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>

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

Node *sum,*num;

void xu(int k);
Node* fan(int k);
void delete(int k);
void malon(Node *x);
void rin(Node *x);

int main(){
	int i,n,x;	scanf("%d",&n);
	char rum[10];

	for(i=0;i<n;i++){
		scanf("%s",rum);
		if(rum[0]=='i'){
			scanf("%d",&x);
			xu(x);

		}else if(rum[0]=='p'){
			malon(sum);
			printf("\n");
			rin(sum);
			printf("\n");
		}else if(rum[0]=='f'){
			scanf("%d",&x);
			if(fan(x)!=num)printf("yes\n");
			else printf("no\n");
		}else{
			scanf("%d",&x);
			delete(x);
		}
	}
	return 0;
}

void xu(int k){
	Node *y=num, *x=sum, *z;

	z=(Node*)malloc(sizeof(Node));

	z->key=k;	z->left=num;	z->right=num;

	while(x!=num){
		y=x;
		if(k < x->key){
			x=x->left;
		}else{
			x=x->right;
		}
	}
	z->parent=y;

	if(y==num)sum=z;
	else{
		if(k < y->key){
			y->left = z;
		}else{
			y->right=z;
		}
	}
}

Node* fan(int k){
	Node* p=sum;

	while(p!=num){
		if(p->key==k){
			return p;
		}

		if(k < p->key)p=p->left;
		else p=p->right;
	}

	return num;
}

void delete(int k){
	Node *tgt=fan(k),*ma,*lon;

	if(tgt->left==num || tgt->right==num){
		ma=tgt;
	}else{
		ma=tgt->right;
		while(ma->left!=num)ma=ma->left;
	}

	if(ma->left!=num){
		lon=ma->left;
	}else{
		lon=ma->right;
	}
	if(lon!=num)	lon->parent=ma->parent;

	if(ma->parent==num){
		sum=lon;
	}else{
		if(ma==ma->parent->left){
			ma->parent->left=lon;
		}else{
			ma->parent->right=lon;
		}
	}

	if(ma!=tgt)tgt->key=ma->key;

	free(ma);
	return;
}

void malon(Node* x){
	if(x==num)return;
    malon(x->left);
	printf(" %d",x->key);
	malon(x->right);
}
void rin(Node* x){
	if(x==num)return;
	printf(" %d",x->key);
	rin(x->left);
	rin(x->right);
}