1119 Pre- and Post-order Traversals (30 分)

本文探讨了二叉树的遍历序列,包括前序、中序和后序遍历,以及如何通过这些序列确定二叉树的结构。特别讨论了在给定前序和后序遍历序列的情况下,二叉树可能不唯一的问题,并提供了相应的算法解决方案。

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Suppose that all the keys in a binary tree are distinct positive integers. A unique binary tree can be determined by a given pair of postorder and inorder traversal sequences, or preorder and inorder traversal sequences. However, if only the postorder and preorder traversal sequences are given, the corresponding tree may no longer be unique.

Now given a pair of postorder and preorder traversal sequences, you are supposed to output the corresponding inorder traversal sequence of the tree. If the tree is not unique, simply output any one of them.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤ 30), the total number of nodes in the binary tree. The second line gives the preorder sequence and the third line gives the postorder sequence. All the numbers in a line are separated by a space.

Output Specification:

For each test case, first printf in a line Yes if the tree is unique, or No if not. Then print in the next line the inorder traversal sequence of the corresponding binary tree. If the solution is not unique, any answer would do. It is guaranteed that at least one solution exists. All the numbers in a line must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input 1:

7
1 2 3 4 6 7 5
2 6 7 4 5 3 1

Sample Output 1:

Yes
2 1 6 4 7 3 5

Sample Input 2:

4
1 2 3 4
2 4 3 1

Sample Output 2:

No
2 1 3 4

#include<bits/stdc++.h>
using namespace std;
typedef struct node
{
    int data;
    struct node *lchild,*rchild;
}node,*Tree;
int pre[100],post[100],n;
bool flag=true;
vector<int>v(n);
Tree Create(int prel,int prer,int postl,int postr)
{
    if(prel>prer)
        return NULL;
    Tree root = new node;
    root->data = pre[prel];
    root->lchild = root->rchild = NULL;///???
    if(prel==prer)
        return root;
    int k;
    for(k=prel+1;k<=prer;k++)
    {
        if(pre[k]==post[postr-1])
            break;
    }
    int leftnum = k-prel;
    if(leftnum>1)
    {
        root->lchild = Create(prel+1,k-1,postl,postl+leftnum-2);///???
        root->rchild = Create(k,prer,postl+leftnum-1,postr-1);///???
    }
    else
    {
        flag=false;
        root->rchild = Create(k,prer,postl+leftnum-1,postr-1);
    }
    return root;
}
void inorder(Tree root)
{
    if(root!=NULL)
    {
        inorder(root->lchild);
        v.push_back(root->data);
        inorder(root->rchild);

    }
}

int main()
{
    cin>>n;
    for(int i=0;i<n;i++)
        cin>>pre[i];
    for(int i=0;i<n;i++)
        cin>>post[i];
    Tree root;
    root = Create(0,n-1,0,n-1);
    if(flag)
        cout<<"Yes"<<endl;
    else
        cout<<"No"<<endl;
    inorder(root);
    for(int i=0;i<v.size()-1;i++)
        cout<<v[i]<<" ";
    cout<<v[v.size()-1]<<endl;
}
 

American Heritage 题目描述 Farmer John takes the heritage of his cows very seriously. He is not, however, a truly fine bookkeeper. He keeps his cow genealogies as binary trees and, instead of writing them in graphic form, he records them in the more linear tree in-order" and tree pre-order" notations. Your job is to create the `tree post-order" notation of a cow"s heritage after being given the in-order and pre-order notations. Each cow name is encoded as a unique letter. (You may already know that you can frequently reconstruct a tree from any two of the ordered traversals.) Obviously, the trees will have no more than 26 nodes. Here is a graphical representation of the tree used in the sample input and output: C / \ / \ B G / \ / A D H / \ E F The in-order traversal of this tree prints the left sub-tree, the root, and the right sub-tree. The pre-order traversal of this tree prints the root, the left sub-tree, and the right sub-tree. The post-order traversal of this tree print the left sub-tree, the right sub-tree, and the root. ---------------------------------------------------------------------------------------------------------------------------- 题目大意: 给出一棵二叉树的中序遍历 (inorder) 和前序遍历 (preorder),求它的后序遍历 (postorder)。 输入描述 Line 1: The in-order representation of a tree. Line 2: The pre-o rder representation of that same tree. Only uppercase letter A-Z will appear in the input. You will get at least 1 and at most 26 nodes in the tree. 输出描述 A single line with the post-order representation of the tree. 样例输入 Copy to Clipboard ABEDFCHG CBADEFGH 样例输出 Copy to Clipboard AEFDBHGC c语言,代码不要有注释
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06-16
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