Binary Search Tree Algorithm
Binary search trees keep their keys in sorted order, so that lookup and other operations can use the principle of binary search: when looking for a key in a tree (or a place to insert a new key), they traverse the tree from root to leaf, make comparisons to keys stored in the nodes of the tree and deciding, on the basis of the comparison, to continue searching in the left or right subtrees. They let fast lookup, addition and removal of items, and can be used to implement either dynamic sets of items, or lookup tables that let finding an item by its key (e.g., finding the telephone number of a person by name).
#include <iostream>
using namespace std;
struct node
{
int val;
node *left;
node *right;
};
struct queue
{
node *t[100];
int front;
int rear;
};
queue q;
void enqueue(node *n)
{
q.t[q.rear++] = n;
}
node *dequeue()
{
return (q.t[q.front++]);
}
void Insert(node *n, int x)
{
if (x < n->val)
{
if (n->left == NULL)
{
node *temp = new node;
temp->val = x;
temp->left = NULL;
temp->right = NULL;
n->left = temp;
}
else
{
Insert(n->left, x);
}
}
else
{
if (n->right == NULL)
{
node *temp = new node;
temp->val = x;
temp->left = NULL;
temp->right = NULL;
n->left = temp;
}
else
{
Insert(n->right, x);
}
}
}
int findMaxInLeftST(node *n)
{
while (n->right != NULL)
{
n = n->right;
}
return n->val;
}
void Remove(node *p, node *n, int x)
{
if (n->val == x)
{
if (n->right == NULL && n->left == NULL)
{
if (x < p->val)
{
p->right = NULL;
}
else
{
p->left = NULL;
}
}
else if (n->right == NULL)
{
if (x < p->val)
{
p->right = n->left;
}
else
{
p->left = n->left;
}
}
else if (n->left == NULL)
{
if (x < p->val)
{
p->right = n->right;
}
else
{
p->left = n->right;
}
}
else
{
int y = findMaxInLeftST(n->left);
n->val = y;
Remove(n, n->right, y);
}
}
else if (x < n->val)
{
Remove(n, n->left, x);
}
else
{
Remove(n, n->right, x);
}
}
void BFT(node *n)
{
if (n != NULL)
{
cout << n->val << " ";
enqueue(n->left);
enqueue(n->right);
BFT(dequeue());
}
}
void Pre(node *n)
{
if (n != NULL)
{
cout << n->val << " ";
Pre(n->left);
Pre(n->right);
}
}
void In(node *n)
{
if (n != NULL)
{
In(n->left);
cout << n->val << " ";
In(n->right);
}
}
void Post(node *n)
{
if (n != NULL)
{
Post(n->left);
Post(n->right);
cout << n->val << " ";
}
}
int main()
{
q.front = 0;
q.rear = 0;
int value;
int ch;
node *root = new node;
cout << "\nEnter the value of root node :";
cin >> value;
root->val = value;
root->left = NULL;
root->right = NULL;
do
{
cout << "\n1. Insert";
cout << "\n2. Delete";
cout << "\n3. Breadth First";
cout << "\n4. Preorder Depth First";
cout << "\n5. Inorder Depth First";
cout << "\n6. Postorder Depth First";
cout << "\nEnter Your Choice : ";
cin >> ch;
int x;
switch (ch)
{
case 1:
cout << "\nEnter the value to be Inserted : ";
cin >> x;
Insert(root, x);
break;
case 2:
cout << "\nEnter the value to be Deleted : ";
cin >> x;
Remove(root, root, x);
break;
case 3:
BFT(root);
break;
case 4:
Pre(root);
break;
case 5:
In(root);
break;
case 6:
Post(root);
break;
}
} while (ch != 0);
}
