二叉树的建立和遍历的各种问题

链表声明：

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//基本结构声明

#include<iostream>
#include<queue>
#include<stack>
#include<cstdio>

#define NoInfo 0        // 0表示没有结点 
using namespace std;
typedef int ElementType;
typedef struct TNode* Position;
typedef Position BinTree;
//二叉树链表结构 
struct TNode{
    ElementType Data;    //结点数据 
    BinTree Left;        //左子树 
    BinTree Right;        //右子树 
};

1.先序建立二叉树

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//先序建立二叉树
BinTree CreateBinTree(){
    ElementType data;
    scanf("%d",&data);
    if(data==NoInfo) return NULL;
       BinTree P;
       P=new TNode;
    P->Data=data;
    P->Left=CreateBinTree();
    P->Right =CreateBinTree();
    return P;
}

2.层序建立二叉树

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//层序建立二叉树
BinTree CreateBinTree(){
    ElementType data;
    BinTree BT,T;
    queue<BinTree> q;//创建队列
    scanf("%d",&data);
    if(data!=NoInfo){
        BT=new TNode;
        BT->Data =data;
        BT->Left =BT->Right =NULL;
        q.push(BT);
    }
    else return NULL;//第一个数据为0则返回空树
    
    while(!q.empty()){
        T=q.front();//取出结点 
        q.pop();
        scanf("%d",&data);//读入T的左孩子 
        if(data==NoInfo) T->Left =NULL;
        else{
            T->Left =new TNode;
            T->Left ->Data=data;
            T->Left ->Left=T->Left ->Right=NULL;
            q.push(T->Left );
        }
        scanf("%d",&data);//读入T的右孩子 
        if(data==NoInfo) T->Right =NULL;
        else{
            T->Right =new TNode;
            T->Right ->Data=data;
            T->Right ->Left=T->Right ->Right=NULL;
            q.push(T->Right );
        }
    }
    return BT; 
}

3.递归先序遍历

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void PreorderTraversal_1(BinTree BT){
    if(BT){
        printf("%d",BT->Data );
        PreorderTraversal_1(BT->Left );
        PreorderTraversal_1(BT->Right );
    }
}

4.非递归先序遍历

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void PreorderTraversal_2(BinTree BT){
    BinTree T=BT;
    stack<BinTree> s;
    while(T||!s.empty()){
        while(T){
            printf("%d",T->Data );
            s.push(T);
            T=T->Left ;
        }
        T=s.top();
        s.pop();
        T=T->Right ;
    }
}

5.递归中序遍历

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void InorderTraversal_1(BinTree BT){
    if(BT){
        InorderTraversal_1(BT->Left );
        printf("%d",BT->Data );
        InorderTraversal_1(BT->Right );
    }
}

6.非递归中序遍历

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//非递归中序遍历
void InorderTraversal_2(BinTree BT){
    BinTree T=BT;
    stack<BinTree> s;
    while(T||!s.empty()){
        while(T){
            s.push(T);
            T=T->Left ;
        }
        T=s.top();
        s.pop();
        printf("%d",T->Data );
        T=T->Right ;
    }
}

7.递归后序遍历

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//递归后序遍历
void PostorderTraversal_1(BinTree BT){
    if(BT){
        PostorderTraversal_1(BT->Left );
        PostorderTraversal_1(BT->Right );
        printf("%d",BT->Data );
    }
}

8.非递归后序遍历

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//非递归后序遍历
void PostorderTraversal_2(BinTree BT){
    BinTree T,Pre=NULL;
    stack<BinTree> s;
    s.push(BT);
    while(!s.empty()){
        T=s.top();
        if( (T->Left ==NULL&&T->Right ==NULL) || 
        (Pre!=NULL&& (T->Left==Pre ||T->Right==Pre ) ) ){
            printf("%d",T->Data );
            s.pop();
            Pre=T;
        }
        else{
            if(T->Right !=NULL) s.push(T->Right );
            if(T->Left !=NULL) s.push(T->Left );
        }
    }
}

