二叉树

      在计算机科学中，二叉树是每个节点最多有两个子树的有序树。通常子树被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用于实现二叉查找树和二叉堆。

      二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树属于有序树，所以二叉树的子树有左右之分，次序不能颠倒。二叉树的第i层至多有2^{i − 1}个结点；深度为k的二叉树至多有2^k − 1个结点；对任何一棵二叉树T，如果其终端结点数为n₀，度为2的结点数为n₂，则n₀ = n₂ + 1。二叉树有多种存储形式。本文采用经常用的二叉链表形式存储。对二叉树的部分操作进行了代码实现。上代码：

typedef struct _BINARY_TREE_NODE_{string strElement;struct _BINARY_TREE_NODE_ *LChild,*RChild;}BTreeNode,*PBTree;class BTree{public:BTree():Root(NULL){nDepth = CreateBTree(Root);}~BTree(){DestroyBTree();}int GetDepth() const {return nDepth;} void PreOrderTraverseRecur()// previous order using recursion{PreOrder(Root);}void PreOrderTraverseNotRecur();// previous order not using recursionvoid InOrderTraverseRecur()// in order using recursion{InOrder(Root);}void InOrderTraverseNotRecur();// in order not using recursionvoid PostOrderTraverseRecur()//post order using recursion{PostOrder(Root);}void PostOrderTraverseNotRecur();// post order not using recursionvoid LevelOrderTraverse();//traverse BTree by layerprivate:PBTree Root;int nDepth;private:int CreateBTree(PBTree& pointer);//create BTreevoid DestroyBTree();//delete all nodes created in heapvoid PreOrder(PBTree pointer);void InOrder(PBTree pointer);void PostOrder(PBTree pointer);};

/***************二叉树********************/int BTree::CreateBTree(PBTree& pointer){pointer = new BTreeNode;cin>>pointer->strElement;if (pointer->strElement == "null"){delete pointer;pointer = NULL;return 0;}else{int i,j;i = CreateBTree(pointer->LChild);j = CreateBTree(pointer->RChild);if(i>j)return (i+1);elsereturn (j+1);}}void BTree::DestroyBTree(){list<PBTree> PNodeList;if(Root)PNodeList.push_back(Root);while(!PNodeList.empty()){PBTree temp = PNodeList.front();PNodeList.pop_front();if(temp->LChild)PNodeList.push_back(temp->LChild);if(temp->RChild)PNodeList.push_back(temp->RChild);delete temp;}}void BTree::PreOrder(PBTree pointer){if (pointer){cout<<pointer->strElement<<endl;PreOrder(pointer->LChild);PreOrder(pointer->RChild);}}void BTree::InOrder(PBTree pointer){if (pointer){InOrder(pointer->LChild);cout<<pointer->strElement<<endl;InOrder(pointer->RChild);}}void BTree::PostOrder(PBTree pointer){if (pointer){PostOrder(pointer->LChild);PostOrder(pointer->RChild);cout<<pointer->strElement<<endl;}}/*traverse tree by previous orderusing list instead of stack because I would not like to include<stack>and as well the last three functions */void BTree::PreOrderTraverseNotRecur(){list<PBTree> ListNode;if (Root){ListNode.push_front(Root);}while(!ListNode.empty()){PBTree temp = ListNode.front();ListNode.pop_front();cout<<temp->strElement<<endl;if(temp->RChild)ListNode.push_front(temp->RChild);if(temp->LChild)ListNode.push_front(temp->LChild);}}void BTree::InOrderTraverseNotRecur(){list<PBTree> ListNode;PBTree temp = Root;if(temp)ListNode.push_back(temp);while(temp->LChild){ListNode.push_front(temp->LChild);temp = temp->LChild;}while(!ListNode.empty()){temp = ListNode.front();ListNode.pop_front();cout<<temp->strElement<<endl;if(temp->RChild){ListNode.push_front(temp->RChild);temp = ListNode.front();while(temp->LChild){ListNode.push_front(temp->LChild);temp = temp->LChild;}}}}void BTree::PostOrderTraverseNotRecur(){//somebody help me or let me take a consideration. haha...list<string> strResult;list<PBTree> ListTree;if(Root)ListTree.push_front(Root);while(! ListTree.empty()){PBTree pointer;pointer = ListTree.front();ListTree.pop_front();while(pointer){strResult.push_front(pointer->strElement);if(pointer->LChild)ListTree.push_front(pointer->LChild);pointer = pointer->RChild;}}while(!strResult.empty()){cout<<strResult.front()<<endl;strResult.pop_front();}}void BTree::LevelOrderTraverse(){list<PBTree> ListNode;if(Root)ListNode.push_front(Root);while(!ListNode.empty()){PBTree temp = ListNode.back();ListNode.pop_back();if(temp->LChild)ListNode.push_front(temp->LChild);if(temp->RChild)ListNode.push_front(temp->RChild);cout<<temp->strElement<<endl;}}

根据先序和中序的序列，重建二叉树。代码如下：

typedef struct _BINARY_TREE_NODE_{char chValue;struct _BINARY_TREE_NODE_ *Left,*Right;}BTreeNode,*PBTree;void RebuildBTree(const char* pPreOrder,const char* pInOrder,int nLen,PBTree& pRoot){if (nLen==1){pRoot = (BTreeNode*)malloc(sizeof(BTreeNode));(pRoot)->chValue=pPreOrder[0];(pRoot)->Left = NULL;(pRoot)->Right = NULL;return;}else{(pRoot) = (BTreeNode*)malloc(sizeof(BTreeNode));(pRoot)->chValue=pPreOrder[0];//search first char in InOrderint i=0;for (i=0;i<nLen;++i ){if(pInOrder[i]==pPreOrder[0])break;}if(i>0)RebuildBTree(pPreOrder+1,pInOrder,i,((pRoot)->Left));elsepRoot->Left= NULL;if(i<nLen-1)RebuildBTree(&(pPreOrder[i+1]),&(pInOrder[i+1]),nLen-i-1,((pRoot)->Right));elsepRoot->Right=NULL;}}void PreOr(PBTree pRoot){if (pRoot){printf(" %c ",pRoot->chValue);PreOr(pRoot->Left);PreOr(pRoot->Right);}}void InOrder1(PBTree pRoot){if(pRoot->Left)InOrder1(pRoot->Left);if(pRoot)printf(" %c ",pRoot->chValue);if (pRoot->Right){InOrder1(pRoot->Right);}}void Last(PBTree pRoot){if(pRoot->Left)Last(pRoot->Left);if(pRoot->Right)Last(pRoot->Right);if(pRoot)printf(" %c ",pRoot->chValue);}int main(){PBTree Root;char Pre[]={"abdcef"};char InOrder[]={"dbaecf"};RebuildBTree(Pre,InOrder,6,Root);printf("Previous Order\n");PreOr(Root);printf("\n");printf("In Order\n");InOrder1(Root);printf("\n");printf("Last Order\n");Last(Root);printf("\n");return 0;}