Optimized version for Today's POTD (01/12/2023)

[Niraj-Node]

Title:
Optimized Algorithm to Detect Dead-End Nodes in a Binary Search Tree

Introduction:
This optimized algorithm aims to efficiently identify dead-end nodes within a Binary Search Tree (BST) without utilizing additional data structures. The algorithm traverses the BST in a recursive manner, analyzing the node values and their ranges to determine if a dead-end scenario exists.

Description:
The algorithm uses a recursive approach, passing down the current node's value range as parameters during traversal. It checks for dead-end situations by examining if the current node falls within a range where insertion of a new node is impossible without violating the BST properties.

The core logic involves:
Checking if the node's value is at a range limit where insertion of a new node (with values incrementing or decrementing by 1) is infeasible due to existing node values.
Recursively exploring left and right subtrees while updating the value ranges accordingly to identify dead-end scenarios throughout the BST.
Key Features:

Solution:

class Solution {
public:
    bool isDeadEnd(Node* root, int low = 1, int high = INT_MAX) 
    {
        if(!root) return false;

        if(low == high) return true; 

        if(root->left && isDeadEnd(root->left, low, root->data - 1)) return true;

        if(root->right && isDeadEnd(root->right, root->data + 1, high)) return true;

        return false;
    }
};

Space Optimization:
It minimizes space complexity by not relying on auxiliary data structures, avoiding the need to store the entire tree in vectors or arrays. The space complexity is O(h), where h is the height of the BST. In balanced trees, this reduces to O(log n), optimizing memory usage.

Linear Time Complexity:
With a time complexity of O(n), where n is the number of nodes in the BST, the algorithm efficiently examines each node once, ensuring a linear time performance.