Binary Search Tree III Aizu - ALDS1_8_C
Write a program which performs the following operations to a binary search tree by adding delete operation to B: Binary Search Tree II.
insert : Insert a node containing as key into .
find : Report whether has a node containing .
delete : Delete a node containing .
print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.
The operation delete for deleting a given node containing key from can be implemented by an algorithm which considers the following cases:
If has no children, we modify its parent to replace with NIL as its child (delete ).
If has only a single child, we “splice out” by making a new link between its child and its parent.
If has two children, we splice out 's successor and replace 's key with 's key.
Input
In the first line, the number of operations is given. In the following lines, operations represented by insert , find , delete or print are given.
Output
For each find operation, print “yes” if has a node containing , “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
The number of print operations .
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;
}
