PAT 2019-3 7-4 Structure of a Binary Tree
Description:
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 (≤), 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 1 and are separated by a space.
Then another positive integer M (≤) is given, followed by M lines of statements. It is guaranteed that both
A
andB
in the statements are in the tree.
Output Specification:
For each statement, print in a line
Yes
if it is correct, orNo
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 tree
Sample Output:
Yes
No
Yes
No
Yes
Yes
Yes
Keys:
- 二叉树的存储和遍历
Attention:
- sscanf(s.c_str(), "%d %*s %d", &a, &b);
- s.find("s") != string::npos;
- map<int,node*> mp;
Code:
/*
二叉树中各结点值为互不相同的正整数
给出后序遍历和中序遍历 判断所给语句是否正确
根节点
兄弟
父结点
左孩子
右孩子
同一层
满二叉树 基本思路:
建树,存储<键值,结点>的映射,存储结点所在层次,判断是否为满二叉树
sscanf读取字符串
*/
#include<cstdio>
#include<string>
#include<unordered_map>
#include<iostream>
using namespace std;
const int M=1e3+;
struct node
{
int data,high;
node *lchild,*rchild;
};
int in[M],pt[M],hs[M]={},fa[M]={},isfull=;
unordered_map<int,node*> mp; node *Create(int ptL, int ptR, int inL, int inR, int layer, int father)
{
if(ptL > ptR)
return NULL;
node *root = new node;
root->data = pt[ptR];
root->high = layer;
int k;
for(k=inL; k<=inR; k++)
if(in[k]==pt[ptR])
break;
int numLeft = k-inL;
root->lchild = Create(ptL,ptL+numLeft-,inL,k-,layer+, root->data);
root->rchild = Create(ptL+numLeft,ptR-,k+,inR,layer+, root->data);
hs[root->data]=;
fa[root->data]=father;
mp[root->data] = root;
if((root->lchild==NULL&&root->rchild!=NULL) || (root->lchild!=NULL&&root->rchild==NULL))
isfull=;
return root;
} int main()
{
#ifdef ONLINE_JUDGE
#else
freopen("Test.txt", "r", stdin);
#endif // ONLINE_JUDEG int n,m;
scanf("%d", &n);
for(int i=; i<n; i++)
scanf("%d", &pt[i]);
for(int i=; i<n; i++)
scanf("%d", &in[i]); node *root=Create(,n-,,n-,,-);
scanf("%d\n", &m);
while(m--)
{
int v1,v2;
string st;
getline(cin,st);
if(st.find("root") != string::npos)
{
sscanf(st.c_str(), "%d is the root", &v1);
if(v1 == pt[n-])
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("siblings") != string::npos)
{
sscanf(st.c_str(), "%d and %d are siblings", &v1,&v2);
if(hs[v1]== && hs[v2]== && fa[v1]==fa[v2])
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("parent") != string::npos)
{
sscanf(st.c_str(), "%d is the parent of %d", &v1,&v2);
if(hs[v1]== && hs[v2]== && fa[v2]==v1)
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("left") != string::npos)
{
sscanf(st.c_str(), "%d is the left child of %d", &v1,&v2);
if(hs[v1]== && hs[v2]== && mp[v2]->lchild==mp[v1])
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("right") != string::npos)
{
sscanf(st.c_str(), "%d is the right child of %d", &v1,&v2);
if(hs[v1]== && hs[v2]== && mp[v2]->rchild==mp[v1])
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("same") != string::npos)
{
sscanf(st.c_str(), "%d and %d are on the same level", &v1,&v2);
if(hs[v1]== && hs[v2]== && mp[v1]->high==mp[v2]->high)
printf("Yes\n");
else
printf("No\n");
}
else if(st.find("full") != string::npos)
{
if(isfull)
printf("Yes\n");
else
printf("No\n");
}
} return ;
}
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