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 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:
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
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<iostream>
#include<string>
#include<sstream>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<vector>
using namespace std;
#define inf 0x3f3f3f3f
#define LL long long
int post[1055],in[1055],le[1055];
int l[1005],r[1005],n;
int dfs(int postl,int postr,int inl,int inr)
{
if(postl>postr)return -1;
int root=post[postr];
int pos=inl;
while(in[pos]!=root)pos++;
int cnt=pos-inl;
l[root]=dfs(postl,postl+cnt-1,inl,pos-1);
r[root]=dfs(postl+cnt,postr-1,pos+1,inr);
return root;
}
void level(int x,int h)
{
le[x]=h;
if(l[x]!=-1) level(l[x],h+1);
if(r[x]!=-1) level(r[x],h+1);
}
int main()
{
int m,i,j;
memset(l,-1,sizeof l);
memset(r,-1,sizeof r);
scanf("%d",&n);
for(i=1;i<=n;i++)
scanf("%d",&post[i]);
for(i=1;i<=n;i++)
scanf("%d",&in[i]);
dfs(1,n,1,n);
int root=post[n];
scanf("%d",&m);
getchar();
while(m--)
{
string s,op,a[1005];
int p=0,f=1,x,y;
getline(cin,s);
stringstream ss(s);
while(ss>>op)
a[p++]=op;
if(s.find("root")!=-1)
{
stringstream su(a[0]);
su>>x;
if(x==root) f=0;
}
else if(s.find("siblings")!=-1)
{
stringstream su(a[0]);
su>>x;
stringstream sp(a[2]);
sp>>y;
int xf=0;
for(i=1;i<=n;i++)
{
if(l[post[i]]==x&&r[post[i]]==y)
{
xf=1;
break;
}
if(l[post[i]]==y&&r[post[i]]==x)
{
xf=1;
break;
}
}
if(xf)f=0;
}
else if(s.find("parent")!=-1)
{
stringstream su(a[0]);
su>>x;
stringstream sp(a[5]);
sp>>y;
//cout<<x<<" !!" <<y<<endl;
if(l[x]==y||r[x]==y)
f=0;
}
else if(s.find("left")!=-1)
{
stringstream su(a[0]);
su>>x;
stringstream sp(a[6]);
sp>>y;
if(l[y]==x)f=0;
}
else if(s.find("right")!=-1)
{
stringstream su(a[0]);
su>>x;
stringstream sp(a[6]);
sp>>y;
if(r[y]==x)f=0;
}
else if(s.find("level")!=-1)
{
level(root,0);
stringstream su(a[0]);
su>>x;
stringstream sp(a[2]);
sp>>y;
if(le[x]==le[y]) f=0;
}
else if(s.find("tree")!=-1)
{
int xf=0;
for(i=1;i<=n;i++)
{
if(l[post[i]]==-1&&r[post[i]]==-1)continue;
if(l[post[i]]!=-1&&r[post[i]]!=-1)continue;
xf=1;
}
if(xf==0)f=0;
}
if(f==0)printf("Yes\n");
else printf("No\n");
}
}