Problem:
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 $\leq 500,000$

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.

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

struct node {
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL

Node root;

Node treeMinimum(Node x) {
  while(x -> left != NIL) {
    x = x -> left;
  }
  return x;
}

Node treeSearch(Node u, int k) {
  if(u == NIL || k == u -> key) {
    return u;
  }
  if(k < u -> key) {
    return treeSearch(u -> left, k);
  }
  else {
    return treeSearch(u -> right, k);
  }
}

Node treeSuccessor(Node x) {
  Node y;
  if(x -> right != NIL) {
    return treeMinimum(x -> right);
  }
  y = x -> parent;
  while(y != NIL && x == y -> right) {
    x = y;
    y = y -> parent;
  }
  return y;
}

void treeDelete(Node z) {
  Node y;
  Node x;
} 

void insert(int k) {
  Node y = NIL;
  Node x = root;
  Node z;
  
  z = malloc(sizeof(struct node));
  z -> key = k;
  z -> left = NIL;
  z -> right = NIL;
  
  while(x != NIL) {
    y = x;
    if(z -> key < x -> key) {
      x = x -> left;
    }
    else {
      x = x -> right;
    }
  }
  z -> parent = y;
  if(y == NIL) {
    root = z;
  }
  else if(z -> key < y -> key) {
    y -> left = z;
  }
  else {
    y -> right = z;
  }
}

void inorder(Node u) {
  if(u != NIL) {
    inorder(u -> left);
    printf(" %d", u -> key);
    inorder(u -> right);
  }
}

void preorder(Node u) {
  printf(" %d", u -> key);
  if(u != NIL) {
    if(u -> left != NIL) preorder(u -> left);
    if(u -> right != NIL) preorder(u -> right);
  }
}

main() {
  int n, i, x;
  char com[20];
  scanf("%d", &n);

  for(i = 0; i < n; i++) {
    scanf("%s", com);
    if(com[0] == 'f') {
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if(t != NIL) printf("yes\n");
      else printf("no\n");
    }
    else if(com[0] == 'i') {
      scanf("%d", &x);
      insert(x);
    }
    else if(com[0] == 'p') {
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(com[0] == 'd') {
      scanf("%d", &x);
      treeDelete(treeSearch(root, x));
    }
  }
  return 0;
}