This course introduces data structures and algorithms, focusing on practical implementation in Python.

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Data structures and algorithms are essential in computer science since they play a crucial role in efficient information retrieval and processing, dealing with files, storing contacts on phones, social networks and web searches.

In this course, you’ll learn about the array-based implementation of various linear data structures, stack, and queues. You’ll also learn about linked list-based implementation. Next, you’ll explore advanced data structures like skiplists and hashing. You’ll learn how to implement a variety of trees and graphs, and data structures related to bits of an integer. Toward the end of the course, you’ll learn the implementation of structures based on external storage.

After completing this course, you’ll be able to create reusable programs with template-based collections that can efficiently analyze how to optimize the storage and retrieval of very large amounts of data. Overall, this course will enhance your productivity and performance as a software developer.

Data Structures with Generic Types in Python

## Task

Implement the `remove(i)` method, that removes the value stored in `a[i]` in a `BinaryHeap`. This method should run in $O(\log n)$ time.

**Sample input**

The sample input will be as follows:
```text
[0, 1, 2, 3, 4, 5, 6]
```

**Expected output**

The expected output will be as follows:
```text
Original Heap:
[0, 1, 2, 3, 4, 5, 6]
Heap after removal from index 2:
[0, 1, 5, 3, 4, 6]
```

# Task

Implement the `remove(i)` method, that removes the value stored in `a[i]` in a `BinaryHeap`. This method should run in $O(\log n)$ time.

**Sample input**

The sample input will be as follows:
```text
[0, 1, 2, 3, 4, 5, 6]
```

**Expected output**

The expected output will be as follows:
```text
Original Heap:
[0, 1, 2, 3, 4, 5, 6]
Heap after removal from index 2:
[0, 1, 5, 3, 4, 6]
```

Implement the remove(i) method in the binary heap.

Overview

Array-Based Lists

Linked Lists

Skiplists

Hash Tables

Binary Trees

Random Binary Search Trees

Scapegoat Trees

Red-Black Trees

Heaps

Sorting Algorithms

Graphs

Data Structures for Integers

External Memory Searching

Wrap Up

Exercise: Heaps

Task