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 MAX 100

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

Node *root, *NIL;

void insert(int);
Node *find(int, Node *);
void inorder(Node *);
void preorder(Node *);
void delete(Node *);
Node *successor(Node *);
Node *min(Node *);

int main()
{
    int m, i, k, j, con;
    char com[MAX], judge[MAX];
    char y = 'y', n = 'n';

    scanf("%d", &m);
    for (i = 0; i < m; i++)
    {
        scanf("%s", com);
        if (com[0] == 'f')
        {
            scanf("%d", &k);
            Node *u = find(k, root);
            if (u != NIL)
            {
                printf("yes\n");
            }
            else
            {
                printf("no\n");
            }
        }
        else if (com[0] == 'i')
        {
            scanf("%d", &k);
            insert(k);
        }
        else if (com[0] == 'p')
        {
            inorder(root);
            printf("\n");
            preorder(root);
            printf("\n");
        }
        else if (com[0] == 'd')
        {
            scanf("%d",&k);
            delete(find(k,root));
        }
    }
    return 0;
}

void insert(int k)
{
    Node *y = NIL;
    Node *x = root;
    Node *z;

    z = (Node *)malloc(sizeof(Node)); //ノードを作る
    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; //insertした値の親を設定する
    if (y == NIL)
    { //親がない場合insertした値がそのままroot
        root = z;
    }
    else
    {
        if (z->key < y->key)
        {
            y->left = z;
        }
        else
        {
            y->right = z;
        }
    }
}

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

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);
}

void delete(Node *z)
{
    Node *y; //削除する対象
    Node *x;//yの子
    
    if(z->left == NIL || z->right == NIL){
        y=z;
    }else y = successor(z);

    // yの子xを決める
    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);
}

Node *successor(Node *x){
    if(x->right != NIL) return min(x->right);
    Node *y=x->parent;
    while(y!=NIL && x==y->right){
        x=y;
        y=y->parent;
    }
    return y;
}

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