern void rb_augment_insert(struct rb_node *node,
                  rb_augment_f func, void *data);
extern struct rb_node *rb_augment_erase_begin(struct rb_node *node);
extern void rb_augment_erase_end(struct rb_node *node,
                 rb_augment_f func, void *data);
 
/* Find logical next and previous nodes in a tree */
extern struct rb_node *rb_next(const struct rb_node *);
extern struct rb_node *rb_prev(const struct rb_node *);
extern struct rb_node *rb_first(const struct rb_root *);
extern struct rb_node *rb_last(const struct rb_root *);
 
/* Fast replacement of a single node without remove/rebalance/add/rebalance */
extern void rb_replace_node(struct rb_node *victim, struct rb_node *new,
                struct rb_root *root);
 
static inline void rb_link_node(struct rb_node * node, struct rb_node * parent,
                struct rb_node ** rb_link)
{
    node->rb_parent_color = (unsigned long )parent;
    node->rb_left = node->rb_right = NULL;
 
    *rb_link = node;
}
 
#endif    /* _LINUX_RBTREE_H */

/*
  Red Black Trees
  (C) 1999  Andrea Arcangeli <andrea@suse.de>
  (C) 2002  David Woodhouse <dwmw2@infradead.org>
 
  This program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation; either version 2 of the License, or
  (at your option) any later version.
 
  This program is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
  linux/lib/rbtree.c
*/
 
#include "rbtree.h"
 
static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *right = node->rb_right;
    struct rb_node *parent = rb_parent(node);
 
    if ((node->rb_right = right->rb_left))
        rb_set_parent(right->rb_left, node);
    right->rb_left = node;
 
    rb_set_parent(right, parent);
 
    if (parent)
    {
        if (node == parent->rb_left)
            parent->rb_left = right;
        else
            parent->rb_right = right;
    }
    else
        root->rb_node = right;
    rb_set_parent(node, right);
}
 
static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *left = node->rb_left;
    struct rb_node *parent = rb_parent(node);
 
    if ((node->rb_left = left->rb_right))
        rb_set_parent(left->rb_right, node);
    left->rb_right = node;
 
    rb_set_parent(left, parent);
 
    if (parent)
    {
        if (node == parent->rb_right)
            parent->rb_right = left;
        else
            parent->rb_left = left;
    }
    else
        root->rb_node = left;
    rb_set_parent(node, left);
}
 
void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *parent, *gparent;
 
    while ((parent = rb_parent(node)) && rb_is_red(parent))
    {
        gparent = rb_parent(parent);
 
        if (parent == gparent->rb_left)
        {
            {
                register struct rb_node *uncle = gparent->rb_right;
                if (uncle && rb_is_red(uncle))
                {
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }
 
            if (parent->rb_right == node)
            {
                register struct rb_node *tmp;
                __rb_rotate_left(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }
 
            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_right(gparent, root);
        } else {
            {
                register struct rb_node *uncle = gparent->rb_left;
                if (uncle && rb_is_red(uncle))
                {
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }
 
            if (parent->rb_left == node)
            {
                register struct rb_node *tmp;
                __rb_rotate_right(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }
 
            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_left(gparent, root);
        }
    }
 
    rb_set_black(root->rb_node);
}
 
static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
                 struct rb_root *root)
{
    struct rb_node *other;
 
    while ((!node || rb_is_black(node)) && node != root->rb_node)
    {
        if (parent->rb_left == node)
        {
            other = parent->rb_right;
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_left(parent, root);
                other = parent->rb_right;
            }
            if ((!other->rb_left || rb_is_black(other->rb_left)) &&
                (!other->rb_right || rb_is_black(other->rb_right)))
            {
                rb_set_red(other);
                node = parent;
                parent = rb_parent(node);
            }
            else
            {
                if (!other->rb_right || rb_is_black(other->rb_right))
                {
                    rb_set_black(other->rb_left);
                    rb_set_red(other);
                    __rb_rotate_right(other, root);
                    other = parent->rb_right;
                }
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                rb_set_black(other->rb_right);
                __rb_rotate_left(parent, root);
                node = root->rb_node;
                break;
            }
        }
        else
        {
            other = parent->rb_left;
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_right(parent, root);
                other = parent->rb_left;
            }
            if ((!other->rb_left || rb_is_black(other->rb_left)) &&
                (!other->rb_right || rb_is_black(other->rb_right)))
            {
                rb_set_red(other);
                node = parent;
                parent = rb_parent(node);
            }
            else
            {
                if (!other->rb_left || rb_is_black(other->rb_left))
                {
                    rb_set_black(other->rb_right);
                    rb_set_red(other);
                    __rb_rotate_left(other, root);
                    other = parent->rb_left;
                }
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                rb_set_black(other->rb_left);
                __rb_rotate_right(parent, root);
                node = root->rb_node;
                break;
            }
        }
    }
    if (node)
        rb_set_black(node);
}
 
