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)

/* C Binary Search Tree III */

#include<stdio.h>
#include<stdlib.h>

struct Node{
  int key;
  struct Node *parent;
  struct Node *left;
  struct Node *right;
};

struct Node *nil;
struct Node *root;
void init(){
  nil->key=-1;
  nil->parent=nil;
  nil->left=nil;
  nil->right=nil;
}

void Preorder(struct Node *u);
void Inorder(struct Node *u);

void TreeInsert(struct Node *T, struct Node *z);
struct Node *IterativeTreeSearch(struct Node *x, int k);
struct Node *TreeMinimum(struct Node *x);
struct Node *TreeSuccessor(struct Node *x);
struct Node *TreeDelete(struct Node *T, struct Node *z);

int main(){
  int n; /* command number */
  int k; 
  char com[6],c;
  int i;
  int j;
  struct Node *T;
  struct Node *z;
  struct Node *x;
  nil=malloc(sizeof(struct Node));
  init();
  /*scan*/
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s",com);
    if(com[0]=='i'){
      scanf("%d",&k);
      z=malloc(sizeof(struct Node));
      z->key=k;
      z->left=nil;
      z->right=nil;
      if(i==0)root=z;
      TreeInsert(T,z);
      T=z;
    }else if(com[0]=='p'){
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }else if(com[0]=='f'){
      scanf("%d",&k);
      x=IterativeTreeSearch(root,k);
      if(x==nil)printf("no\n");
      else printf("yes\n");
      //printf("find %d\n",k);
    }else{
      scanf("%d",&k);
      x=IterativeTreeSearch(root,k);
      TreeDelete(T,x);
    }
  }
  free(z);
  free(nil);
  return 0;
}
struct Node *TreeMinimum(struct Node *x){
  while(x->left!=nil){
    x=x->left;
  }
  return x;
}

struct Node *TreeSuccessor(struct Node *x){
  struct Node *y;
  if(x->right!=nil){
    return TreeMinimum(x->right);
  }
  y=x->parent;
  while(y!=nil&&x==y->right){
    x=y;
    y=y->parent;
  }
  return y;
}

struct Node *TreeDelete(struct Node *T, struct Node *z){
  struct Node *x;
  struct Node *y;
  if(z->left==nil||z->right==nil){
    y=z;
  }else{
    y=TreeSuccessor(z);
  }
  if(y->left!=nil){
    x=y->left;
  }else{
    x=y->right;
  }

  if(x!=nil){
    x->parent=y->parent;
  }
  if(y->parent==nil){
    root=x;
  }else if(y==y->parent->left){
    y->parent->left=x;
  }else{
    y->parent->right=x;
  }
  if(y!=z){
    z->key=y->key;
  }
  return y;
}

struct Node *IterativeTreeSearch(struct Node *x, int k){
  while(x!=nil&&x->key!=k){
    if(k<x->key){
      x=x->left;
    }else{
      x=x->right;
    }
  }
  return x;
}

void TreeInsert(struct Node *T, struct Node *z){
  struct Node *y;
  struct Node *x;
  y=nil;
  x=root;

  while(x!=nil){
    if(z==x)break;
    y=x;
    if(z->key<x->key){
      x=(x->left);
    }else{
      x=(x->right);
    }
  }
  z->parent=y;     
  if(y==nil){
    root=z; /* if T is empty */
  }else if(z->key<=y->key){
    y->left=z;
  }else{
    y->right=z;
  }
}

void Preorder(struct Node *u){
  if(u!=nil){
    printf(" %d",u->key);
    Preorder(u->left);
    Preorder(u->right);
  }
}

void Inorder(struct Node *u){
  if(u!=nil){
    Inorder(u->left);
    printf(" %d",u->key);
    Inorder(u->right);
  }
}