二叉树

该篇文章介绍二叉树的一些常用算法。

头文件：BinaryTree.h

#pragma once#include<iostream>struct BinaryTreeNode{int                    m_nValue;BinaryTreeNode*        m_pLeft;BinaryTreeNode*        m_pRight;};//===二叉树的基本操作运算BinaryTreeNode* CreateBinaryTreeNode(int value);//创建一个节点void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight);//连接根节点和左右子节点void PrintTreeNode(BinaryTreeNode* pNode);void PrintTree(BinaryTreeNode* pRoot);//输出节点void DestroyTree(BinaryTreeNode* pRoot);//销毁节点BinaryTreeNode *FindNode(BinaryTreeNode*proot, int x);//查找结点int BinaryTreeHeight(BinaryTreeNode *proot);//求二叉树的高度//===二叉树的遍历算法--递归版void PreOrder(BinaryTreeNode *proot);//前序遍历void InOrder(BinaryTreeNode *proot);//中序遍历void PostOrder(BinaryTreeNode *proot);//后序遍历//===二叉树的遍历算法--迭代版void PreOrderIter(BinaryTreeNode *proot);//前序遍历void InOrderIter(BinaryTreeNode *proot);//中序遍历void PostOrderIter(BinaryTreeNode *proot);//后序遍历//===二叉树的层次遍历void LevelOrder(BinaryTreeNode *proot);//层次遍历//===二叉树的其他操作运算--递归版int NodeCount(BinaryTreeNode *proot);//二叉树的结点个数void AllLeavesNode(BinaryTreeNode *proot);//求二叉树的所有叶子结点void CopyOneToAnthor(BinaryTreeNode *proot, BinaryTreeNode *&other);//由一棵二叉树复制产生另一棵二叉树void ConvertArrayToBT(int a[], int n, int i, BinaryTreeNode *&proot);//由数组转化为二叉树int Level(BinaryTreeNode *proot, int x, int h);//x所在的层bool Ancestor(BinaryTreeNode *proot, int x);//输出节点x的所有祖先结点BinaryTreeNode *ConstructBTbyPreInOrder(int pre[], int prebegin, int mid[], int midbegin, int n);//由前序和中序构造二叉树BinaryTreeNode *ConstructBTbyPostInOrder(int post[], int postbegin, int mid[], int midbegin, int n);//由后序和中序构造二叉树//===二叉树的其他操作运算--迭代版bool AncestorIter(BinaryTreeNode *proot, int x);//输出节点x的所有祖先结点

