1159 Structure of a Binary Tree – PAT甲级真题

Suppose that all the keys in a binary tree are distinct positive integers. Given the postorder and inorder traversal sequences, a binary tree can be uniquely determined.

Now given a sequence of statements about the structure of the resulting tree, you are supposed to tell if they are correct or not. A statment is one of the following:

  • A is the root
  • A and B are siblings
  • A is the parent of B
  • A is the left child of B
  • A is the right child of B
  • A and B are on the same level
  • It is a full tree


  • Two nodes are on the same level, means that they have the same depth.
  • full binary tree is a tree in which every node other than the leaves has two children.

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 postorder sequence and the third line gives the inorder sequence. All the numbers in a line are no more than 103 and are separated by a space.

Then another positive integer M (≤30) is given, followed by M lines of statements. It is guaranteed that both A and B in the statements are in the tree.

Output Specification:

For each statement, print in a line Yes if it is correct, or No if not.

Sample Input:

16 7 11 32 28 2 23 8 15
16 23 7 32 11 2 28 15 8
15 is the root
8 and 2 are siblings
32 is the parent of 11
23 is the left child of 16
28 is the right child of 2
7 and 11 are on the same level
It is a full tree

Sample Output:


题目大意:假设二叉树中的所有值都是不同的正整数,给定后序和中序遍历可以唯一确定一棵二叉树。给出一系列关于二叉树结构的语句,判断它们是否正确,语句是以下之一:A是根结点,A和B是兄弟姐妹,A是B的父结点,A是B的左孩子,A是B的右孩子,A和B在同一层,这是一棵full tree。(两个结点在同一层,意味着这两个结点具有同样深度;full binary tree是指除了叶子结点外,每个结点都有两个孩子)。输入样例:第一行给出正整数N,即二叉树中结点的总数;第二行给出后序遍历序列,第三行给出中序遍历序列。一行中所有数字不超过10的3次方,并且用空格分隔。然后给出一个正整数M,然后是M行语句,保证语句的A和B都在树中。输出样例:对于每条语句,如果正确,则输出Yes,否则输出No。
分析:中序存储在In数组中,后序存储在Post数组中,根据中序和后序建树,Tree中存储树上结点的相关信息,下标即表示结点的值,其中lchild存储左孩子下标,rchild存储右孩子下标,parent存储父结点下标,将这些初始化为-1表示不存在,level存储深度,此外,root为根节点的值,Full标记是否是full tree,f判断当前语句是否正确,最后根据f的值输出Yes或No~ 


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