A Few of My Favourite Algorithms

August 23, 2020

There comes a time in every nerd’s life when he realizes that he is, in fact, even nerdier than he thought.

For me, this realization came when I heard myself unironically say: “Well, my favourite algorithm is this linear majority voting algorithm.”

It was on that fateful day when I realized that my life had taken a turn. I was that guy who has a favourite algorithm…

And so, I present to you, a few of this nerd’s favourite algorithms 🤓

Caveat: These are off the top of my head and are prone to recency bias. I’m not saying that these are the world’s greatest algorithms.

Boyer-Moore Voting Algorithm

This one is my reigning favourite due to its simplicity. It’s basically a little math problem that a grade schooler could easily understand, bottled up into a slick, tasty, little nugget of linear time complexity.

The Problem: On Leetcode

Find the majority element in an array, where the majority element fills more than half of the array (instances > array.length / 2).

Here is an example implementation:

def majorityElement(nums: List[int]) -> int:
        # Voting algorithm - O(n) time
        majority = None
        count = 0
        for num in nums:
            # If count has reached zero, the majority is unknown.
            # Current element becomes the majority.
            if count == 0:
                majority = num

            # Current majority votes for itself
            if majority == num:
                count += 1
            # All other values vote against current majority
                count -= 1
        return majority

In addition to using linear time, this algorithm also uses constant space. My initial solution involved storing a dictionary with a count of every element (linear space), so this implementation was a clear improvement.

The Boyer-Moore algorithm obviously solves a very specific problem, but it does it so well that I can’t help but appreciate it.

Tree Traversal

Okay, so this one is arguably not a specific algorithm. In a way, it’s the opposite of the previous one. Instead of being used to solve a very specific problem, it can be used in a wide variety of domains.

A great thing about tree traversal is that it can be completely decoupled from the application logic. For example, the traverse function from Babel allows you to write simple functions that modify the AST without ever worrying about how the AST is structured.

I’ll illustrate a few basic tree traversals here.

Binary Tree

Given the typical Leetcode TreeNode:

# Definition for a binary tree node.
class TreeNode:
  def __init__(self, val=0, left=None, right=None):
    self.val = val
    self.left = left
    self.right = right

We can perform some basic traversals, which accept a visit function as an argument. You could imagine visit to be the implementation of business logic for that node.

def traverse(root: TreeNode, visit):
    # Base case
    if not root:
        return root
    # In-order Traversal
    traverse(root.left, visit)
    traverse(root.right, visit)
    return root
def traverse(root: TreeNode, visit):
    # Base case
    if not root:
        return root
    # Pre-order Traversal
    traverse(root.left, visit)
    traverse(root.right, visit)
    return root
def traverse(root: TreeNode, visit):
    # Base case
    if not root:
        return root
    # Post-order Traversal
    traverse(root.left, visit)
    traverse(root.right, visit)
    return root

Oh yeah… Did I mentioned how much I love recursion?

I adore the fact that you can completely change the order in which the entire tree is explored just by changing the order in which you visit the nodes. Recursion takes care of the heavy lifting.

N-Ary Trees

Admittedly, I like this Breadth-First algorithm a lot less than the Depth-First ones above, but the processing queue is a useful pattern that I first learned from problems such as n-ary tree traversal, so I need to pay my respktz.

Assuming that the child nodes live in an iterable, stored at a children attribute:

def traverse(root, visit):
  if not root:
    return root

  queue = [root]

  while queue:
    # Dequeue node to process
    node = queue.pop(0)

    # Enqueue next node(s) for processing
    for child in node.children:
      # Perform business logic on this node
  return root

There isn’t much else to say about this algorithm. It benefits from using a non-recursive implementation (memory performance) while still being very readable.

For these reasons, as well as the processing queue pattern, I would still consider it – while perhaps not a “favourite” per-say – a very important algorithm to keep in my brain.

Detect Linked List Cycle

This is another algorithm that I love for its simplicity. While it’s great on its own, it is very specific. So, I’m picking it out here as a representative of a larger pattern that I reach for quite often: two pointers.

The Problem: On Leetcode

Given a singly-linked list defined as:

class ListNode:
  def __init__(self, x):
    self.val = x
    self.next = None

We can detect a cycle like so:

def hasCycle(head: ListNode) -> bool:
  slow = fast = head

  while slow and fast:
    if fast.next is None:
      # Reached end with no cycles
      return False
      slow = slow.next
      fast = fast.next.next

      # Pointing to the same instance (cycle occurred)
      if slow is fast:
        return True

This uses the runner pattern, where we have a “slow” pointer and a “fast” pointer. If there’s a cycle, the fast pointer will never hit the “end” because there is no end.

In the case of no end, the fast pointer will continue to cycle around until it hits the slow pointer, at which point we’ve detected a cycle!

Easy peasy. 🍋

That’s it for Today

You’ve probably noticed that these are all very simple algorithms. The most “complex” piece is probably the recursive logic within the tree traversals.

I know that some people love “clever” or “concise” code. When it comes to algorithms, my personal preference is simplicity, readability, and expressiveness. If the algorithm leverages a common and/or useful pattern in a unique or powerful way, all the better.

But cleverness is not a virtue that I extol in my favourite algorithms, at least not right now.

👋 Bye


A dev blog by Nathan Calvank. I'm just trying to seem more interesting than I actually am.