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>
#include<string.h>
struct Node{
    int key;
    struct Node* per;
    struct Node* l;
    struct Node* r;
};
typedef struct Node node;
node* insert(node* px,int k);
void printI(node* x);
void printP(node* x);
node* find(node* px,int k);
void delete(node* px,int k);
node* next(node* px);

int main(void){
    int i;
    int n,k;
    node* x=NULL;
    char com[10];
    scanf("%d",&n);
    for(i=0;i<n;i++){
        scanf("%s",&com);
        if(strcmp(com,"insert")==0){
            scanf("%d",&k);
            x=insert(x,k);
        }else if(strcmp(com,"print")==0){
            printI(x);
            printf("\n");
            printP(x);
            printf("\n");
        }else if(strcmp(com,"find")==0){
            scanf("%d",&k);
            if(find(x,k)==NULL){
                printf("no\n");
            }else{
                printf("yes\n");
            }
        }else{
            scanf("%d",&k);
            delete(x,k);
        }
    }
    return 0;
}

node* insert(node* px,int k){
    node* x=px;
    node* y=NULL;
    node* z=(node*)malloc(sizeof(node));
    z->key=k;
    z->l=NULL;
    z->r=NULL;
    z->per=NULL;
    while(x!=NULL){
        y=x;
        if(z->key<x->key){
            x=x->l;
        }else{
            x=x->r;
        }
    }
    z->per=y;
    if(y==NULL){
        px=z;
    }else if(z->key<y->key){
        y->l=z;
    }else{
        y->r=z;
    }
    return px;
}

void printI(node* x){
    if(x->l != NULL){
        printI(x->l);
    }
    printf(" %d",x->key);
    if(x->r != NULL){
        printI(x->r);
    }
}

void printP(node* x){
    printf(" %d",x->key);
    if(x->l != NULL){
        printP(x->l);
    }
    if(x->r != NULL){
        printP(x->r);
    }
}

node* find(node* px,int k){
    while(1){
        if(px==NULL){
            return NULL;
        }
        if(px->key==k){
            return px;
        }
        if(px->key>k){
            px=px->l;
        }else{
            px=px->r;
        }
    }
}

void delete(node* px,int k){
    node* del;
    node* temp;
    int tk;
    del=find(px,k);
    if(del->l==NULL&&del->r==NULL){
        if(del->per->l==del){
            del->per->l=NULL;
        }else{
            del->per->r=NULL;
        }
        free(del);
    }else if(del->l!=NULL&&del->r==NULL){
        if(del->per->l==del){
            del->per->l=del->l;
            del->l->per=del->per;
        }else{
            del->per->r=del->l;
            del->l->per=del->per;
        }
        free(del);
    }else if(del->l==NULL&&del->r!=NULL){
        if(del->per->l==del){
            del->per->l=del->r;
            del->r->per=del->per;
        }else{
            del->per->r=del->r;
            del->r->per=del->per;
        }
        free(del);
    }else{
        tk=next(del)->key;
        delete(px,tk);
        del->key=tk;
    }
}

node* next(node* px){
    node* x;
    if(px->r!=NULL){
        px=px->r;
        while(px->l!=NULL){
            px=px->l;
        }
        return px;
    }
    x=px->per;
    while(x!=NULL&&px==x->r){
        px=x;
        x=x->per;
    }
    return x;
}