Binary Search Tree III Aizu

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.

Code

/*
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 */
// Virtual_Judge —— Binary Search Tree III Aizu - ALDS1_8_C.cpp created by VB_KoKing on 2019-05-10:08.
/* Procedural objectives：

 Variables required by the program:

 Procedural thinking：

 Functions required by the program:
 
 Determination algorithm:
 
 Determining data structure:
 

*/
/* My dear Max said：
"I like you,
So the first bunch of sunshine I saw in the morning is you,
The first gentle breeze that passed through my ear is you,
The first star I see is also you.
The world I see is all your shadow."

FIGHTING FOR OUR FUTURE！！！
*/
#include <iostream>
#include <cstdlib>
#include <string>

using namespace std;

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

Node *root, *NIL;

Node *tree_minimum(Node *x) {
    while (x->left != NIL)
        x = x->left;
    return x;
}

Node *find(Node *u, int k) {
    while (u != NIL && k != u->key) {
        if (k<u->key) u=u->left;
        else u=u->right;
    }
    return u;
}

Node *tree_successor(Node *x){
    if (x->right!=NIL) return tree_minimum(x->right);
    Node *y=x->parent;
    while(y!=NIL&&x==y->right){
        x=y;
        y=y->parent;
    }
    return y;
}

void tree_delete(Node *z){
    Node *x,*y;
    if (z->left==NIL||z->right==NIL) y=z;
    else y=tree_successor(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;

    free(y);
}

void insert(int k) {
    Node *y = NIL;
    Node *x = root;
    Node *z;

    z = (Node *) malloc(sizeof(Node));
    z->key = k;
    z->left = NIL;
    z->right = NIL;

    while (x != NIL) {
        y = x;
        if (z->key < x->key)
            x = x->left;
        else
            x = x->right;
    }

    z->parent = y;
    if (y == NIL)
        root = z;
    else {
        if (z->key < y->key)
            y->left = z;
        else y->right = z;
    }
}

//前序遍历
void pre_parse(Node *u) {
    if (u == NIL) return;
    cout << " " << u->key;
    pre_parse(u->left);
    pre_parse(u->right);
}

//中序遍历
void in_parse(Node *u) {
    if (u == NIL) return;
    in_parse(u->left);
    cout << " " << u->key;
    in_parse(u->right);
}

int main() {
    int n;
    string com;
    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> com;
        if (com == "insert") {
            int x;
            cin >> x;
            insert(x);
        } else if (com == "print") {
            in_parse(root);
            cout << endl;
            pre_parse(root);
            cout << endl;
        } else if (com=="find"){
            int x;
            cin>>x;
            Node *t=find(root,x);
            if (t!=NIL) cout<<"yes"<<endl;
            else cout<<"no"<<endl;
        } else if (com=="delete"){
            int x;
            cin>>x;
            tree_delete(find(root,x));
        }
    }
    return 0;
}