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 id;
struct node* parentNode;
struct node* leftChild;
struct node* rightChild;
   
};
   
struct node *createNode(int);
void insert(struct node*);
void printNodes(void);
struct node* findNode(int, struct node*);
void deleteNode(struct node*);
struct node* getSuccessor(struct node*);
void preOrder(struct node *);
void inOrder(struct node *);
   
struct node* nodes[500002];
struct node* root;
  
int num_nodes=0, n; 
  
main(){
   
int i, id;
char com[7];
 struct node* tmpNode;
   
scanf("%d",&n);
   
for(i=0; i<n; i++){
   
scanf("%s",com);
if(com[0]=='i'){
scanf("%d",&id);
insert(createNode(id));
}else if(com[0]=='d'){
scanf("%d",&id);
deleteNode(findNode(id, root));
}else if(com[0]=='p'){
printNodes();
}else if(com[0]=='f'){
scanf("%d",&id);
    if(findNode(id, root)!=NULL){
        printf("yes\n");    
    }else{
        printf("no\n"); 
    }
}
   
}/* END OF LOOP */
  
 return 0;
   
}
  
struct node *createNode(int id){
  struct node *newNode;
  if(id<0) return NULL;
  
  newNode=(struct node*)malloc(sizeof(struct node));
  newNode->id=id;
  newNode->parentNode=NULL;
  newNode->rightChild=NULL;
  newNode->leftChild=NULL;
    
  nodes[num_nodes++]=newNode;
  return newNode;
}
   
void insert(struct node* z){
   
  struct node* y = NULL;
  struct node* x = root;
  
  while(x != NULL){
    y = x;
    if(z->id < x->id){
      x = x->leftChild;
    }else{
      x = x->rightChild;
    }
  }
  z->parentNode = y;
  if(y == NULL){
    root = z;
  }else{
    if(z->id < y->id){
      y->leftChild = z;
    }else{
      y->rightChild = z;
    }
  }
   
}
   
void printNodes(void){
     
  inOrder(root);
  printf("\n");
  preOrder(root);
  printf("\n"); 
  
}
 
struct node* findNode(int searchingId, struct node* nd){
     
    if(nd->id == searchingId) return nd;
    if(nd->id < searchingId && nd->rightChild){
        return findNode(searchingId, nd->rightChild);
    }
    if(nd->id > searchingId && nd->leftChild){
        return findNode(searchingId, nd->leftChild);
    }
    return NULL;
     
}

struct node* getSuccessor(struct node* nd){
	
	struct node* tmp;
	struct node* y;
	
	if(nd->rightChild != NULL){
		tmp = nd->rightChild;
		while(tmp->leftChild != NULL){
			tmp = tmp->leftChild;
		}
		return tmp;
	}
	y = nd->parentNode;
	while(y != NULL && nd == y->rightChild){
		nd = y;
		y = y->parentNode;
	}
	return y;
	
}

void deleteNode(struct node* z){
	
	struct node* x;
	struct node* y;
	
	if(z==NULL) return;
	
	if(z->leftChild == NULL
	|| z->rightChild == NULL){
		y = z;	
	}else{
		y = getSuccessor(z);	
	}
	
	if(y->leftChild != NULL){
		x = y->leftChild;	
	}else{
		x = y->rightChild;	
	}
	
	if(x != NULL){
		x->parentNode = y->parentNode;	
	}
	
	if(y->parentNode == NULL){
		root = x;	
	}else{
		if(y == y->parentNode->leftChild){
			y->parentNode->leftChild = x;
		}else{
			y->parentNode->rightChild = x;	
		}
	}
	
	if(y != z){
		z->id = y->id;	
	}
	
}
   
void preOrder(struct node* nd){
  printf(" %d",nd->id);
  if(nd->leftChild){
    preOrder(nd->leftChild);
  }
  if(nd->rightChild){
    preOrder(nd->rightChild);
  }
   
}
   
void inOrder(struct node* nd){
  if(nd->leftChild){
    inOrder(nd->leftChild);
  }
  printf(" %d",nd->id);
  if(nd->rightChild){
    inOrder(nd->rightChild);
  }
   
}