Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ 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

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

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);
  }
    
}