红黑树是一棵二叉搜索树，它在每个节点上增加了一个存储位来表示节点的颜色，可以是Red或Black。通过对任何一条从根到叶子简单路径上的颜色来约束，红黑树保证最长路径不超过最短路径的两倍，因而近似于平衡。
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每个节点，不是红色就是黑色的
根节点是黑色的
如果一个节点是红色的，则它的两个子节点是黑色的(没有连续的红节点)
对每个节点，从该节点到其所有后代叶节点的简单路径上，均包含相同数目的黑色节点。（每条路径的黑色节点的数量相等）
每个叶子节点都是黑色的（这里的叶子节点是指的NIL节点（空节点））
#include
using namespace std;
enum COL
{
RED,
BLACK
};
template
struct RBTreeNode
{
K _key;
V _val;
RBTreeNode* _left;
RBTreeNode* _right;
RBTreeNode* _parent;
COL _col;
RBTreeNode(K& key, V& val)
:_key(key)
, _val(val)
, _left(NULL)
, _right(NULL)
, _parent(NULL)
, _col(RED)
{}
};
template
class RBTree{
typedef RBTreeNode Node;
public:
RBTree()
:_root(NULL)
{}
bool Insert(K& key, V& val)
{
if (_root == NULL)
{
_root = new Node(key, val);
}
else
{
Node* parent = NULL;
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key>key)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(key, val);
if (parent->_key < key)
parent->_right = cur;
else
parent->_left = cur;
cur->_parent = parent;
//符合红黑树规范
while (cur != _root&&parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)
{
Node* uncle = grandfather->_right;
if (uncle&&uncle->_col == RED)//1.
{
parent->_col = uncle->_col=BLACK;
grandfather->_col = RED;
//继续往上调
cur = grandfather;
parent = cur->_parent;
}
else
{
if (cur == parent->_right)
{
RotateL(parent);
swap(parent, cur);//*左旋后，指针位置yibian
}
parent->_col = BLACK;
grandfather->_col = RED;
RotateR(grandfather);
break;
}
}
else//反的情况
{
Node* uncle = grandfather->_left;
if (uncle&&uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
//继续往上调
cur = grandfather;
parent = cur->_parent;
}
else
{
if (cur == parent->_left)
{
RotateR(parent);
swap(cur, parent);
}
parent->_col = BLACK;
grandfather->_col = RED;
RotateL(grandfather);
break;
}
}
}
}
_root->_col = BLACK;
return true;
}
Node* Find(const K& key)
{
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
cur = cur->_right;
else if (cur->_key>key)
cur = cur->_left;
else
return cur;
}
return NULL;
}
bool Remove(const K& key)
{
}
bool isBalance()
{
if (_root == NULL)
return true;
if (_root->_col == RED)
return false;
int k = 0;
Node* cur = _root;
while (cur)
{
if (cur->_col==BLACK)
++k;
cur = cur->_left;
}
int count = 0;
return _IsBalance(_root, k, count);
}
void InOrder()
{
_InOrder(_root);
}
protected:
void _InOrder(Node* root)
{
if (root == NULL)
return;
_InOrder(root->_left);
cout << root->_key << " ";
// cout << root->_key << "color"<_col << " ";
_InOrder(root->_right);
}
bool _IsBalance(Node* root, const int k, int count)
{
if (root == NULL)
return true;
if (root->_col == RED)
{
if (root->_parent->_col == RED)
{
cout << "颜色不正确" << root->_key << endl;
return false;
}
}
else
++count;
if (root->_left == NULL&&root->_right == NULL)
{
if (count == k)
return true;
else
{
cout << "黑色节点个数不对" << root->_key<_left, k, count) && _IsBalance(root->_right, k, count);
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
Node* ppNode = parent->_parent;
subR->_left = parent;
parent->_parent = subR;
if (ppNode == NULL)
{
subR->_parent = NULL;
_root = subR;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subR;
}
else
{
ppNode->_right = subR;
}
subR->_parent = ppNode;
}
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
Node* ppNode = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (ppNode == NULL)
{
subL->_parent = NULL;
_root = subL;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subL;
}
else
{
ppNode->_right = subL;
}
subL->_parent = ppNode;
}
}
private:
Node* _root;
};
void Test1()
{
RBTree t;
int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
for (int i = 0; i < sizeof(a) / sizeof(a[0]); ++i)
{
t.Insert(a[i], i);
}
t.InOrder();
t.isBalance();
}
#include"RBtree.h"
int main()
{
Test1();
system("pause");
return 0;
}
新闻名称：RBTree(RED,BLACK)Tree
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