源文件：BinaryTree.cpp

#include "BinaryTree.h"#include<iostream>#include<stack>#include<queue>BinaryTreeNode* CreateBinaryTreeNode(int value){BinaryTreeNode* pNode = new BinaryTreeNode();pNode->m_nValue = value;pNode->m_pLeft = NULL;pNode->m_pRight = NULL;return pNode;}void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight){if (pParent != NULL){pParent->m_pLeft = pLeft;pParent->m_pRight = pRight;}}void PrintTreeNode(BinaryTreeNode* pNode){if (pNode != NULL){printf("value of this node is: %d\n", pNode->m_nValue);if (pNode->m_pLeft != NULL)printf("value of its left child is: %d.\n", pNode->m_pLeft->m_nValue);elseprintf("left child is null.\n");if (pNode->m_pRight != NULL)printf("value of its right child is: %d.\n", pNode->m_pRight->m_nValue);elseprintf("right child is null.\n");}else{printf("this node is null.\n");}printf("\n");}void PrintTree(BinaryTreeNode* pRoot){PrintTreeNode(pRoot); if (pRoot != NULL){if (pRoot->m_pLeft != NULL)PrintTree(pRoot->m_pLeft);if (pRoot->m_pRight != NULL)PrintTree(pRoot->m_pRight);}}void DestroyTree(BinaryTreeNode* pRoot){if (pRoot != NULL){BinaryTreeNode* pLeft = pRoot->m_pLeft;BinaryTreeNode* pRight = pRoot->m_pRight;delete pRoot;pRoot = NULL;DestroyTree(pLeft);DestroyTree(pRight);}}BinaryTreeNode *FindNode(BinaryTreeNode*proot, int x){if (proot == NULL)return NULL;else if (proot->m_nValue == x)return proot;else{BinaryTreeNode *p = FindNode(proot->m_pLeft, x);if (p == NULL)return FindNode(proot->m_pRight, x);elsereturn p;}}int BinaryTreeHeight(BinaryTreeNode *proot){if (proot == NULL)return 0;else {int leftheight = BinaryTreeHeight(proot->m_pLeft);int righrheight = BinaryTreeHeight(proot->m_pRight);return leftheight > righrheight ? leftheight + 1 : righrheight + 1;}}void PreOrder(BinaryTreeNode *proot){if (proot){std::cout << proot->m_nValue << " ";PreOrder(proot->m_pLeft);PreOrder(proot->m_pRight);}}void InOrder(BinaryTreeNode *proot){if (proot){InOrder(proot->m_pLeft);std::cout << proot->m_nValue << " ";InOrder(proot->m_pRight);}}void PostOrder(BinaryTreeNode *proot){if (proot){PostOrder(proot->m_pLeft);PostOrder(proot->m_pRight);std::cout << proot->m_nValue << " ";}}void PreOrderIter(BinaryTreeNode *proot){if (proot == NULL)return;std::stack<BinaryTreeNode*> temp;temp.push(proot);while (!temp.empty()){BinaryTreeNode *p = temp.top();temp.pop();std::cout << p->m_nValue << " ";if (p->m_pRight)temp.push(p->m_pRight);if (p->m_pLeft)temp.push(p->m_pLeft);}std::cout << std::endl;}void InOrderIter(BinaryTreeNode *proot){if (proot == NULL)return;BinaryTreeNode*p = proot;std::stack<BinaryTreeNode *> temp;while (!temp.empty()||p!=NULL){while (p){temp.push(p);p = p->m_pLeft;}if (!temp.empty()){p = temp.top();temp.pop();std::cout << p->m_nValue << " ";p = p->m_pRight;}}std::cout << std::endl;}void PostOrderIter(BinaryTreeNode *proot){if (proot == NULL)return;BinaryTreeNode *p = proot, *q = NULL;std::stack<BinaryTreeNode*>temp;bool flag;do{while (p){temp.push(p);p = p->m_pLeft;}q = NULL;flag = true;while (!temp.empty() && flag){p = temp.top();if (p->m_pRight == q){std::cout << p->m_nValue << " ";q = p;temp.pop();}else{p = p->m_pRight;flag = false;}}} while (!temp.empty());std::cout << std::endl;}void LevelOrder(BinaryTreeNode *proot){if (proot == NULL)return;std::queue<BinaryTreeNode*>temp;temp.push(proot);while (!temp.empty()){BinaryTreeNode *p = temp.front();std::cout << p->m_nValue << " ";temp.pop();if (p->m_pLeft)temp.push(p->m_pLeft);if (p->m_pRight)temp.push(p->m_pRight);}std::cout << std::endl;}int NodeCount(BinaryTreeNode *proot){if (proot){return 1 + NodeCount(proot->m_pLeft) + NodeCount(proot->m_pRight);}elsereturn 0;}void AllLeavesNode(BinaryTreeNode *proot){if (proot){if (proot->m_pLeft == NULL&&proot->m_pRight == NULL)std::cout << proot->m_nValue << " ";AllLeavesNode(proot->m_pLeft);AllLeavesNode(proot->m_pRight);}}void CopyOneToAnthor(BinaryTreeNode *proot, BinaryTreeNode * &other){if (proot){other = CreateBinaryTreeNode(proot->m_nValue);CopyOneToAnthor(proot->m_pLeft, other->m_pLeft);CopyOneToAnthor(proot->m_pRight, other->m_pRight);}else{other = NULL;}}void ConvertArrayToBT(int a[], int n,int i,BinaryTreeNode *&proot){if (i < n){proot = CreateBinaryTreeNode(a[i]);ConvertArrayToBT(a, n, i * 2 + 1, proot->m_pLeft);ConvertArrayToBT(a, n, i * 2 + 2, proot->m_pRight);}elseproot = NULL;}int Level(BinaryTreeNode *proot, int x, int h){if (proot == NULL)return 0;if (proot->m_nValue == x)return h;else{int height = Level(proot->m_pLeft, x, h + 1);if (height != 0)return height;elsereturn Level(proot->m_pRight, x, h + 1);}}bool Ancestor(BinaryTreeNode *proot, int x){if (proot == NULL)return false;if (proot->m_pLeft != NULL&&proot->m_pLeft->m_nValue == x){std::cout << proot->m_nValue << " ";return true;}if (proot->m_pRight != NULL&&proot->m_pRight->m_nValue == x){std::cout << proot->m_nValue << " ";return true;}if (Ancestor(proot->m_pLeft, x) || Ancestor(proot->m_pRight, x)){std::cout << proot->m_nValue << " ";return true;}elsereturn false;}BinaryTreeNode *ConstructBTbyPreInOrder(int pre[], int prebegin, int mid[], int midbegin, int n){if (n <= 0)return NULL;BinaryTreeNode *proot = CreateBinaryTreeNode(pre[prebegin]);int index;for (int i = midbegin; i < midbegin + n; i++){if (pre[prebegin] == mid[i]){index = i;break;}}int k = index - midbegin;proot->m_pLeft = ConstructBTbyPreInOrder(pre, prebegin + 1, mid, midbegin,k);proot->m_pRight = ConstructBTbyPreInOrder(pre, prebegin+k + 1, mid, index + 1, n - k-1);return proot;}BinaryTreeNode *ConstructBTbyPostInOrder(int post[], int postbegin, int mid[], int midbegin, int n){if (n <= 0)return NULL;BinaryTreeNode *proot = CreateBinaryTreeNode(post[postbegin + n - 1]);int index;for (int i = midbegin;i < midbegin + n; i++){if (post[postbegin + n - 1] == mid[i]){index = i;break;}}int k = index - midbegin;proot->m_pLeft = ConstructBTbyPostInOrder(post, postbegin, mid, midbegin, k);proot->m_pRight = ConstructBTbyPostInOrder(post, postbegin+k, mid, index + 1, n - k- 1);return proot;}bool AncestorIter(BinaryTreeNode *proot, int x){if (proot == NULL)return false;BinaryTreeNode *p = proot, *q = NULL;std::stack<BinaryTreeNode*>temp;bool flag;do{while (p){temp.push(p);p = p->m_pLeft;}q = NULL;flag = true;while (!temp.empty() && flag){p = temp.top();if (p->m_nValue == x){temp.pop();while (!temp.empty()){std::cout << temp.top()->m_nValue << " ";temp.pop();}return true;}else{if (p->m_pRight == q){q = p;temp.pop();}else{p = p->m_pRight;flag = false;}}}} while (!temp.empty());std::cout << std::endl;return false;}

