代码如下:

#include <iostream>
#include <ctime>
using namespace std;enum COLOR
{BLACK,RED
};template<typename T>
struct RBTreeNode
{RBTreeNode<T> * _parent;RBTreeNode<T> * _left;RBTreeNode<T> * _right;T _val;COLOR _color;RBTreeNode(const T & val = T()):_parent(nullptr),_left(nullptr),_right(nullptr),_val(val),_color(RED){}};template<typename T>
class RBTree
{
public:typedef RBTreeNode<T> Node;RBTree():_root(nullptr){}bool insert(const T & val){if (_root == nullptr) {_root = new Node(val);_root->_color = BLACK;return true;}Node *cur = _root;Node *parent = nullptr;//1.寻找要插入的结点的位置while (cur){parent = cur;if (cur->_val == val) return false;else if (cur->_val > val) cur = cur->_left;else cur = cur->_right;}//2.创建结点cur = new Node(val);if (parent->_val > cur->_val) parent->_left = cur;else parent->_right = cur;cur->_parent = parent;//3.颜色的修改或者结构的调整while (cur != _root && cur->_parent->_color == RED)//不为根且存在连续红色，则需要调整{parent = cur->_parent;Node *gfather = parent->_parent;if (gfather->_left == parent){Node *uncle = gfather->_right;//情况1.uncle存在且为红if (uncle && uncle->_color == RED){parent->_color = uncle->_color = BLACK;gfather->_color = RED;//向上追溯cur = gfather;}else{if (parent->_right == cur){RotateL(parent);swap(cur, parent);}//情况2.uncle不存在或者uncle为黑RotateR(gfather);parent->_color = BLACK;gfather->_color = RED;break;}}else{Node *uncle = gfather->_left;if (uncle && uncle->_color == RED){parent->_color = uncle->_color = BLACK;gfather->_color = RED;//向上追溯cur = gfather;}else{if (parent->_left == cur){RotateR(parent);swap(cur, parent);}RotateL(gfather);parent->_color = BLACK;gfather->_color = RED;break;}}}//根结点都为黑色_root->_color = BLACK;return true;}void RotateL(Node *parent){Node *subR = parent->_right;Node *subRL = subR->_left;parent->_right = subRL;if (subRL) subRL->_parent = parent;if (parent == _root){_root = subR;subR->_parent = nullptr;}else{Node *gfather = parent->_parent;if (gfather->_left == parent) gfather->_left = subR;else gfather->_right = subR;subR->_parent = gfather;}subR->_left = parent;parent->_parent = subR;}void RotateR(Node * parent){Node *subL = parent->_left;Node *subLR = subL->_right;parent->_left = subLR;if (subLR) subLR->_parent = parent;if (parent == _root){_root = subL;subL->_parent = nullptr;}else{Node *gfather = parent->_parent;if (gfather->_left == parent) gfather->_left = subL;else gfather->_right = subL;subL->_parent = gfather;}subL->_right = parent;parent->_parent = subL;}void inorder(){_inorder(_root);cout << endl;}
//红黑树的性质:
//	1.每个结点的颜色只有红色和黑色，且根结点必须为黑色
//	2.不能存在连续的红色结点
//	3.对于每个结点来说，从该结点到其所有后代结点的简单路径上，经过的黑色结点的数目应该是相同的bool isRBTree(){if (_root == nullptr) return true;//空树也属于红黑树if (_root->_color == RED) return false;//不满足性质2：根结点必须为黑色int bCount = 0;//从某条路径上的黑色结点数Node *cur = _root;while (cur){if (cur->_color == BLACK) ++bCount;cur = cur->_left;}int pathCount = 0;return _isRBTree(_root, bCount, pathCount);}bool _isRBTree(Node *root, const int bCount, int pathCount){if (root == nullptr)//路径走完，判断黑色结点个数{if (pathCount == bCount) return true;else return false;//不满足性质3：每一条路径上的黑色结点个数相同}if (root->_color == BLACK) ++pathCount;Node *parent = root->_parent;if (parent && parent->_color == RED && root->_color == RED) return false;//不满足性质2：不能存在连续的红色结点return _isRBTree(root->_left, bCount, pathCount) && _isRBTree(root->_right, bCount, pathCount);}private:Node *_root;void _inorder(Node *root){if (root){_inorder(root->_left);cout << root->_val << " ";_inorder(root->_right);}}
};int main()
{RBTree<int> rbt;srand(time(nullptr));int n;cout << "num = " << endl;cin >> n;for (int i = 0; i < n; i++){rbt.insert(rand());}rbt.inorder();if (rbt.isRBTree()) cout << "yes" << endl;else cout << "no" << endl;return 0;
}

测试结果: