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>

int get_int() {
    int n = 0;
    int c = getchar_unlocked();
    if(c == 45) {
        c = getchar_unlocked();
        while(47 < c && c < 58) n = 10 * n + (c & 0xf), c = getchar_unlocked();
        return -n;
    } else if(c < 48 || 57 < c) return c;
    while(47 < c && c < 58) n = 10 * n + (c & 0xf), c = getchar_unlocked();
    return n;
}
int get_str(char *str) {
    int c;
    while((c = getchar_unlocked()) > 32) *str++ = (char)c;
    *str = 0;
    return c;
}
void put_int(int n) {
    if(!n) {
        putchar_unlocked('0');
        return;
    }
    if(n < 0) n = -n, putchar_unlocked('-');
    char buf[11];
    int i = 0;
    while(n) buf[i++] = (char)(n % 10 + '0'), n /= 10;
    while(i--)putchar_unlocked(buf[i]);
}
void put_str(char *str) { while(*str) putchar_unlocked(*str++); }

typedef struct Node {
    int key;
    struct Node *left, *right;
} Node;
typedef struct BST {
    Node *root;
    size_t size;
} BST;
void bst_init(BST *BST) {
    BST->root = NULL;
    BST->size = 0;
}
void bst_insert(BST *BST, int key) {
    Node *new_node = malloc(sizeof(Node));
    new_node->key = key;
    new_node->left = NULL;
    new_node->right = NULL;
    Node *tmp;
    Node *root = BST->root;
    while(root != NULL) {
        tmp = root;
        if(key < root->key) root = root->left;
        else root = root->right;
    }
    if(BST->size == 0) BST->root = new_node;
    else if(key < tmp->key) tmp->left = new_node;
    else tmp->right = new_node;
    BST->size++;
}
Node *bst_find(const Node *root, const int key) {
    while(root != NULL && root->key != key) {
        if(key < root->key) root = root->left;
        else root = root->right;
    }
    return root;
}
Node *bst_get_min(Node *root) {
    while(root->left != NULL) root = root->left;
    return root;
}
Node *bst__delete(Node *root, int key) {
    if(root == NULL) return NULL;
    if(key < root->key) root->left = bst__delete(root->left, key);
    else if(key > root->key) root->right = bst__delete(root->right, key);
    else if(root->left && root->right) {
        Node *tmp = bst_get_min(root->right);
        root->key = tmp->key;
        root->right = bst__delete(root->right, tmp->key);
    } else {
        Node *tmp = root;
        if(root->left) root = root->left;
        else if(root->right) root = root->right;
        else root = NULL;
        free(tmp);
    }
    return root;
}
void bst_delete(BST *BST, int key) {
    bst__delete(BST->root, key);
    BST->size--;
}
void bst_inorder(Node *root) {
    if(root == NULL) return;
    bst_inorder(root->left);
    putchar_unlocked(' '), put_int(root->key);
    bst_inorder(root->right);
}
void bst_preorder(Node *root) {
    if(root == NULL) return;
    putchar_unlocked(' '), put_int(root->key);
    bst_preorder(root->left);
    bst_preorder(root->right);
}
int main(int argc, char **argv) {
    BST BST;
    bst_init(&BST);
    int m = get_int();
    int key;
    char c[8];
    for(int i = 0; i < m; ++i) {
        get_str(c);
        switch(*c) {
        case 'i':
            key = get_int();
            bst_insert(&BST, key);
            break;
        case 'f':
            key = get_int();
            put_str(bst_find(BST.root, key) ? "yes\n" : "no\n");
            break;
        case 'd':
            key = get_int();
            bst_delete(&BST, key);
            break;
        default:
            bst_inorder(BST.root);
            putchar_unlocked('\n');
            bst_preorder(BST.root);
            putchar_unlocked('\n');
            break;
        }
    }
    return 0;
}