紅黑樹是一棵二叉搜索樹，它在每個節點上增加了一個存儲位來表示節點的顏色，可以是Red或Black。通過對任何一條從根到葉子簡單路徑上的顏色來約束，紅黑樹保證最長路徑不超過最短路徑的兩倍，因而近似於平衡。
紅黑樹是滿足下面紅黑性質的二叉搜索樹：
（1）每個節點，不是紅色就是黑色的。
（2）根節點是黑色的。
（3）如果一個節點是紅色的，則它的兩個子節點是黑色的(沒有連續的紅節點)。
（4）對每個節點，從該節點到其所有後代葉節點的簡單路徑上，均包含相同數目的黑色節點。（每條路徑的黑色節點的數量相等）
（5）每個空節點都是黑色的。
插入的幾種情況
ps:cur爲當前節點，p爲父節點，g爲祖父節點，u爲叔叔節點。
（1）第一種情況
cur爲紅，p爲紅，g爲黑，u存在且爲紅。
則將p,u改爲黑，g改爲紅，然後把g當成cur，繼續向上調整。
（2）第二種情況
cur爲紅，p爲紅，g爲黑，u不存在/u爲黑。
p爲g的左孩子，cur爲p的左孩子，則進行右單旋。
轉；相反，p爲g的右孩子，cur爲p的右孩子，則進 行左單旋轉。p、g變色--p變黑，g變紅。
（3）第三種情況
cur爲紅，p爲紅，g爲黑，u不存在/u爲黑。
p爲g的左孩子，cur爲p的右孩子，則針對p做左單旋轉；相反，p爲g的右孩子，cur爲p的左孩子，則針對p做右單旋轉，則轉換成了情況2。
代碼實現：
#include<iostream>
using namespace std;
enum Color
{
RED,
BLACK
};
template<class K,class V>
struct RBTreeNode{
RBTreeNode<K, V>* _left;
RBTreeNode<K, V>* _right;
RBTreeNode<K, V>* _parent;
K _key;
V _value;
Color _col; //節點的顏色
RBTreeNode(const K& key, const V& value)
:_left(NULL)
, _right(NULL)
, _parent(NULL)
, _key(key)
, _value(value)
, _col(RED)
{}
};
template<class K,class V>
class RBTree{
typedef RBTreeNode<K, V> Node;
public:
RBTree()
:_root(NULL)
{}
bool Insert(const K& key, const V& value)
{
if (_root == NULL)
{
_root = new Node(key,value);
_root->_col = BLACK;
return true;
}
Node* cur = _root;
Node* parent = NULL;
while (cur)
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else
{
return false;
}
}
cur = new Node(key, value);
if (parent->_key > key)
{
parent->_left = cur;
cur->_parent = parent;
}
else
{
parent->_right = cur;
cur->_parent = parent;
}
while (cur != _root&&parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (parent == grandfather->_left)
{
Node* uncle = grandfather->_right;
//第1種情況
if (uncle&&uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
//繼續向上調整
cur = grandfather;
parent = cur->_parent;
}
else
{
//第3種情況轉換成第2種情況
if (cur == parent->_right)
{
_RotateL(parent);
swap(parent,cur);
}
//第2種情況
_RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
break;
}
}
else //parent=grandfather->_right
{
Node* uncle = grandfather->_left;
//第1種情況
if (uncle&&uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
//向上繼續調整
cur = grandfather;
parent = cur->_parent;
}
else
{
//第3種情況
if (cur == parent->_left)
{
_RotateR(parent);
swap(parent,cur);
}
//第2種情況
_RotateL(grandfather);
grandfather->_col = RED;
parent->_col = BLACK;
break;
}
}
}
_root->_col = BLACK;
return true;
}
Node* Find(const K& key)
{
if (_root == NULL)
return NULL;
Node* cur = _root;
while (cur)
{
if (cur->_key > key)
cur = cur->_left;
else if (cur->_key < key)
cur = cur->_right;
else
return cur;
}
return NULL;
}
void InOrder()
{
_InOrder(_root);
cout << endl;
}
bool IsBlance()
{
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 _IsBlance(_root,k,count);
}
protected:
void _RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
subL->_right = parent;
Node* ppNode = parent->_parent;
parent->_parent = subL;
if (ppNode == NULL)
{
_root = subL;
subL->_parent = NULL;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subL;
subL->_parent = ppNode;
}
else
{
ppNode->_right = subL;
subL->_parent = ppNode;
}
}
}
void _RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
subR->_left = parent;
Node* ppNode = parent->_parent;
parent->_parent = subR;
if (ppNode == NULL)
{
_root = subR;
subR->_parent = NULL;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subR;
subR->_parent = ppNode;
}
else
{
ppNode->_right = subR;
subR->_parent = ppNode;
}
}
}
void _InOrder(Node* root)
{
if (root == NULL)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}
bool _IsBlance(Node* root, const int k, int count)
{
if (root == NULL)
return true;
//規則3：沒有連續的紅節點
if (root->_col == RED&&root->_parent->_col == RED)
{
cout << "出現連續的紅色節點" << root->_key<<endl;
return false;
}
if (root->_col == BLACK)
++count;
//規則4：每條路徑的黑色節點的數量相等
if (root->_left == NULL&&root->_right == NULL&&count != k)
{
cout << "黑色節點個數不相等" << root->_key<<endl;
return false;
}
return _IsBlance(root->_left, k, count) && _IsBlance(root->_right, k, count);
}
protected:
Node* _root;
};
#include "RBTree.h"
void Test1()
{
int a[] ={16, 3, 7, 11, 9, 26, 18, 14, 15};
RBTree<int, int> rbt;
for (int i = 0; i < sizeof(a) / sizeof(a[0]); ++i)
{
rbt.Insert(a[i],i);
}
rbt.InOrder();
cout << rbt.IsBlance() << endl;
RBTreeNode<int, int>* ret1=rbt.Find(15);
if (ret1)
{
cout << ret1->_key << ":" << ret1->_value << endl;
}
else
{
cout << "沒有找到ret1" << endl;
}
RBTreeNode<int, int>* ret2 = rbt.Find(8);
if (ret2)
{
cout << ret2->_key << ":" << ret2->_value << endl;
}
else
{
cout << "沒有找到ret2" << endl;
}
}
int main()
{
Test1();
return 0;
}運行結果：