9.层序遍历

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void LevelorderTravelsal(BinTree BT){
    queue<BTree> q;
    BinTree T;
    if(!BT) return;
    q.push(BT);
    while(!q.empty()){
        T=q.front();
        q.pop();
        printf("%d ",T->Data);
        if(T->Left ) q.push(T->Left );
        if(T->Right ) q.push(T->Right );
    }
}

10.二叉树高度

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//二叉树高度
int GetHeight(BinTree BT){
    if(BT) return max(GetHeight(BT->Left),GetHeight(BT->Right ))+1;
    else return 0;//空树高度为0 
}

11.求二叉树所有结点

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//求二叉树所有结点
int    CountNode(BinTree BT){
    if(BT)    return CountNode(BT->Left )+CountNode(BT->Right )+1;
    else return 0;
} 

12.求二叉树叶子结点

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void LeaveCount(BinTree BT){
    if(BT){
        if(BT->Left ==NULL&&BT->Right ==NULL)
            count++;
        LeaveCount(BT->Left );
        LeaveCount(BT->Right );    
    }
}

int LeafcountofBinTree(BinTree BT){
    if(BT){
        if(BT->Left ==NULL&&BT->Right ==NULL)
            return LeafcountofBinTree(BT->Left )+LeafcountofBinTree(BT->Right )+1;
    }
    else return 0;
}

13.先序输出二叉树叶子结点 

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void PreorderPrintLeaves(BinTree BT){
    if(BT!=NULL){
        if((BT->Left==NULL)&&(BT->Right==NULL))
            printf(" %c",BT->Data);
        PreorderPrintLeaves(BT->Left);
        PreorderPrintLeaves(BT->Right);
    }
}

14.镜面反转，将所有非叶结点的左右孩子对换 

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void Inversion(BinTree BT){
    if(BT){
        Inversion(BT->Left);
        Inversion(BT->Right);
        BinTree temp;
        temp=BT->Left ;
        BT->Left =BT->Right ;
        BT->Right =temp;
    }
}

15.销毁二叉树

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void DestroyBinTree(BinTree BT){
    if(BT){
        DestroyBinTree(BT->Left );
        DestroyBinTree(BT->Right );
        delete BT;
        BT=NULL;
    }
}

16.根据前序和中序遍历还原二叉树 

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//根据前序和中序遍历还原二叉树 
BinTree PreInoRestoreBinTree(int* inorder ,int* preorder, int length)
{
  if(length==0) return NULL;
  BinTree T=new TNode;
  int rootIndex;
  T->Data  = *preorder;
  for(rootIndex=0;rootIndex < length; rootIndex++)
      if(inorder[rootIndex] == *preorder)
          break;
  T->Left = PreInoRestoreBinTree(inorder,preorder +1 , rootIndex);
  T->Right = PreInoRestoreBinTree(inorder + rootIndex + 1 ,preorder + rootIndex + 1 , length - (rootIndex + 1));
  return T;
}

17.根据后序和中序遍历还原二叉树 

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BinTree InoPosRestoreBinTree(int *inorder,int *postorder,int length)
{
    if(length==0) return NULL;
    BinTree T;
    int rootindex;
    T =new TNode;
    T->Data=postorder[length-1];
    T->Left=T->Right=NULL;
    for(rootindex=0; rootindex < length; rootindex++)
        if(inorder[rootindex] == postorder[length-1])
            break;
    T->Left =InoPosRestoreBinTree(inorder,postorder,rootindex);
    T->Right =InoPosRestoreBinTree(inorder+rootindex+1,postorder+rootindex,length-(rootindex+1));
    return T;
}

 17.1 根据中序和后序输出前序

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#include<iostream>
#include<vector>
#include<string>
using namespace std;
string in, post, ans="";
void pre(int root, int l, int r){
    if(l>r) return ;
    int i=l;
    while(in[i] != post[root]) i++;
    //printf("%d %d %d %d\n",root,l,r,i);
    ans += post[root];
    //cout<<"L"<<endl;
    pre(root-r+i-1, l, i-1);
    //cout<<"R"<<endl;
    pre(root-1, i+1, r);
}
int main(){
    cin>>in>>post;
    pre(post.size()-1,0,post.size()-1);
    cout<<ans<<endl;
    return 0;
}