DSA/algorithms/CPlusPlus/Trees/binary-search-tree.cpp

#include <iostream>
#include <cmath>


//Structure of the Tree
struct TreeNode{
    int data;
    TreeNode* left;
    TreeNode* right;
    TreeNode(const int& data): data(data), left(nullptr), right(nullptr){}
};

TreeNode* find(TreeNode* root, const int& data){
    /**
     * Find the node that contains the given data and
     * return that node
     *
     * @params: `root` root/parent node of the tree
     * @params: `data` data to be find in the tree
     * @return: tree node that contains the data
     *
     * Average case Time Complexity: O(log(n))
     * Worst case Time Complexity: O(n)
     *
     */

    if(root == nullptr)         { throw std::runtime_error("Error: find() cannot find the data. The data doesn't exist."); }
    else if(root->data == data) { return root; }
    else if(root->data < data)  { return find(root->right, data); }
    else                { return find(root->left, data); }
}

void Insert(TreeNode*& root, const int& data){
    /**
     * Create and Insert the node in the appropriate place of the tree
     *
     * @params: `root` root/parent node of the tree
     * @params: `data` data to be inserted in the tree
     * @return: void
     *
     * Average case Time Complexity: O(log(n))
     * Worst case Time Complexity: O(n)
     *
     */

    if(root == nullptr)         { root = new TreeNode(data); }
    else if(root->data == data) { throw std::runtime_error("The node already exist. Duplicates not allowed"); }
    else if(root->data < data)  { Insert(root->right, data); }
    else                { Insert(root->left, data); }
}


bool isfull(TreeNode* root){
        /**
         *
         * Check if a binary tree is full or not
         * A binary tree is full when every node in the 
         * tree has either two or zero child nodes.
         *
         * @params: `root` root/parent node of the tree
         *
         * @return: true if it the binary tree is full else false
         */

        if(root == nullptr)                                     { return true; }
        if(root->left == nullptr && root->right == nullptr)     { return true; }
        if((root->left != nullptr && root->right != nullptr) )  { return isfull(root->left) && isfull(root->right); }
        return false;
}

int depth(TreeNode* root){
        /**
         * Find the depth of the left most tree.
         * Here the depth of the left most tree is found but 
         * it is only a matter of preference.
         *
         * @params: `root` root/parent node of the tree
         *
         * @return: `d` returns the depth of the left most tree
         */

        int d = 0;
        while(root != nullptr){
                root = root->left;
                d++;
        }
        return d;
}


bool perfect_recursive(TreeNode* cur, int depth, int level = 0){
        /**
         * A Recursive strategy to check if a tree is perfect or not
         *
         * A binary tree is perfect if when all the inner node's
         * has two children and the all the leaf node's are at the
         * same level.
         *
         * @params: `cur`  node of the tree
         * @params: `depth` depth of the left most tree
         * @params: `level` level of the cur node
         *
         * @return: true if the binary tree is perfect else false
         */

        if(cur == nullptr)                                { return true; }
        if(cur->left == nullptr && cur->right == nullptr) { return depth == level; }
        if(cur->left != nullptr && cur->right != nullptr) {
                return perfect_recursive(cur->left, depth, level+1) && perfect_recursive(cur->right, depth, level+1);
        }
    return false;
}

int count_nodes(TreeNode* cur){
        /**
         * Count the number of node's in the tree
         * @params: `cur`  node of the tree
         */

        if(cur != nullptr){ return 1 + count_nodes(cur->left) + count_nodes(cur->right); }
    return 0;
}


int height(TreeNode* cur){
        /**
         * Find the height of the tree
         *
         * @params: `cur`  node of the tree
         */

        if(cur != nullptr){ return 1 + std::max(height(cur->left),  height(cur->right)); }
    return 0;
}

bool perfect(TreeNode* cur){
        /**
         * Knowing the height and the number of node's of
         * the tree we can find whether the tree is perfect or not
         *
         * A binary tree is perfect if when all the inner node's
         * has two children and the all the leaf node's are at the
         * same level.
         */

        int h = height(cur) - 1;
        int N = count_nodes(cur);
        if(N == pow(2, h+1) - 1) { return true; }
        return false;
}

bool isperfect(TreeNode* root){
        /**
         *
         * @params: `root` root/parent node of the tree
         *
         * @return: true if the binary tree is perfect else false
         */

