Introduction to Trees (Data Structures & Algorithms #9)

Introduction

• The video introduces the topic of trees and explains how they are a data structure similar to linked lists, but with the ability for nodes to link to multiple other nodes.

Linked lists vs Trees

• Linked lists consist of nodes that are connected in a single direction, with each node having two attributes: an integer data and a "next" attribute pointing to the next node.

• Trees, on the other hand, allow nodes to link to multiple other nodes. Each node in a tree has an integer data and a set of children nodes.

• A tree structure can be represented using a class named "Node", which contains the data and children attributes.

Examples of Trees

• Showed an example of a tree structure where each node is linked to multiple other nodes, with some nodes having no children.

• Another example showed a tree structure drawn from top to bottom, with each node having two children.

• Explained that a tree with at most two children is called a binary tree.

What is a Tree?

• A tree is a data structure where nodes are connected to each other, and there is a way to go from the root node to every other node in the structure.

• The root node is a node without any parents.

• One important constraint of a tree is that there are no two references that link to the same node.

• If there is a cycle in the structure, it is not considered a tree.

Tree Traversal and Summing Nodes

• A problem is introduced where the goal is to find the sum of all the values within a given tree.

• The solution is implemented recursively and involves checking for the base case of an empty tree.

• The sum is calculated by adding the current value to the sum of the values in the left and right subtrees.

Time Complexity

• The time complexity of the solution is analyzed.

• The function is called for each node in the tree, resulting in a total of approximately 2n calls.

• Each call takes constant time, resulting in a total time complexity of O(n).

Conclusion

• Trees are a data structure that allow nodes to link to multiple other nodes.

• Nodes in a tree are connected, and there is always a way to go from the root node to every other node in the structure.

• The sum of all the values in a tree can be calculated recursively by summing the values of the current node and the values in the left and right subtrees.

Time Complexity of the Function

• The function takes a constant amount of time to execute each time it is called.

"A constant amount of time and so each time this function is called, it only takes one and it's called."

• The function is called o(n) times.

"O of n times so multiplying them together, we get the total amount of time this function takes to execute or the time complexity of this function, and that's going to be o(n)."

Conclusion

• This concludes the discussion on the time complexity of the function and the introduction to trees.

Additional Practice

• For more practice with using trees, there is another interesting and more challenging problem discussed in a previous video as a coding interview question.

• A link to that video can be found in the description below.

Closing Remarks

• Thank you, as always, for watching the videos.

• Stay tuned for the next one!