19年春季第四题 PAT甲级 1159 Structure of a Binary Tree（30分）
汇总贴
2020年3月PAT甲级满分必备刷题技巧
题目
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
Note:
- Two nodes are on the same level, means that they have the same depth.
- A 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 10^3 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:
9
16 7 11 32 28 2 23 8 15
16 23 7 32 11 2 28 15 8
7
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 treeSample Output:
Yes
No
Yes
No
Yes
Yes
Yes题目分析
1.postorder and inorder traversal sequences
给定后序和中序，这个是PAT甲级题库中很常见的知识点“二叉树的遍历”，可以参考《算法笔记》9.2节和题库的1086、1119、1138。
2.因为可能不是完全二叉树，同时输出的东西也挺复杂的，所以应该果断用DFS建二叉树。建树方法略有不同于1135（https://www.liuchuo.net/archives/4099），是采用map和结构体。
3.本题有7种输出，对应7个数据，都可以在DFS建树中体现：
（1）root，建树的返回就是root的值
（2）siblings，等价于两个节点的祖先是同一个
（3）parent，每个节点存父亲的值
（4）leftchild，A节点的左孩子是B，为了访问A的时候就能读出B节点的值，要用map和结构体
（5）rightchild，B节点的左孩子是A
（6）same level，记录节点的深度
（7）full tree，记录节点有没有左右孩子
满分代码
来源致谢：https://blog.csdn.net/lianwaiyuwusheng/article/details/88084378
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