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 N_MAX       500001
#define FOUND       1
#define NOT_FOUND   0

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

typedef struct node *Node;
Node root = NULL;

void delete(Node z){
    Node y;
    int tmpkey;
    
    if( z->left != NULL ){              /* 左の子を持つ */
        if( z->right != NULL ){         /* 右の子を持つ */
            /* 子を2つ持つ場合 */
            /* 探索用ノードに削除対象ノードをコピー */
            y = z->right;
            /* 探索用ノードが左の子を持たなくなるまで探索を続ける */
            while( y->left != NULL ){
                y = y->left;
            }
            /* 探索用ノードのキーを削除対象ノードのキーにコピー */
            z->key = y->key;
            /* yを削除する */
            delete(y);
        }else{                          /* 左の子を持ち、右の子を持たない */
            if(z == z->parent->left){   /* zの親の左の子がz */
                /* zの親の子をzの子に変更 */
                z->parent->left = z->left;
            }else{                      /* zの親の右の子がz */
                /* zの親の子をzの子に変更 */
                z->parent->right = z->left;
            }
            /* zの子の親をzの親に変更 */
            z->left->parent = z->parent;
            z = NULL;
        }
    }else if( z->right != NULL ){       /* 左の子を持たない、右の子を持つ */
            if(z == z->parent->left){      /* zの親の子が左の子 */
                /* zの親の子をzの子に変更 */
                z->parent->left = z->right;
            }else{
                /* zの親の子をzの子に変更 */
                z->parent->right = z->right;
            }
            /* zの子の親をzの親に変更 */
            z->right->parent = z->parent;
            z = NULL;
    }else{                              /* zが子を持たない */
        if(z == z->parent->left){       /* zの親の左の子がz */
            z->parent->left = NULL;
        }else{
            z->parent->right = NULL;
        }
    }
}


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

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

/* 中間順アルゴリズム */
void inorder(Node u){
    if(u == NULL){
        return;
    }
    inorder(u->left);
    printf(" %d",u->key);
    inorder(u->right);
}

/* 先行順アルゴリズム */
void preorder(Node u){
    if(u == NULL){
        return;
    }
    printf(" %d",u->key);
    preorder(u->left);
    preorder(u->right);
}

int main(){
    int n, i, x;
    Node findNode;
    char com[20];
    scanf("%d", &n);
    for( i = 0; i < n; i++ ){
        scanf("%s", com);
        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] == 'f' ){
            scanf("%d", &x);
            if(find(x,root) != NULL ){
                printf("yes\n");
            }else{
                printf("no\n");
            }
        }else if( com[0] == 'd' ){
            scanf("%d", &x);
            findNode = find(x,root);
            if(findNode != NULL){
                delete(findNode);
            }
        }
    }
    return 0;
}