演算法導論-紅/黑樹狀結構C++實現

紅/黑樹狀結構的定義：

一棵二叉尋找樹如果滿足下面的紅黑性質，則為一棵紅/黑樹狀結構：

1）每個節點或是紅的，或是黑的。

2）根節點是黑的。

3）每個分葉節點（NIL）是黑節點。

4）如果一個節點是紅的，則它的兩個兒子都是黑的。

5）對每個節點，從該節點到其子孫節點的所有路徑上包含相同節點數目的黑節點。

C++代碼實現：

BRTreeNode.h

#ifndef BRTREENODE_H_INCLUDED#define BRTREENODE_H_INCLUDED#include<iostream>using namespace std;class BRTree;class BRTreeNode{private:friend class BRTree;int key;bool color;BRTreeNode* left;BRTreeNode* right;BRTreeNode* parent;public:BRTreeNode():key(-1),color(0),left(NULL),right(NULL),parent(NULL){}BRTreeNode(BRTreeNode* node):key(node->key),color(node->color),left(node->left),right(node->right),parent(node->parent){}BRTreeNode(int num,bool flag):key(num),color(flag),left(NULL),right(NULL),parent(NULL){}~BRTreeNode(){}int Getkey(){return key;}bool Getcolor(){return this->color;}BRTreeNode* GetLeft(){return this->left;}BRTreeNode* Getright(){return this->right;}BRTreeNode* Getparent(){return this->parent;}void Inorder(){if(this!=NULL){this->left->Inorder();cout<<this->key<<" ";this->right->Inorder();}}void Preorder(){if(this!=NULL){cout<<this->key<<" ";this->left->Preorder();this->right->Preorder();}}void Postorder(){if(this!=NULL){this->left->Postorder();this->right->Postorder();cout<<this->key<<" ";}}void MakeEmpty(){if(this!=NULL){this->left->MakeEmpty();this->right->MakeEmpty();delete this;}}int GetHeight(){int L,R;if(this==NULL){return 0;}L=this->left->GetHeight();R=this->right->GetHeight();return 1+(L>R? L:R);}};#endif // BRTREENODE_H_INCLUDED