主函数：main.cpp

#include "BinaryTree.h"#include<iostream>using namespace std;// ====================测试代码====================//            8//        6      10//       5 7    9  11int main(){//===BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);BinaryTreeNode* pNode5 = CreateBinaryTreeNode(5);BinaryTreeNode* pNode7 = CreateBinaryTreeNode(7);BinaryTreeNode* pNode9 = CreateBinaryTreeNode(9);BinaryTreeNode* pNode11 = CreateBinaryTreeNode(11);ConnectTreeNodes(pNode8, pNode6, pNode10);ConnectTreeNodes(pNode6, pNode5, pNode7);ConnectTreeNodes(pNode10, pNode9, pNode11);//===============二叉树的基本操作运算==================//输出二叉树===//PrintTree(pNode8);//查找结点===//int findnode = 10;//BinaryTreeNode *findres = FindNode(pNode8, findnode);//if (findres) cout << findres->m_nValue << endl;//二叉树的高度===//int btheight = BinaryTreeHeight(pNode8);//cout << "二叉树的高度:" << btheight << endl;//===============二叉树的遍历-递归版=================//前序遍历===//PreOrder(pNode8);cout << endl;//中序遍历===//InOrder(pNode8); cout << endl;//后序遍历===//PostOrder(pNode8); cout << endl;//===============二叉树的遍历-迭代版=================//前序遍历===//PreOrderIter(pNode8);//中序遍历===//InOrderIter(pNode8); //后序遍历===//PostOrderIter(pNode8); //================二叉树的层次遍历===================//LevelOrder(pNode8);//==================二叉树的其他操作运算--递归版======//二叉树的结点个数===//int nodecount = NodeCount(pNode8);//cout << nodecount << endl;//二叉树的所有叶子结点===//AllLeavesNode(pNode8);//二叉树的复制===//BinaryTreeNode *other = NULL;//CopyOneToAnthor(pNode8, other);//PrintTree(other);//DestroyTree(other);//由数组转化为二叉树===//const int n = 7;//int a[n] = { 8, 6, 10, 5, 7, 9, 11 };//BinaryTreeNode *proot = NULL;//ConvertArrayToBT(a, n, 0, proot);//PrintTree(proot);//DestroyTree(proot);//x所在的层//int x = 0;//int height = Level(pNode8, x, 1);//cout << height << endl;//输出x的祖先结点//int x = 8;//Ancestor(pNode8, x);//由前序和中序构造二叉树===const int n = 7;int pre[n] = { 8, 6, 5, 7, 10, 9, 11 };int mid[n] = { 5, 6, 7, 8, 9, 10, 11 };int post[n] = { 5, 7, 6, 9, 11, 10, 8 };//BinaryTreeNode *proot1 = ConstructBTbyPreInOrder(pre, 0, mid, 0, n);//PrintTree(proot1);//DestroyTree(proot1);//由后序和中序构造二叉树===//BinaryTreeNode *proot2 = ConstructBTbyPostInOrder(post, 0, mid, 0, n);//PrintTree(proot2);//DestroyTree(proot2);//====================二叉树的其他操作运算--迭代版======//输出x的祖先结点//int x = 9;//AncestorIter(pNode8, x);//销毁二叉树===DestroyTree(pNode8);}