Implementing Forward Iterator in BST

Given a Binary search tree, the task is to implement forward iterator on it with the following functions.

curr(): returns the pointer to current element.
next(): iterates to the next smallest element in the Binary Search Tree.
isEnd(): returns true if there no node left to traverse else false.

Iterator traverses the BST in sorted order(increasing). We will implement the iterator using a stack data structure.

Initialisation:

We will create a stack named “q” to store the nodes of BST.

Create a variable “curr” and initialise it with pointer to root.

While “curr” is not NULL

Push “curr” in the stack ‘q’.

Set curr = curr -> left

curr()

Returns the value at the top of the stack ‘q’.
Note: It might throw segmentation fault if the stack is empty.

Time Complexity: O(1)

next()

Declare pointer varaible “curr” which points to node.

Set curr = q.top()->right.

Pop top most element of stack.

While “curr” is not NULL

Push “curr” in the stack ‘q’.

Set curr = curr -> left.

Time Complexity: O(1) on average of all calls. Can be O(h) for a single call in the worst case.

isEnd()

Returns true if stack “q” is empty else return false.

Time Complexity: O(1)
Worst Case space complexity for this implementation of iterators is O(h). It should be noticed that
iterator points to the top-most element of the stack.

Below is the implementation of the above approach:

// C++ implementation of the approach 
#include <bits/stdc++.h> 
using namespace std; 
  
// Node of the binary tree 
struct node { 
    int data; 
    node* left; 
    node* right; 
    node(int data) 
    { 
        this->data = data; 
        left = NULL; 
        right = NULL; 
    } 
}; 
  
// Iterator for BST 
class bstit { 
private: 
    // Stack to store the nodes 
    // of BST 
    stack<node*> q; 
  
public: 
    // Constructor for the class 
    bstit(node* root) 
    { 
        // Initializing stack 
        node* curr = root; 
        while (curr != NULL) 
            q.push(curr), curr = curr->left; 
    } 
  
    // Function to return 
    // current element iterator 
    // is pointing to 
    node* curr() 
    { 
        return q.top(); 
    } 
  
    // Function to iterate to next 
    // element of BST 
    void next() 
    { 
        node* curr = q.top()->right; 
        q.pop(); 
        while (curr != NULL) 
            q.push(curr), curr = curr->left; 
    } 
  
    // Function to check if 
    // stack is empty 
    bool isEnd() 
    { 
        return !(q.size()); 
    } 
}; 
  
// Function to iterator to every element 
// using iterator 
void iterate(bstit it) 
{ 
    while (!it.isEnd()) 
        cout << it.curr()->data << " ", it.next(); 
} 
  
// Driver code 
int main() 
{ 
    node* root = new node(5); 
    root->left = new node(3); 
    root->right = new node(7); 
    root->left->left = new node(2); 
    root->left->right = new node(4); 
    root->right->left = new node(6); 
    root->right->right = new node(8); 
  
    // Iterator to BST 
    bstit it(root); 
  
    // Function to test iterator 
    iterate(it); 
  
    return 0; 
} 

Output:

2 3 4 5 6 7 8

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