Big O notation is used in computer science to describe the complexity of an algorithm. It tells us how the time and space requirements of an algorithm grow with the input size.

The Big O notation is represented by the letter O followed by parentheses containing an expression that describes the upper bound of the algorithm. Here are some common examples:

• O(1) describes an algorithm that takes constant time to run, regardless of the size of the input. For example, accessing an array element by index is a constant time operation:

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  const arr = [1, 2, 3];
  const element = arr[0]; // takes constant time O(1)
  

• O(n) describes an algorithm that takes time proportional to the size of the input. For example, iterating through an array is a linear time operation:

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  const arr = [1, 2, 3];
  for(let i = 0; i < arr.length; i++) { // takes linear time O(n)
  console.log(arr[i]);
  }
  

• O(n²⁾ describes an algorithm that takes time proportional to the square of the input size. For example, a nested loop over an array is a quadratic time operation:

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  const arr = [1, 2, 3];
  for(let i = 0; i < arr.length; i++) {
  for(let j = 0; j < arr.length; j++){
  console.log(arr[i] + arr[j]); // takes quadratic time O(n^2)
  }
  }
  

These are just a few examples, and there are many different variations of Big O notation that can describe different types of algorithms.

Bubble sort is a sorting algorithm that repeatedly compares adjacent elements in a collection of items and swaps them if they are in the wrong order. It is called "bubble sort" because the smaller elements rise to the top of the collection like bubbles.

In terms of runtime, bubble sort has a worst-case and average-case time complexity of O(n^2), where n is the number of elements in the collection. This means that as the size of the collection increases, the time taken to sort it also increases exponentially.

Here's an example implementation of bubble sort in Python:

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def bubble_sort(arr):
    n = len(arr)

    # Traverse through all elements in array
    for i in range(n):

        # Last i elements are already sorted
        for j in range(0, n-i-1):

            # Swap if the element found is greater than the next element
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]

    return arr

In this implementation, we have an outer loop that iterates over all the elements in the array, and an inner loop that iterates over the unsorted elements. Within the inner loop, we compare adjacent elements and swap them if they're in the wrong order. We repeat this process until the array is sorted.

However, as mentioned earlier, bubble sort has a time complexity of O(n^2), which makes it inefficient for larger data sets. There are other sorting algorithms such as merge sort or quicksort with a lower time complexity that are more suitable for large data sets.

The hardest type of coding is relative and depends on a variety of factors, such as the complexity of the task, the language being used and the skill level of the coder. Some of the most challenging coding tasks include artificial intelligence and machine learning, distributed systems, and browser-based applications.