void rb_erase(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *child, *parent;
    int color;
 
    if (!node->rb_left)
        child = node->rb_right;
    else if (!node->rb_right)
        child = node->rb_left;
    else
    {
        struct rb_node *old = node, *left;
 
        node = node->rb_right;
        while ((left = node->rb_left) != NULL)
            node = left;
 
        if (rb_parent(old)) {
            if (rb_parent(old)->rb_left == old)
                rb_parent(old)->rb_left = node;
            else
                rb_parent(old)->rb_right = node;
        } else
            root->rb_node = node;
 
        child = node->rb_right;
        parent = rb_parent(node);
        color = rb_color(node);
 
        if (parent == old) {
            parent = node;
        } else {
            if (child)
                rb_set_parent(child, parent);
            parent->rb_left = child;
 
            node->rb_right = old->rb_right;
            rb_set_parent(old->rb_right, node);
        }
 
        node->rb_parent_color = old->rb_parent_color;
        node->rb_left = old->rb_left;
        rb_set_parent(old->rb_left, node);
 
        goto color;
    }
 
    parent = rb_parent(node);
    color = rb_color(node);
 
    if (child)
        rb_set_parent(child, parent);
    if (parent)
    {
        if (parent->rb_left == node)
            parent->rb_left = child;
        else
            parent->rb_right = child;
    }
    else
        root->rb_node = child;
 
 color:
    if (color == RB_BLACK)
        __rb_erase_color(child, parent, root);
}
 
static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
{
    struct rb_node *parent;
 
up:
    func(node, data);
    parent = rb_parent(node);
    if (!parent)
        return;
 
    if (node == parent->rb_left && parent->rb_right)
        func(parent->rb_right, data);
    else if (parent->rb_left)
        func(parent->rb_left, data);
 
    node = parent;
    goto up;
}
 
/*
 * after inserting @node into the tree, update the tree to account for
 * both the new entry and any damage done by rebalance
 */
void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
{
    if (node->rb_left)
        node = node->rb_left;
    else if (node->rb_right)
        node = node->rb_right;
 
    rb_augment_path(node, func, data);
}
 
/*
 * before removing the node, find the deepest node on the rebalance path
 * that will still be there after @node gets removed
 */
struct rb_node *rb_augment_erase_begin(struct rb_node *node)
{
    struct rb_node *deepest;
 
    if (!node->rb_right && !node->rb_left)
        deepest = rb_parent(node);
    else if (!node->rb_right)
        deepest = node->rb_left;
    else if (!node->rb_left)
        deepest = node->rb_right;
    else {
        deepest = rb_next(node);
        if (deepest->rb_right)
            deepest = deepest->rb_right;
        else if (rb_parent(deepest) != node)
            deepest = rb_parent(deepest);
    }
 
    return deepest;
}
 
/*
 * after removal, update the tree to account for the removed entry
 * and any rebalance damage.
 */
void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
{
    if (node)
        rb_augment_path(node, func, data);
}
 
/*
 * This function returns the first node (in sort order) of the tree.
 */
struct rb_node *rb_first(const struct rb_root *root)
{
    struct rb_node    *n;
 
    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_left)
        n = n->rb_left;
    return n;
}
 
struct rb_node *rb_last(const struct rb_root *root)
{
    struct rb_node    *n;
 
    n = root->rb_node;
    if (!n)
        return NULL;
    while (n->rb_right)
        n = n->rb_right;
    return n;
}
 
struct rb_node *rb_next(const struct rb_node *node)
{
    struct rb_node *parent;
 
    if (rb_parent(node) == node)
        return NULL;
 
    /* If we have a right-hand child, go down and then left as far
       as we can. */
    if (node->rb_right) {
        node = node->rb_right;
        while (node->rb_left)
            node=node->rb_left;
        return (struct rb_node *)node;
    }
 
    /* No right-hand children.  Everything down and left is
       smaller than us, so any 'next' node must be in the general
       direction of our parent. Go up the tree; any time the
       ancestor is a right-hand child of its parent, keep going
       up. First time it's a left-hand child of its parent, said
       parent is our 'next' node. */
    while ((parent = rb_parent(node)) && node == parent->rb_right)
        node = parent;
    return parent;
}
struct rb_node *rb_prev(const struct rb_node *node)
{
    struct rb_node *parent;
    if (rb_parent(node) == node)
        return NULL;
    /* If we have a left-hand child, go down and then right as far
       as we can. */
    if (node->rb_left) {
        node = node->rb_left;
        while (node->rb_right)
            node=node->rb_right;
        return (struct rb_node *)node;
    }
    /* No left-hand children. Go up till we find an ancestor which
       is a right-hand child of its parent */
    while ((parent = rb_parent(node)) && node == parent->rb_left)
        node = parent;
    return parent;
}
void rb_replace_node(struct rb_node *victim, struct rb_node *new,
             struct rb_root *root)
{
    struct rb_node *parent = rb_parent(victim);
    /* Set the surrounding nodes to point to the replacement */
    if (parent) {
        if (victim == parent->rb_left)
            parent->rb_left = new;
        else
            parent->rb_right = new;
    } else {
        root->rb_node = new;
    }
    if (victim->rb_left)
        rb_set_parent(victim->rb_left, new);
    if (victim->rb_right)
        rb_set_parent(victim->rb_right, new);
    /* Copy the pointers/colour from the victim to the replacement */
    *new = *victim;
}