BRTree.h

#ifndef BRTREE_H_INCLUDED#define BRTREE_H_INCLUDED#define maxSize 30#define maxWidth 30#include"BRTreeNode.h"class BRTree{private:BRTreeNode* root;BRTreeNode* nil;public:BRTree():nil(new BRTreeNode()){nil->color=0;nil->key=-1;nil->left=nil->right=nil->parent=NULL;root=nil;}~BRTree(){MakeEmpty(root);delete nil;}//清空以node為根節點的樹void MakeEmpty(BRTreeNode*node){if(node!=nil){MakeEmpty(node->left);MakeEmpty(node->right);delete node;}}int Getkey(BRTreeNode* node){return node->Getkey();}bool Getcolor(BRTreeNode* node){return node->Getcolor();}BRTreeNode* Getroot(){return root;}BRTreeNode* GetParent(BRTreeNode*node){return node->parent;}int GetHeight(BRTreeNode* node){int L,R;if(node==nil)return 0;L=GetHeight(node->left);R=GetHeight(node->right);return 1+(L>R? L:R);}    int GetBlackHeight(BRTreeNode* node){int L,R;if(node==nil) return 0;L=GetHeight(node->left);R=GetHeight(node->right);if(node->Getcolor()) return(L>R? L:R);else return 1+(L>R? L:R);}void Inorder(BRTreeNode*node){if(node!=nil){Inorder(node->left);cout<<node->key<<" ";Inorder(node->right);}}void Preorder(BRTreeNode*node){if(node!=nil){cout<<node->key<<" ";Preorder(node->left);Preorder(node->right);}}void Posetorder(BRTreeNode*node){if(node!=nil){Posetorder(node->left);Posetorder(node->right);cout<<node->key<<" ";}}//層次法列印樹void DispTree(BRTreeNode*BT){    BRTreeNode stack[maxSize],p;    int level[maxSize][2],top,n,i,width=4;    if(BT!=NULL)    {        cout<<"Display a tree by hollow means."<<endl;        top=1;        stack[top]=BT;//push root point to stack.        level[top][0]=width;        while(top>0)        {            p=stack[top];            n=level[top][0];            for(i=1;i<=n;i++)                cout<<" ";            //輸出資訊            if(p.key==0)            {                cout<<")";            }            else{            if(p.key==-1) cout<<"Nil";            else if(p.left&&p.right) cout<<"("<<p.key;            else cout<<p.key;            if(p.Getcolor()) cout<<"R,";            else cout<<"B,";            }            for(i=n+1;i<maxWidth;i+=2)                cout<<"--";            cout<<endl;            top--;            if(p.right!=NULL)            {                //插入一個括弧節點，key值為0                top++;                BRTreeNode* tmp=new BRTreeNode();                tmp->key=0;                stack[top]=tmp;                level[top][0]=n+width;                level[top][1]=2;                top++;                stack[top]=p.right;                level[top][0]=n+width;                level[top][1]=2;            }            if(p.left!=NULL)            {                top++;                stack[top]=p.left;                level[top][0]=n+width;                level[top][1]=1;            }        }    }}//左旋節點nodebool LeftRotate(BRTreeNode* node){BRTreeNode*y;if(node->right==nil){cout<<"can't left rotate!"<<endl;return 0;}y=node->right;node->right=y->left;if(y->left!=nil){y->left->parent=node;}y->parent=node->parent;if(node->parent==nil){root=y;}else if(node->parent->left==node){node->parent->left=y;}else{node->parent->right=y;}y->left=node;node->parent=y;return 1;}//右旋節點bool RightRotate(BRTreeNode* node){if(node->left==nil){cout<<"can't rightrotate!"<<endl;return 0;}BRTreeNode* x;x=node->left;node->left=x->right;if(x->right!=nil){x->right->parent=node;}x->parent=node->parent;if(node->parent==nil){root=x;}else if(node->parent->left==node){node->parent->left=x;}else{node->parent->right=x;}node->parent=x;x->right=node;return 1;}void Insert(int num){BRTreeNode* node=new BRTreeNode(num,1);node->left=nil;node->right=nil;node->parent=nil;BRTreeNode* p=root,*q=nil;if(root==nil){node->color=0;root=node;root->left=root->right=root->parent=nil;return ;}while(p!=nil){if(p->key==num){cout<<num<<"  has exist!"<<endl;return ;}else if(p->key>num){q=p;p=p->left;}else{q=p;p=p->right;}}if(q->key>num){q->left=node;node->parent=q;}else{q->right=node;node->parent=q;}RBInsertAdjust(node);}void RBInsertAdjust(BRTreeNode* node){BRTreeNode* y;while(node->parent->color==1){if(node->parent==node->parent->parent->left){y=node->parent->parent->right;if(y->color==1){node->parent->color=0;y->color=0;y->parent->color=1;node=node->parent->parent;}//此時y的顏色是黑色else{//第二種情況if(node==node->parent->right){node=node->parent;LeftRotate(node);}//第三種情況node->parent->color=0;node->parent->parent->color=1;RightRotate(node->parent->parent);}}else{y=node->parent->parent->left;if(y->color==1){node->parent->color=0;y->color=0;y->parent->color=1;node=node->parent->parent;}else{if(node==node->parent->left){node=node->parent;RightRotate(node);}node->parent->color=0;node->parent->parent->color=1;LeftRotate(node->parent->parent);}}}root->color=0;}BRTreeNode* Search(int num){BRTreeNode* p=root;while(p!=nil){if(p->key==num){return p;}else if(p->key>num){p=p->left;}else{p=p->right;}}cout<<"there is no "<<num<<" in this tree!"<<endl;return nil;}//擷取以node節點為根節點的樹的最小元素，並返回該最小值int Minnum(BRTreeNode*node){BRTreeNode*p=node;while(p->left!=nil){p=p->left;}return p->key;}//擷取以node節點為根節點的樹的最da元素，並返回該最da值int Maxnum(BRTreeNode*node){BRTreeNode*p=node;while(p->right!=nil){p=p->right;}return p->key;}//擷取以node節點為根節點的樹的最小元素，並返回該節點BRTreeNode* MinNum(BRTreeNode*node){BRTreeNode*p=node;while(p->left!=nil){p=p->left;}return p;}//擷取以node節點為根節點的樹的最大元素BRTreeNode* MaxNum(BRTreeNode*node){BRTreeNode*p=node;while(p->right!=nil){p=p->right;}return p;}BRTreeNode*InorderSuccessor(BRTreeNode*node){if(node->right!=nil){return MinNum(node->right);}else{BRTreeNode*p=GetParent(node);while(p&&node==p->right){node=p;p=GetParent(node);}return p;}}//中序遍曆的前趨BRTreeNode*InordePredecessor(BRTreeNode*node){if(node->left!=nil){return MaxNum(node->left);}else{BRTreeNode*p=GetParent(node);while(p&&node==p->left){node=p;p=GetParent(node);}return p;}}bool Delete(int num){BRTreeNode*z,*y,*x;        //尋找key值為num的節點p        z=Search(num);//如果沒有該節點則返回0        if(z==nil)        {            return 0;        }if(z->left==nil||z->right==nil){y=z;}elsey=InorderSuccessor(z);if(y->left!=nil)x=y->left;elsex=y->right;x->parent=y->parent;if(x->parent==nil)root=x;else if(y=y->parent->left)y->parent->left=x;elsey->parent->right=x;if(y!=z){z->key=y->key;}if(y->color==0){RBTreeFixup(x);}return 1;}void RBTreeFixup(BRTreeNode* x){BRTreeNode*w;while(x!=root&&x->color==0){if(x==x->parent->left){w=x->parent->right;if(w->color==1){w->color=0;x->parent->color=1;LeftRotate(x->parent);w=x->parent->right;}if(w->left->color==0&&w->right->color==0){w->color=1;x=x->parent;}else{if(w->right->color==0){w->color=1;RightRotate(w);w=x->parent->right;}w->color=x->parent->color;x->parent->color=0;w->right->color=0;LeftRotate(x->parent);x=root;}}else{w=x->parent->left;if(w->color==1){w->color=0;x->parent->color=1;RightRotate(x->parent);w=x->parent->left;}if(w->right->color==0&&w->left->color==0){w->color=1;x=x->parent;}else{if(w->left->color==0){w->color=1;LeftRotate(w);w=x->parent->left;}w->color=x->parent->color;x->parent->color=0;w->left->color=0;RightRotate(x->parent);x=root;}}}x->color=0;}};#endif // BRTREE_H_INCLUDED

測試程式

#include <iostream>#include"BRTree.h"#include "BRTreeNode.h"using namespace std;int main(){    BRTree tree;    cout<<"Insert 9 numbers:"<<endl;    int a[9]={8,11,17,15,6,1,22,25,27};    int i;    for(i=0;i<9;i++)    {        tree.Insert(a[i]);    }    tree.DispTree(tree.Getroot());    cout<<"Delete 11:"<<endl;    tree.Delete(11);    tree.DispTree(tree.Getroot());    cout << "blackHeight:" <<tree.GetBlackHeight(tree.Getroot())<<endl;    return 0;}

運行結果：

參考：

教你透徹瞭解紅/黑樹狀結構-http://blog.csdn.net/v_JULY_v/article/details/6105630