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>
#include <limits.h>

typedef struct Node* NodePointer;

struct Node{
    NodePointer parent;
    NodePointer left,right;
    int key;
};

void treeInitialize(void);
NodePointer makeNode(int);
void treeInsert(NodePointer,int);
NodePointer treeSearch(NodePointer,int);
NodePointer treeSuccessor(NodePointer);
NodePointer treeMaximum(NodePointer);
NodePointer treeMinimum(NodePointer);
void treeDelete(int);
void inorder(NodePointer);
void preorder(NodePointer);
NodePointer getNext(NodePointer,int);

NodePointer head,tail;

int main(){
    int i,N,x;
    char str[7];
    NodePointer p;
    treeInitialize();
    scanf("%d",&N);
    for(i = 0 ; i < N ; i++){
        scanf("%s",str);
        if(str[0] == 'i'){
            scanf("%d",&x);
            treeInsert(head, x);
        }else if(str[0] == 'f'){
            scanf("%d",&x);
            p = treeSearch(head, x);
            if(p == tail){
                printf("no\n");
            }else{
                printf("yes\n");
            }
        }else if(str[0] == 'd'){
            scanf("%d",&x);
            treeDelete(x);
        }else{
            inorder(head->right);
            printf("\n");
            preorder(head->right);
            printf("\n");
        }
    }
    return 0;
}

void treeInitialize(){
    head = makeNode(INT_MIN);
    tail = makeNode(INT_MIN);
    head->left = head->right = tail;
    head->parent = tail->parent = head;
}

NodePointer makeNode(int key){
    NodePointer x = malloc(sizeof(struct Node));
    x->left = x->right = tail;
    x->key = key;
    return x;
}

void treeInsert(NodePointer p,int key){
    NodePointer next = getNext(p, key);
    if(next == tail){
        if(key < p->key){
            p->left = makeNode(key);
            p->left->parent = p;
        }else{ 
            p->right = makeNode(key);
            p->right->parent = p;
        }
    }else{
        treeInsert(next,key);
    }
}

NodePointer treeSearch(NodePointer p,int key){
    if(p == tail) return tail;
    return (p->key == key ? p : treeSearch(getNext(p,key),key));
}

NodePointer treeSuccessor(NodePointer p){
    NodePointer x = p->parent;
    if(p->right != tail){
        return treeMinimum(p->right);
    }
    while(x != head && p == x->right){
        p = x;
        x = x->parent;
    }
    return x;
}

NodePointer treeMinimum(NodePointer p){
    return (p->left == tail ? p : treeMinimum(p->left));
}

NodePointer treeMaximum(NodePointer p){
    return (p->right == tail ? p : treeMaximum(p->right));
}

void treeDelete(int key){
    NodePointer x,y;
    NodePointer z = treeSearch(head,key);
    if(z == tail) return;
    if(z->left == tail || z->right == tail){
        y = z;
    }else{
        y = treeSuccessor(z);
    }
    if(y->left != tail){
        x = y->left;
    }else{
        x = y->right;
    }
    if(x != tail){
        x->parent = y->parent;
    }
    if(y->parent == head){
        head = 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 inorder(NodePointer p){
    if(p != tail){
        inorder(p->left);
        printf(" %d",p->key);
        inorder(p->right);
    }
}

void preorder(NodePointer p){
    if(p != tail){
        printf(" %d",p->key);
        preorder(p->left);
        preorder(p->right);
    }
}

NodePointer getNext(NodePointer p,int key){
    return (key < p->key ? p->left : p->right);
}