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#ifndef RB_TREE_H
#define RB_TREE_H
const int BLACK = -1;
const int RED = 1;
static int number1 = 0; //////用于统计插入的各种情况次数的
static int number2 = 0;
static int number3 = 0;
static int number4 = 0;
static int number5 = 0;
static int number6 = 0;
struct RB_TREE_NODE{
public:
RB_TREE_NODE(int a)
{
key = a;
color = BLACK;
p =0;
left = 0;
right = 0;
}
~RB_TREE_NODE()
{
}
int key;
int color;
RB_TREE_NODE* p;
RB_TREE_NODE* left;
RB_TREE_NODE* right;
};
static RB_TREE_NODE NIL = { 0 };
#define PNIL (&NIL)
struct RB_TREE
{
RB_TREE()
{
root->left = PNIL;
root->right = PNIL;
root->p = PNIL;
}
RB_TREE_NODE* root=PNIL;
////插入节点z
void RB_TREE_INSERT(RB_TREE* root, RB_TREE_NODE* z);
///插入节点z后对该树进行调整，使之重新满足红黑树的条件
void RB_TREE_INSERT_FIXUP(RB_TREE*root, RB_TREE_NODE* z);
////删除节点z
void RB_TREE_DELETE(RB_TREE* root, RB_TREE_NODE* z);
///删除节点z后对该树进行调整，使该树重新满足红黑树的条件
void RB_TREE_DELETE_FIXUP(RB_TREE* root, RB_TREE_NODE*z);
///x的前驱,否则返回nullptr
RB_TREE_NODE* RB_TREE_PREDECESSOR(RB_TREE* root, RB_TREE_NODE* x);
///x的后驱，否则返回nullptr
RB_TREE_NODE* RB_TREE_SUCCESSOR(RB_TREE* root, RB_TREE_NODE* x);
///以x为根的树中最小值
RB_TREE_NODE* RB_TREE_MINMUM(RB_TREE_NODE* x);
///以x为根的树中的最大值
RB_TREE_NODE* RB_TREE_MAXMUM(RB_TREE_NODE* x);
///对x节点进行左旋转
void RB_LEFT_ROTATE(RB_TREE* root, RB_TREE_NODE* x);
///对x节点进行右旋转
void RB_RIGHT_ROTATE(RB_TREE*root, RB_TREE_NODE* x);
///用以节点v为根的树替换以节点u为根的树
void RB_TRANSPLANT(RB_TREE* root, RB_TREE_NODE* u, RB_TREE_NODE*v);
///搜索节点值为value的节点，并返回，搜索不到返回PNIL
RB_TREE_NODE* RB_SEARCH(RB_TREE* root, int value);
};
void RB_TREE::RB_TREE_INSERT(RB_TREE* root, RB_TREE_NODE* z)
{
z->left = PNIL; ////哨兵并非空节点，new 出的RB_TREE_NODE的左右孩子为空节点不是哨兵，所以插入前，先将左右孩子置为哨兵
z->right = PNIL;
RB_TREE_NODE* x = RB_TREE::root;
RB_TREE_NODE* y=PNIL;
while (x != PNIL)
{
y = x;
if (z->key < x->key)
x = x->left;
else
x = x->right;
}
z->p = y;
if (y == PNIL)root->root = z;
else if (z->key < y->key)y->left = z;
else y->right = z;
z->color = RED;
RB_TREE_INSERT_FIXUP(root, z);
}
void RB_TREE::RB_TREE_INSERT_FIXUP(RB_TREE* root, RB_TREE_NODE*z)
{
while (z->p->color == RED&&z->p != PNIL)
{
if (z->p->p->left == z->p)
{
RB_TREE_NODE* y = z->p->p->right;
if (y->color == RED)
{
number1++;
z->p->color = BLACK;
y->color = BLACK;
z->p->p->color = RED;
z = z->p->p;
}
else
{
number2++;
if (z == z->p->right)
{
number3++;
z = z->p;
RB_LEFT_ROTATE(root, z);
}
z->p->color = BLACK;
z->p->p->color = RED;
RB_RIGHT_ROTATE(root, z->p->p);
}
}
else
{
RB_TREE_NODE* y = z->p->p->left;
if (y->color == RED)
{
number4++;
z->p->color = BLACK;
y->color = BLACK;
z->p->p->color = RED;
z = z->p->p;
}
else
{
number5++;
if (z == z->p->left)
{
number6++;
z = z->p;
RB_RIGHT_ROTATE(root, z);
}
z->p->color = BLACK;
z->p->p->color = RED;
RB_LEFT_ROTATE(root, z->p->p);
}
