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

typedef struct node * Node;


Node root;

Node treeMim(Node x){

    while(x->left != NULL){
        x = x->left;
    }
    return x;
}


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


Node TreeSuccessor(Node x){
    Node y, p;
    if(x->right != NULL){
        return treeMim(x->right);
    }
    y = x->parent;
    while(y != NULL && x == y->right){
        x = y;
        y = y->parent;
    }
    return y;
}

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

    if(z->left == NULL || z->right == NULL){
        y = z;
    }else{
        y = TreeSuccessor(z);
    }
    if(y->left != NULL){
        x = y->left;
    }else{
        x = y->right;
    }
    if(x != NULL){
        x->parent = y->parent;
    }
    if(y->parent == NULL){
        root = x;
    }else if(y == y->parent->left){
        y->parent->left = x;
    }else{
        y->parent->right = x;
    }

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

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


int main(){
    int n=0, i, x;
    char com[20];
    scanf("%d", &n);

    for (i=0; i<n; i++){
        scanf("%s", &com[0]);
        x = 0;
        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;
}