C++实现一个简单的红黑树（RB_TREE）

红黑树遵守的规则：一头（根）一脚（叶子节点）黑（黑色），黑同（从任意节点开始至NULL结点的黑色节点的个数相等）红不连（红色节点不能相连）

以下是红黑树的插入和旋转函数的简易实现：

#include <iostream>
#include <assert.h>
#include <string.h>

using namespace std;

typedef int Type;
typedef enum{RED=0, BLACK}Color;    //节点的颜色

typedef struct Node{
    Color color;   //节点颜色
    Type key;      //节点的值
    struct Node *left, *right, *parent;  //左，右及父节点指针
}*PNode;   //节点指针


//树的结构定义
typedef struct RB_TREE{
    Node *root;   //根结点
    Node *Nil;    //一个实现技巧，用于判断节点是否为空等
}RB_TREE;


Node *Buynode()
{
    Node *p = new Node;
    assert(p != NULL);
    memset(p, 0, sizeof(Node));

    return p;
}


//构造一个空树
void InitTree(RB_TREE &t)
{
    t.Nil = Buynode();
    t.root = t.Nil;
    t.Nil->color = BLACK;
    t.Nil->key = -1;
}


//左旋
void RotateLeft(RB_TREE &t, Node *p)
{
    Node *s = p->right;  //s为不平衡节点p的右树
    p->right = s->left;   //将s的左树挂接至p的右树
    if(s->left != t.Nil){  //若s的左树不为空,就改变其左树的父节点
        s->left->parent = p;
    }
    s->parent = p->parent;  //改变s的父节点

    if(p->parent == t.Nil){  //说明为p为根结点，旋转之后s为根结点
        t.root = s;
    }else if(p = p->parent->left){  //p之前位于左树就将s作为新的左树
        p->parent->left = s;
    }else{
        p->parent->right = s;   //否则s为p的父节点的右树
    }

    s->left = p;   //p作s的左树
    p->parent = s;  //更改p的父节点
}


//右旋
void RotateRight(RB_TREE &t, Node *p)
{
    Node *s = p->left;
    p->left = s->right;
    if(s->right != t.Nil){
        s->right->parent = p;
    }
    s->parent = p->parent;

    if(p->parent == t.Nil){
        t.root = s;
    }else if(p = p->parent->left){
        p->parent->left = s;
    }else{
        p->parent->right = s;
    }

    s->right = p;
    p->parent = s;
}

//调整树的平衡
void Insert_Fixup(RB_TREE &t, Node *z)
{
    Node *y;

    while(z->parent->color == RED){   //红红相连不平衡
        if(z->parent == z->parent->parent->left){   //左侧插入
            y = z->parent->parent->right;   //y为插入节点的伯父节点
            if(y->color == RED){
                z->parent->color = BLACK;
                z->parent->parent->color = RED;

                y->color = BLACK;
                z = z->parent->parent;
                continue;
            }else if(z == z->parent->right){  //左侧的内侧插入
                z = z->parent;
                RotateLeft(t, z);    //左旋
            }

            z->parent->color = BLACK;
            z->parent->parent->color = RED;
            RotateRight(t, z->parent->parent);   //右旋
        }else{   //右侧插入
            y = z->parent->parent->left;
            if(y->color == RED){
                z->parent->color = BLACK;
                z->parent->parent->color = RED;

                y->color = BLACK;
                z = z->parent->parent;
                continue;
            }else if(z == z->parent->left){   //右侧的内侧插入
                z = z->parent;
                RotateRight(t, z);
            }

            z->parent->color = BLACK;
            z->parent->parent->color = RED;
            RotateLeft(t, z->parent->parent);
        }
    }

    t.root->color = BLACK;
}


bool Insert(RB_TREE &t, Type x)
{
    Node *p = t.Nil;
    Node *s = t.root;

    //找到合适的插入位置
    while(s != t.Nil){
        p = s;
        if(x == s->key){
            return false;
        }else if(x < s->key){
            s = s->left;
        }else{
            s = s->right;
        }
    }

    //构造节点
    Node *q = Buynode();
    q->key = x;
    q->parent = p;

    //将节点插入树中的合适位置
    if(p == t.Nil){   //则说明该树之前没有节点，则此节点为其根结点
        t.root = q;
    }else if(x < p->key){  //插入节点在节点p的左子树
        p->left = q;
    }else{    //插入节点在右子树
        p->right = q;
    }

    //设置插入节点的信息
    q->left = q->right = t.Nil;
    q->color = RED;
    //调整树的平衡
    Insert_Fixup(t, q);
    return true;
}

int main()
{
    int ar[] = {100, 40, 6};
    RB_TREE rb;
    InitTree(rb);

    int n = sizeof(ar) / sizeof(int);
    for(int i = 0; i < n; ++i){
        Insert(rb, ar[i]);
    }

    return 0;
}