        //if(perfect(root))                           { return true; }
        if(perfect_recursive(root, depth(root) - 1)) { return true; }
    return false;
}

void leaf_nodes(TreeNode* root) //Print all leafnode in BST
{ 
    /* * Node which does not have a child is called as LEAF Node.
       * Printing the nodes whose left and right pointer are null.
       * @params: `root` root/parent node of the tree
    */
   if (!root) 
       return; 

   if (root->left==NULL && root->right==NULL) 
   { 
       std::cout<<root->data<< " "; 
       return; 
   } 

   if (root->left) 
       leaf_nodes(root->left); 

   if (root->right) 
       leaf_nodes(root->right); 
} 

TreeNode* f_min(TreeNode* root) //Find Minimum element from root
{ 
    /**
     * Print the minimum value of the tree
     * 
     * @params: `root` root/parent node of the tree
     * @return: void
     */
    if(root==NULL)
    {
        std::cout<<"No value present in the tree"<< std::endl;
        return NULL;
    }
    TreeNode* p=root; 
    while(p->left!=NULL) 
    { 
        p=p->left; 
    } 
    return p;
} 

TreeNode* f_max(TreeNode* root) //Find Maximum element from root
{ 
    /**
     * Print the maximum value of the tree
     * 
     * @params: `root` root/parent node of the tree
     * @return: void
     */
    if(root==NULL)
    {
        std::cout<<"No value present in the tree"<< std::endl;
        return NULL;
    }
    TreeNode* p=root; 
    while(p->right!=NULL) 
    { 
        p=p->right; 
    }
    return p;
} 

TreeNode* bstdelete(TreeNode* root, int x) 
{ 
    TreeNode* m; 
    if(root==NULL) 
    { 
        std::cout<<"NOT FOUND!!"; 
        return root; 
    } 
    if(x < root->data) 
    { 
        root->left=bstdelete(root->left,x); 
        return root; 
    } 
    if(x>root->data) 
    { 
        root->right=bstdelete(root->right,x); 
        return root; 
    } 
    if(root->left==NULL && root->right==NULL) 
    { 
        m=root; 
        delete m; 
        return (NULL); 
    } 
    else if(root->left==NULL) 
    { 
        m=root; 
        root=root->right; 
        delete m; 
        return (root); 
    } 
    else if(root->right==NULL) 
    { 
        m=root; 
        root=root->left; 
        delete m; 
        return (root); 
    } 
    m=f_min(root->right); 
    root->data=m->data; 
    root->right=bstdelete(root->right, m->data); 
    return (root); 
}


void print(TreeNode* root){
    /**
     * Print the tree in an inorder fashion
     * 
     * @params: `root` root/parent node of the tree
     * @return: void
     */
    if(root != nullptr){
        print(root->left);
        std::cout << root->data << " ";
        print(root->right);
    }   
}

void free(TreeNode* root){
    /*
     * Free up the memory in the heap
     *
     * @params: `root` root/parent node of the tree
     */

    if(root != nullptr){
        free(root->left);
        free(root->right);
        delete root;
        root = nullptr;
    }
}

int main(){
    TreeNode* root = nullptr;

    Insert(root, 37);
    Insert(root, 19);
    Insert(root, 4);
    Insert(root, 22);
    Insert(root, 51);
    Insert(root, 55);
    Insert(root, 42);
    Insert(root, 20);
    Insert(root, 11);
    Insert(root, 2);
    
    print(root);

    TreeNode* n = find(root, 19);
    std::cout << "\nValue of n: " << n->data << std::endl;

    if(isfull(root)) { std::cout << "The binary tree is FULL" << std::endl; }
    else        { std::cout << "The binary tree is not FULL" << std::endl; }

    if(isperfect(root)) { std::cout << "The binary tree is PERFECT" << std::endl; }
    else           { std::cout << "The binary tree is not PERFECT" << std::endl; }

    std::cout << "Leaf Nodes present in the binary tree are : ";
    leaf_nodes(root);
    std::cout<< std::endl;
    
    n = f_max(root);
    if(n)
    {
        std::cout<<"Maximum Value Present in the tree is : "<<n->data<< std::endl;
    }

    n=f_min(root);
    if(n)
    {
        std::cout<<"Minimum Value Present in the tree is : "<<n->data<< std::endl;
    }

    root = bstdelete(root, 19);
    std::cout<<"Binary search Tree after Deletion is : "<<std::endl;;
    print(root);

    /* 
    Tree structure

            37
           /  \
          19  51
         / \   / \
        4  22 42 55
       /\   /   
      2 11  20

    OUTPUT:
     2 4 11 19 20 22 37 42 51 55 
     Value of n: 19
     The binary tree is not FULL
     The binary tree is not PERFECT
     Leaf Nodes present in the binary tree are : 2 11 20 42 55 
     Maximum Value Present in the tree is : 55
     Minimum Value Present in the tree is : 2
     Binary search Tree after Deletion is : 
     2 4 11 20 22 37 42 51 55 
    
     Tree structure after deletion
            37
           /  \
          11  51
         / \   / \
        4  22 42 55
       /   /   
      2   20
    
    */

    // free the memory
    free(root);
    return 0;
}