958 || Check Completeness of a Binary Tree || Leetcode Daily Problem

Problem Link :- leetcode-958

Problem statement

Given the root of a binary tree, determine if it is a complete binary tree.

In a complete binary tree, every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.

Significance of problem

The "Complete Binary Tree" problem holds significant importance in the domain of binary trees, shedding light on the structural characteristics that define completeness. Understanding and verifying whether a binary tree adheres to the rules of completeness are fundamental in various computational scenarios.

Firstly, the problem emphasizes the practical significance of complete binary trees in data structures. In scenarios where efficient data representation and retrieval are crucial, complete binary trees ensure optimal usage of storage while facilitating swift access to elements. This is particularly relevant in priority queues and heap-based data structures where the underlying tree structure plays a pivotal role.

Secondly, the problem delves into the concept of tree traversal and level-order exploration. The code solution utilizes a queue-based approach, showcasing the efficiency of level-order traversal in evaluating completeness. This insight is transferrable to a myriad of tree-related problems, demonstrating the versatility of traversal techniques in analyzing and validating tree structures.

Moreover, the problem underlines the practical challenges of representing data hierarchies. In fields such as database management or network routing, where hierarchical structures abound, ensuring completeness is essential for maintaining data integrity and optimizing retrieval operations.

Furthermore, the problem bridges theoretical concepts with real-world applications, providing a tangible understanding of how completeness in binary trees contributes to efficient data organization and retrieval. This knowledge is applicable to various domains, guiding learners in designing and implementing optimized data structures.

Easiest Explanation

Imagine you have a tree made up of lots of little boxes connected by lines. Each box is a "node" in the tree. Now, we want to see if the tree is a "complete binary tree".

A "complete binary tree" is a special kind of tree where every level (except maybe the last one) is completely filled with nodes, and all the nodes in the last level are pushed over to the left side.

So, if you imagine the boxes lined up in rows from top to bottom, a complete binary tree would have the same number of boxes in every row except maybe the last one, which might be a little shorter. And all the boxes in that last row would be as far to the left as they could be.

Now, if we have a tree made up of boxes, we can check if it's a complete binary tree by looking at the boxes and checking if they follow these rules. If they do, then we know the tree is complete!

I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.

Python Code :

from queue import Queue
class Solution:
    def isCompleteTree(self, root: Optional[TreeNode]) -> bool:

        ans = False
        que = Queue()
        que.put(root)
        
        while not que.empty():
            node = que.get()
            if node != None and ans == True:
                ans = False
                return ans
            if node == None:
                ans = True
                continue
            que.put(node.left)
            que.put(node.right)
            
        return ans

CPP Code

class Solution {
public:
    bool isCompleteTree(TreeNode* root) {
        bool ans=false;
        queue que;
        que.push(root);
        while(!que.empty()){
            TreeNode* node = que.front();
            que.pop();
            if(node!=NULL && ans == true) 
            {
                ans=false; 
                return ans;
            }
            if(node==NULL) 
            {
                ans = true;
                continue;
            }
            
            que.push(node->left);
            que.push(node->right);
        }
        return ans;
    }
};
    

Here's how the function works:

1. The function isCompleteTree takes a pointer to the root of the binary tree as its argument.

2. A boolean variable ans is initialized to false, which will later store the result of whether the tree is complete or not.

3. A queue of tree nodes is created, and the root node is added to the queue.

4. A loop is started, which continues until the queue is empty.

5. Inside the loop, the front node of the queue is removed and stored in a temporary variable called node.

6. If the value of node is not NULL and the value of ans is true, this means that we have already encountered a NULL node in a previous level. Therefore, the value of ans is set to false, and the function immediately returns false.

7. If the value of node is NULL, this means that we have encountered a NULL node in the current level. Therefore, the value of ans is set to true, and we move on to the next iteration of the loop.

8. If the value of node is not NULL, we push the left and right child nodes of node onto the queue.

After the loop is finished, the value of ans is returned. If the tree is a complete binary tree, ans will be true. Otherwise, it will be false.

Learning Outcomes

Solving the "Complete Binary Tree" problem provides a wealth of learning outcomes, fostering a deeper understanding of binary trees, tree traversal, and the characteristics that define completeness in a structural context.

Firstly, learners gain proficiency in identifying and verifying complete binary trees. This involves a nuanced understanding of the rules governing completeness, where every level, except possibly the last, is fully filled, and nodes in the last level are positioned as far left as possible. This skill extends to various tree-related challenges, enhancing learners' ability to assess and categorize binary tree structures accurately.

Secondly, the problem enriches learners' knowledge of tree traversal techniques, particularly through the utilization of a queue-based level-order approach in the code solution. This methodology exemplifies the efficiency of level-order exploration in analyzing structural properties. The acquired skill is transferable to diverse tree-related problems, offering a versatile tool for navigating and understanding hierarchical structures.

Moreover, learners cultivate a practical understanding of the significance of complete binary trees in data structures. The problem bridges theoretical concepts with real-world applications, highlighting scenarios where efficient storage and retrieval of data are paramount. This knowledge is foundational in designing and implementing optimized data structures, applicable in domains ranging from database management to network routing.

Furthermore, learners develop problem-solving skills by addressing the challenges posed in determining the completeness of a binary tree. This involves the formulation of logical conditions and the application of traversal techniques, fostering a structured approach to problem-solving that extends beyond this specific scenario.

Conclusion

In conclusion, tackling the "Complete Binary Tree" problem results in a multifaceted set of skills and insights crucial for understanding binary trees and their practical implications. Learners grasp the intricacies of completeness in binary trees, honing their ability to assess and categorize tree structures accurately based on defined rules.

The emphasis on queue-based level-order traversal in the code solution reinforces the efficiency of this technique, providing learners with a versatile tool applicable to diverse tree-related challenges. This newfound proficiency in tree traversal extends their problem-solving capabilities, fostering a structured approach to addressing complexities in hierarchical structures.

Furthermore, the problem elucidates the practical significance of complete binary trees in optimizing data storage and retrieval operations. This knowledge transcends theoretical concepts, finding application in real-world scenarios where efficient hierarchical data representation is essential.

In essence, mastering the "Complete Binary Tree" problem not only enhances learners' understanding of tree completeness but also equips them with practical skills applicable in data structure design, problem-solving, and computational domains where hierarchical structures play a crucial role.

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