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 <string.h>
#include <stdlib.h>

struct Node{
	int key;
	struct Node *r,*l,*p;
}Node;

struct Node *root , *NIL;

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->l = NIL;
	z->r = NIL;
	
	while( x != NIL ){
		y = x;
		if( z->key < x->key ){
			x = x->l;
		}else{
			x = x->r;
		}
	}
	z->p = y;
	
	if( y == NIL ){
		root = z;
	}else{
		if( z->key < y->key ){
			y->l = z;
		}else{
			y->r = z;
		}
	}
}

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

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

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

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

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

void treeDelete(struct Node *z ){
	struct Node *y;
	struct Node *x;
	
	if( z->l == NIL || z->r == NIL ){
		y = z;
	}else{
		y = treeSuccessor(z);
	}
	
	if( y->l != NIL ){
		x = y->l;
	}else{
		x = y->r;
	}
	
	if( x != NIL ){
		x->p = y->p;
	}
	
	if( y->p == NIL ){
		root = x;
	}else{
		if( y == y->p->l ){
			y->p->l = x;
		}else{
			y->p->r = x;
		}
	}
	
	if( y != z ){
		z->key = y->key;
	}
	
	free(y);
}

int main( void ){
	
	int n , i , x;
	char com[10];
	
	scanf( "%d" , &n );
	
	for( i = 0; i < n; i++ ){
		
		scanf( "%s" , com );
		if( strcmp(com , "find") == 0 ) {
			scanf( "%d" , &x );
			struct Node *t = find(root,x);
			if( t!= NIL ){
				printf( "yes\n" );
			}else{
				printf( "no\n" );
			}
		}else if( strcmp(com ,"insert") == 0 ){
			scanf( "%d" , &x );
			insert(x);
		}else if( strcmp(com ,"print") == 0 ){
			inorder(root);
			printf( "\n" );
			preorder(root);
			printf( "\n" );
		}else if( strcmp(com ,"delete") == 0 ){
			scanf( "%d" , &x );
			treeDelete( find(root , x ));
		}
	}
	
	return 0;
}