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>

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

struct Node *root,*NIL;

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

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

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

void treeDelete(struct Node *z){
	struct Node *y;
	struct Node *x;
	if(z->left== NIL || z->right==NIL){
		y=z;
	}else {
		y=treeSuccessor(z);
	}
	
	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);
}

void insert(int k){
	struct Node *y = NIL;
	struct Node *x = root;
	struct Node *z;
	
	z = (struct Node *)malloc(sizeof(struct Node));
	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;
	if(y == NIL){
		root = z;
	}else{
		if(z->key < y->key){
			y->left = z;
		}else{
			y->right = z;
		}
	}
}

void inorder(struct Node *u){
	if( u == NIL) return;
	inorder(u->left);
	printf(" %d",u->key);
	inorder(u->right);
}

void preorder(struct Node *u){
	if( u == NIL) return;
	printf(" %d",u->key);
	preorder(u->left);
	preorder(u->right);
}

int main(void){
	int n,i,x;
	scanf("%d",&n);
	int d;
	char string[10];
	
	for(i=0;i<n;i++){
		scanf("%s %d",string,&d);
		if(string[0]=='i'){
			insert(d);
		}else if(string[0]=='p'){
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}else if(string[0]=='f'){
			struct Node *t=find(root,d);
			if(t!=NIL){
				printf("yes\n");
			} else{
				printf("no\n");
			}
		}else if(string[0]=='d'){
			treeDelete(find(root,d));
		}
	}
	return 0;
}