}
}
root->root->color = BLACK;
}
void RB_TREE::RB_LEFT_ROTATE(RB_TREE* root, RB_TREE_NODE* x)
{
RB_TREE_NODE* y = x->right;
x->right = y->left;
if (y->left!=PNIL)
y->left->p = x;
y->p = x->p;
if (x->p == PNIL)root->root = y;
else if (x->p->left ==x)x->p->left = y;
else x->p->right = y;
x->p = y;
y->left = x;
}
void RB_TREE::RB_RIGHT_ROTATE(RB_TREE*root, RB_TREE_NODE* x)
{
RB_TREE_NODE* y = x->left;
x->left = y->right;
if (y->right != PNIL)
y->right->p = x;
y->p = x->p;
if (x->p == PNIL)root->root = y;
else if (x->p->left == x) x->p->left = y;
else x->p->right = y;
x->p = y;
y->right = x;
}
RB_TREE_NODE* RB_TREE::RB_TREE_PREDECESSOR(RB_TREE* root, RB_TREE_NODE* x)
{
if (x == RB_TREE_MINMUM(root->root))return x;
if (x->left != PNIL)return RB_TREE_MAXMUM(x->left);
RB_TREE_NODE* y = x->p;
while (y != PNIL&&x == y->left)
{
x = y;
y = y->p;
}
return y;
}
RB_TREE_NODE* RB_TREE::RB_TREE_SUCCESSOR(RB_TREE* root, RB_TREE_NODE* x)
{
if (x == RB_TREE_MAXMUM(root->root))return x;
if (x->right != PNIL)return RB_TREE_MINMUM(x->right);
RB_TREE_NODE* y = x->p;
while (y != PNIL&&x == y->right)
{
x = y;
y = y->p;
}
return y;
}
RB_TREE_NODE* RB_TREE::RB_TREE_MINMUM(RB_TREE_NODE* x)
{
while (x->left != PNIL)
x = x->left;
return x;
}
RB_TREE_NODE* RB_TREE::RB_TREE_MAXMUM(RB_TREE_NODE* x)
{
while (x->right != PNIL)
x = x->right;
return x;
}
void RB_TREE::RB_TRANSPLANT(RB_TREE* root, RB_TREE_NODE* u, RB_TREE_NODE* v)
{
if (u->p == PNIL)root->root = v;
else if (u == u->p->left)u->p->left=v;
else u->p->right = v;
if (v!=PNIL)
v->p = u->p;
}
RB_TREE_NODE* RB_TREE::RB_SEARCH(RB_TREE* root, int value)
{
RB_TREE_NODE* temp = root->root;
while (temp != PNIL&&temp->key != value)
{
if (value < temp->key)
{
temp = temp->left;
}
else
{
temp = temp->right;
}
}
return temp;
}
void RB_TREE::RB_TREE_DELETE(RB_TREE* root, RB_TREE_NODE* z)
{
RB_TREE_NODE* y = z;
RB_TREE_NODE* x;
int origin_color = y->color;
if (z->left == PNIL)
{
x = z->right;
RB_TRANSPLANT(root, z, z->right);
}
else if (z->right == PNIL)
{
x = z->left;
RB_TRANSPLANT(root, z, z->left);
}
else
{
y = RB_TREE_MINMUM(z->right);
origin_color = y->color;
x = y->right;
if (y->p == z)
{
x->p = y; ////防止y的子节点都是哨兵，进行删除调整时，需要找到x的父节点，而哨兵没有父节点。
}
else
{
RB_TRANSPLANT(root, y, y->right);
y->right = z->right;
y->right->p = y;
}
RB_TRANSPLANT(root, z, y);
y->left = z->left;
y->left->p = y;
y->color = z->color;
z->p = nullptr; ///////删除节点z时，对父节点，子节点指针置为空，只删除节点z的区域
z->right = nullptr;
z->left = nullptr;
delete z;
}
if (origin_color == BLACK)
{
RB_TREE_DELETE_FIXUP(root, x);
}
}
void RB_TREE:: RB_TREE_DELETE_FIXUP(RB_TREE* root, RB_TREE_NODE*z)
{
while (z != root->root&&z->color == BLACK)
{
if (z == z->p->left)
{
RB_TREE_NODE* y = z->p->right;
if (y->color == RED) /////case1
{
y->color = BLACK;
z->p->color = RED;