/**
 * 根据Linux Kernel定义的红黑树(Red Black Tree)
 *
 */
#include <stdio.h>
#include <stdlib.h>
#include "rbtree.h"
 
#define CHECK_INSERT 0    // "插入"动作的检测开关(0，关闭；1，打开)
#define CHECK_DELETE 0    // "删除"动作的检测开关(0，关闭；1，打开)
#define LENGTH(a) ( (sizeof(a)) / (sizeof(a[0])) )
 
typedef int Type;
 
struct my_node {
    struct rb_node rb_node;    // 红黑树节点
    Type key;                // 键值
    // ... 用户自定义的数据
};
 
/*
 * 查找"红黑树"中键值为key的节点。没找到的话，返回NULL。
 */
struct my_node *my_search(struct rb_root *root, Type key)
{
    struct rb_node *rbnode = root->rb_node;
 
    while (rbnode!=NULL)
    {
        struct my_node *mynode = container_of(rbnode, struct my_node, rb_node);
 
        if (key < mynode->key)
            rbnode = rbnode->rb_left;
        else if (key > mynode->key)
            rbnode = rbnode->rb_right;
        else
            return mynode;
    }
 
    return NULL;
}
 
/*
 * 将key插入到红黑树中。插入成功，返回0；失败返回-1。
 */
int my_insert(struct rb_root *root, Type key)
{
    struct my_node *mynode; // 新建结点
    struct rb_node **tmp = &(root->rb_node), *parent = NULL;
 
    /* Figure out where to put new node */
    while (*tmp)
    {
        struct my_node *my = container_of(*tmp, struct my_node, rb_node);
 
        parent = *tmp;
        if (key < my->key)
            tmp = &((*tmp)->rb_left);
        else if (key > my->key)
            tmp = &((*tmp)->rb_right);
        else
            return -1;
    }
 
    // 如果新建结点失败，则返回。
    if ((mynode=malloc(sizeof(struct my_node))) == NULL)
        return -1;
    mynode->key = key;
 
    /* Add new node and rebalance tree. */
    rb_link_node(&mynode->rb_node, parent, tmp);
    rb_insert_color(&mynode->rb_node, root);
 
    return 0;
}
 
/*
 * 删除键值为key的结点
 */
void my_delete(struct rb_root *root, Type key)
{
    struct my_node *mynode;
 
    // 在红黑树中查找key对应的节点mynode
    if ((mynode = my_search(root, key)) == NULL)
        return ;
 
    // 从红黑树中删除节点mynode
    rb_erase(&mynode->rb_node, root);
    free(mynode);
}
 
/*
 * 打印"红黑树"
 */
static void print_rbtree(struct rb_node *tree, Type key, int direction)
{
    if(tree != NULL)
    {
        if(direction==0)    // tree是根节点
            printf("%2d(B) is rootn", key);
        else                // tree是分支节点
            printf("%2d(%s) is %2d's %6s childn", key, rb_is_black(tree)?"B":"R", key, direction==1?"right" : "left");
 
        if (tree->rb_left)
            print_rbtree(tree->rb_left, rb_entry(tree->rb_left, struct my_node, rb_node)->key, -1);
        if (tree->rb_right)
            print_rbtree(tree->rb_right,rb_entry(tree->rb_right, struct my_node, rb_node)->key,  1);
    }
}
 
void my_print(struct rb_root *root)
{
    if (root!=NULL && root->rb_node!=NULL)
        print_rbtree(root->rb_node, rb_entry(root->rb_node, struct my_node, rb_node)->key,  0);
}
 
 
void main()
{
    int a[] = {10, 40, 30, 60, 90, 70, 20, 50, 80};
    int i, ilen=LENGTH(a);
    struct rb_root mytree = RB_ROOT;
 
    printf("== 原始数据: ");
    for(i=0; i<ilen; i++)
        printf("%d ", a[i]);
    printf("n");
 
    for (i=0; i < ilen; i++)
    {
        my_insert(&mytree, a[i]);
#if CHECK_INSERT
        printf("== 添加节点: %dn", a[i]);
        printf("== 树的详细信息: n");
        my_print(&mytree);
        printf("n");
#endif
 
    }
 
#if CHECK_DELETE
    for (i=0; i<ilen; i++) {
        my_delete(&mytree, a[i]);
 
        printf("== 删除节点: %dn", a[i]);
        printf("== 树的详细信息: n");
        my_print(&mytree);
        printf("n");
    }
#endif
}