Binary search trees - Binary Search Tree II

Time Limit : 2 sec, Memory Limit : 65536 KB
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Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

  • insert $k$: Insert a node containing $k$ as key into $T$.
  • find $k$: Report whether $T$ has a node containing $k$.
  • print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.

Constraints

  • The number of operations $\leq 500,001$
  • The number of print operations $\leq 10$.
  • $-2,000,000,000 \leq key \leq 2,000,000,000$
  • The height of the binary tree does not exceed 100 if you employ the above pseudo code.
  • The keys in the binary search tree are all different.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
 1 12 17 20 25 30 88
 30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.