RB_LEFT_ROTATE(root, z->p);
y = z->p->right; ////转到case2，3，4中的一种
}
if (y->left->color == BLACK&&y->right->color == BLACK)
{
y->color = RED; ////case2
z = z->p;
}
else
{
if (y->right->color == BLACK)
{
y->left->color = BLACK;
y->color = RED;
RB_RIGHT_ROTATE(root, y); ////case3 转到case4
y = z->p->right;
}
y->color = z->p->color;
z->p->color = BLACK; ////case4;
y->right->color = BLACK;
RB_LEFT_ROTATE(root, z->p);
z = root->root;
}
}
else ////与以上left和right互换
{
RB_TREE_NODE* y = z->p->left;
if (y->color == RED)
{
y->color = BLACK;
z->p->color = RED;
RB_RIGHT_ROTATE(root, z->p);
y = z->p->left;
}
if (y->right->color == BLACK&&y->left->color == BLACK)
{
y->color = RED;
z = z->p;
}
else
{
if (y->left->color == BLACK)
{
y->right->color = BLACK;
y->color = RED;
RB_LEFT_ROTATE(root, y);
y = z->p->left;
}
y->color = z->p->color;
z->p->color = BLACK;
y->left->color = BLACK;
RB_RIGHT_ROTATE(root, z->p);
z = root->root;
}
}
}
z->color = BLACK;
}
#endif
#include"RB_TREE.h"
#include<iostream>
using namespace std;
void print(RB_TREE* root) /////从小到大输出所有的树节点值
{
RB_TREE_NODE* pmin = root->RB_TREE_MINMUM(root->root);
RB_TREE_NODE* pmax = root->RB_TREE_MAXMUM(root->root);
int i = 0;
while (true)
{
if (i++ % 10 == 0)cout << endl;
cout << pmin->key << " ";
if (pmin == pmax)break;
pmin = root->RB_TREE_SUCCESSOR(root, pmin);
}
}
int main()
{
int a[1000];
for (int i = 0; i < 1000; i++)
{
a[i] = rand() % 100;
}
RB_TREE* root = new RB_TREE();
for (int i = 0; i < 100; i++)
{
RB_TREE_NODE* z = new RB_TREE_NODE(a[i]);
root->RB_TREE_INSERT(root,z);
}
/////对应插入的case情况
cout << endl << number1<<" "<<number2<<" "<<number3<<" "<<number4<<" "<<number5<<" "<<number6<< endl;
cout << endl << "====================" << endl;
cout << root->root->key << " " << root->root->color << endl;
cout << root->root->left->key << " " << root->root->left->color << endl;
cout << root->root->right->key << " " << root->root->right->color << endl;
cout << root->root->left->left->key << " " << root->root->left->left->color << endl;
cout << root->root->left->right->key << " " << root->root->left->right->color << endl;
cout << root->root->right->left->key << " " << root->root->right->left->color << endl;
cout << root->root->right->right->key << " " << root->root->right->right->color << endl;
cout << "++++++++++++++++++++++++++++++++++++++" << endl;
RB_TREE_NODE* pmin = root->RB_TREE_MINMUM(root->root);
RB_TREE_NODE* pmax = root->RB_TREE_MAXMUM(root->root);
print(root);
cout << endl << endl << "++++++++++++++++++++++++++++++++" << endl;
RB_TREE_NODE* t = root->RB_SEARCH(root, 50);
if (t != PNIL)
{
cout << t->key << endl;
root->RB_TREE_DELETE(root, t);
print(root);
}
else cout << "不存在" << endl;
}
参考书目：算法导论
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原文地址：http://www.cnblogs.com/jinweiseu/p/4949380.html
