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>
#define nn 500000

typedef struct nnode_tbl{
	int k;
	int p;
	int l;
	int r;
} nnode;

const int nil=-1;
nnode t[nn];
int root;
int room;
int ix;

int tmin(int u){
  while (t[u].l!=nil)u=t[u].l;
	return u;
}

int find(int u, int k){
	while (u!=nil && k!=t[u].k){
		if (k<t[u].k)u=t[u].l;
		else u=t[u].r;
	}
	return u;
}

int trees(int u){
	if (t[u].r!=nil){
		return tmin(t[u].r);
  }
	int y=t[u].p;
	while (y!=nil && u==t[y].r){
		u=y;
		y=t[y].p;
	}
	return y;
}

void delete(int z){
	int y;
	int x;
	if (t[z].l == nil || t[z].r == nil)y = z;
	else y = trees(z);
	if (t[y].l!=nil)x=t[y].l;
	else{
		x=t[y].r;
  }
	if (x!=nil) t[x].p=t[y].p;
	if (t[y].p == nil)root=x;
	else{
		if (y==t[t[y].p].l){
			t[t[y].p].l=x;
    }
		else{
			t[t[y].p].r=x;
    }
	}
	if (y!=z)t[z].k=t[y].k;
	t[y].r=room;
	room=y;
}

void insert(int k){
	int z;
	int y = nil;
	int x = root;
	if (room==nil) z=ix++;
	else{
		z=room;
		room=t[room].r;
	}
	t[z].k=k;
	t[z].l=nil;
	t[z].r=nil;
	while (x!=nil){
		y=x;
		if (t[z].k<t[x].k)x=t[x].l;
		else x = t[x].r;
	}
	t[z].p=y;
	if (y==nil)root=z;
	else{
		if (t[z].k<t[y].k)t[y].l=z;
		else t[y].r = z;
	}
}

void inorder(int u){
	if (u==nil)return;
	inorder(t[u].l);
	printf(" %d", t[u].k);
	inorder(t[u].r);
}

void preorder(int u){
	if (u == nil) return;
	printf(" %d", t[u].k);
	preorder(t[u].l);
	preorder(t[u].r);
}

int main(int argc, char** argv){
	char com[8];
	int n;
	int x;
	int i;
	root=nil;
	room=-1;
	ix=0;
	scanf("%d", &n);
	for (i=0 ; i<n; i++){
		scanf("%s", com);
		switch (com[0]){
		case 'd':
			scanf("%d", &x);
			delete(find(root, x));
			break;

		case 'f':
			scanf("%d", &x);
			printf("%s\n", find(root, x) != nil ? "yes" : "no");
			break;

		case 'i':
			scanf("%d", &x);
			insert(x);
			break;

		case 'p':
		default:
			inorder(root);
			printf("\n");

			preorder(root);
			printf("\n");
			break;
		}
	}
  return 0;
}