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 *l, *r, *p;
};

struct Node *root, *NIL;

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

struct Node *tSuc(struct Node *v){
	struct Node *y;
	if(v->r != NIL) return tMin(v->r);
	y = v->p;
	while(y != NIL && v == y->r){
		v = y;
		y = y->p;
	}
	return y;
}

void tDelete(struct Node *z){
	struct Node *y; //?????????????±?
	struct Node *x; //y??????

	// ??????????????????????±???????
	if(z->l == NIL || z->r == NIL)y=z;
	else y =tSuc(z);
	//y??????????±???????
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);
}



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;
}

void insert(int v){
struct Node *y = NIL;
struct Node *x = root;
struct Node *z;

z = (struct Node *)malloc(sizeof(struct Node));
z->key = v;
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 Iorder(struct Node *u){
	if(u == NIL){
		return;
	}
	Iorder(u->l);
	printf(" %d", u->key);
	Iorder(u->r);
}
void Porder(struct Node *u){
	if(u == NIL){
		return;
	}
	printf(" %d", u->key);
	Porder(u->l);
	Porder(u->r);
}

int main(){
	int n,i,v;
  struct Node *t;
	char *sent = malloc(7);
char *s1 = "insert";
char *s2 = "print";
char *s3 = "delete";
	scanf("%d",&n);

	for(i = 0;i <n;i++){

		scanf("%6s",sent);
    if(sent[0] == 'f'){
      scanf("%d",&v);
      t = find(root,v);
      if(t != NIL)printf("yes\n");
      else printf("no\n");
    }
		else if(0==strcmp(sent,s1)){
			scanf("%d", &v);
			insert(v);
		}
		else if(0==strcmp(sent,s2)){
			Iorder(root);
			printf("\n");
			Porder(root);
			printf("\n");
		}
		else if(0==strcmp(sent,s3)){
			scanf("%d",&v);
			tDelete(find(root, v));
		}
	}

return 0;
}