Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

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

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

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>
#define NIL NULL

struct node{
    int key;
    struct node *right,*left,*parent;
};

typedef struct node *Node;

Node root;

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

Node find(Node u,int k){
    while(u != NIL && k != u->key){
        if(k < u->key)u = u->left;
        else u = u->right;
    }
    return u;
}


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

void Tdelete(Node z){
    Node x,y;

    if(z->left == NIL || z->right == NIL)y=z;
    else y=Tsuccessor(z);

    if(y->left != NIL){
        x=y->left;
    } else{
        x=y->right;
    }

    if(x != NIL){
        x->parent = y->parent;
    }

    if(y->parent == NIL){
        root=x;
    } else{
        if(y == y->parent->left){
            y->parent->left=x;
        }else{
            y->parent->right=x;
        }
    }

    if(y!=z){
        z->key=y->key;
    }

    free(y);
}

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) return;

    inorder(u->left);
    printf(" %d",u->key);
    inorder(u->right);

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


int main(){
    int i,n,x;
    char com[20];
    Node t;

    scanf("%d",&n);
    for(i=0;i<n;i++){
        scanf("%s",com);
        if(com[0]=='f'){
            scanf("%d",&x);
            t=find(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);
            Tdelete(find(root,x));
        }
    }
    return 0;
}