Find maximum and minimum element in binary tree without using recursion or stack or queue

Given a binary tree. The task is to find out the maximum and minimum element in a binary tree without using recursion or stack or queue i.e, space complexity should be O(1).

Examples:

Input : 
                       12
                     /     \
                   13       10
                          /     \
                       14       15
                      /   \     /  \
                     21   24   22   23

Output : Max element : 24
         Min element : 10

Input : 
                       12
                     /     \
                  19        82
                 /        /     \
               41       15       95
                 \     /         /  \
                  2   21        7   16

Output : Max element : 95
         Min element : 2

Prerequisite : Inorder Tree Traversal without recursion and without stack

Approach :
1. Initialize current as root
2. Take to variable max and min
3. While current is not NULL

  • If the current does not have left child
    • Update variable max and min with current’s data if required
    • Go to the right, i.e., current = current->right
  • Else
    • Make current as the right child of the rightmost
      node in current’s left subtree
    • Go to this left child, i.e., current = current->left

Below is the implementation of the above approach :

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// C++ program find maximum and minimum element
#include <bits/stdc++.h>
using namespace std;
  
// A Tree node
struct Node {
    int key;
    struct Node *left, *right;
};
  
// Utility function to create a new node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}
  
  
// Function to print a maximum and minimum element
// in a tree without recursion without stack
void printMinMax(Node* root)
{
      
    if (root == NULL) 
    {
        cout << "Tree is empty";
        return;
    }
      
    Node* current = root;
      
    Node* pre;
      
    // Max variable for storing maximum value   
    int max_value = INT_MIN; 
      
    // Min variable for storing minimum value   
    int min_value = INT_MAX; 
      
      
    while (current != NULL)
    
        // If left child does nor exists
        if (current->left == NULL)
        
            max_value = max(max_value, current->key);
            min_value = min(min_value, current->key);
              
            current = current->right; 
        
        else 
        
    
            // Find the inorder predecessor of current 
            pre = current->left; 
            while (pre->right != NULL && pre->right != 
                                                 current) 
                pre = pre->right; 
    
            // Make current as the right child 
            // of its inorder predecessor 
            if (pre->right == NULL)
            
                pre->right = current; 
                current = current->left; 
            
    
            // Revert the changes made in the 'if' part to 
            // restore the original tree i.e., fix the 
            // right child of predecessor
            else 
            
                pre->right = NULL; 
                  
                max_value = max(max_value, current->key);
                min_value = min(min_value, current->key);
              
                current = current->right; 
            } // End of if condition pre->right == NULL
              
        } // End of if condition current->left == NULL
          
    } // End of while 
      
    // Finally print max and min value
    cout << "Max Value is : " << max_value << endl;
    cout << "Min Value is : " << min_value << endl;
}
  
// Driver Code
int main()
{
    /* 15
      /  \
    19   11
        /  \
       25   5
      / \   / \
    17  3  23  24
  
    Let us create Binary Tree as shown
    above */
  
    Node* root = newNode(15);
    root->left = newNode(19);
    root->right = newNode(11);
  
    root->right->left = newNode(25);
    root->right->right = newNode(5);
  
    root->right->left->left = newNode(17);
    root->right->left->right = newNode(3);
    root->right->right->left = newNode(23);
    root->right->right->right = newNode(24);
      
    // Function call for printing a max
    // and min element in a tree
    printMinMax(root);
  
    return 0;
}

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Output :

Max Value is : 25
Min Value is : 3

Space complexity: O(1)



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