10 Algorithms That Changed Computer Science Forever

If you strip programming down to its rawest form, you end up with two pillars: data structures and algorithms. Data structures give us a way to organize and store information; algorithms tell us how to manipulate that information efficiently. Think of them as recipes: a list of instructions for solving a problem or achieving a goal.

But not all algorithms are created equal. Some are elegant, some are bizarre, and some have fundamentally reshaped the way we live and compute. Today, we’re going to take a deep dive into 10 of the most interesting algorithms ever devised in computer science—from the practical to the downright mind-bending.

Settle in, because this isn’t just a listicle; it’s a journey through problem-solving ingenuity.

---

1. Quicksort: The Speed Demon of Sorting

Sorting is one of the most common problems in computing. Whether you’re organizing your emails by date or arranging search results by relevance, sorting is everywhere.

Enter Quicksort, developed by Tony Hoare in 1959. Quicksort is famous for its divide-and-conquer strategy:

1. Pick a pivot element.
2. Partition the array so that all values less than the pivot go to the left and all values greater go to the right.
3. Recursively apply the same process to the left and right partitions.

In practice, Quicksort is fast—often faster than more theoretically optimal algorithms like Merge Sort—because it works well with cache memory and requires little overhead.

Here’s a concise Python version to give you a feel:

def quicksort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quicksort(left) + middle + quicksort(right)

Quicksort taught us that sometimes, a simple randomized approach outpaces more “careful” deterministic methods.

---

2. Merge Sort: Stability and Predictability

If Quicksort is the speedster, Merge Sort is the dependable workhorse. Introduced by John von Neumann in 1945, Merge Sort guarantees (O(n \log n)) time complexity no matter what the input looks like.

It works by splitting the array in half, sorting each half recursively, and then merging the results. Its predictable performance makes it a favorite in environments where worst-case scenarios matter—like databases.

Merge Sort also has a neat property: it’s stable, meaning it preserves the relative order of equal elements. That turns out to be crucial in things like sorting people by last name while keeping their first names in order.

---

3. Binary Search: Divide and Conquer in a Single Function

Imagine looking for a word in a dictionary. You don’t start at page one—you flip to somewhere in the middle, check which way to go, and repeat until you find it. That’s Binary Search, one of the most elegant algorithms out there.

Instead of scanning linearly through every element, Binary Search halves the search space at each step, achieving a runtime of (O(\log n)). It’s a reminder of how much power lies in thinking about problems differently.

Practical applications? Everywhere: databases, compiler optimization, gaming leaderboards—you name it.

---

4. Wave Function Collapse: Algorithmic Creativity

This one feels less like math and more like magic. Wave Function Collapse (WFC) is an algorithm that generates procedural content—think textures, game levels, or even city maps—that look organic and human-designed.

It works by borrowing ideas from quantum mechanics. Each tile in a grid starts in a superposition of all possible states (like Schrödinger’s cat). Then, constraints are applied (e.g., grass can’t touch water), and the algorithm “collapses” possibilities until a coherent configuration emerges.

Developers love WFC for its ability to create visually compelling, non-repetitive patterns. You’ve probably played a game that secretly used it to generate its worlds.

---

5. PageRank: The Algorithm That Built Google

When Larry Page and Sergey Brin invented Google, they needed a way to rank search results. Their insight was to treat the web like a graph, where each page is a node and links are edges.

PageRank assigns importance to a page based on how many other important pages link to it. Sort of like academic citations: if lots of high-profile papers cite your work, your work must be significant.

This recursive scoring system allowed Google to cut through the noise of the web and deliver shockingly relevant results. PageRank is a masterclass in turning a messy real-world problem into elegant graph math.

---

6. The RSA Algorithm: Cryptography’s Cornerstone

Without RSA encryption, modern life as we know it (online banking, private messaging, e-commerce) would collapse.

RSA relies on the mathematical difficulty of factoring large numbers. It enables public-key cryptography, where you can share a public key with the world but keep your private key secret. Messages encrypted with the public key can only be decrypted with the private key, ensuring secure communication.

The beauty of RSA is that it balances elegance with practicality—it’s not just theoretically secure, it’s usable at scale.

---

7. Paxos: Agreement in Distributed Systems

Distributed systems—like cloud databases or blockchain networks—need a way for multiple computers to agree on a single truth. That’s where Paxos comes in.

Paxos is a consensus algorithm. It ensures that even if some nodes fail or messages get delayed, the system as a whole can still agree on a consistent state. Without it (or its siblings like Raft), services like Google Cloud Spanner or Amazon DynamoDB wouldn’t be possible.

Consensus algorithms are notoriously tricky to understand. Leslie Lamport (the father of Paxos) even wrote a tongue-in-cheek paper presenting Paxos as a story about ancient Greek legislators to make it more digestible.

---

8. Bogosort: The Worst Sorting Algorithm (That’s Weirdly Useful)

Sometimes, algorithms are interesting not because they’re good, but because they’re so bad they make a point. Bogosort is one of those.

The “algorithm”: shuffle the array randomly until it happens to be sorted. Its expected runtime? Infinite, technically. But Bogosort is still taught, because it highlights what not to do and sparks conversations about algorithmic efficiency.

It’s a meme in algorithm form, but also a reminder that rigor matters.

---

9. Shor’s Algorithm: Quantum Computing’s Trump Card

Most classical cryptography hinges on the difficulty of factoring large numbers—a problem that takes exponential time on traditional computers. Enter Shor’s Algorithm (1994).

Shor showed that a quantum computer could factor integers in polynomial time, making RSA and similar schemes potentially insecure. While practical quantum computers capable of this are still emerging, Shor’s Algorithm was a wake-up call: quantum computing isn’t just faster, it’s a paradigm shift.

If quantum computers scale, we’ll need entirely new cryptographic systems.

---

10. Dijkstra’s Algorithm: Shortest Paths Everywhere

Need to find the fastest route from A to B? Dijkstra’s Algorithm (1956) is your friend. It computes the shortest path in a weighted graph, and it’s still used everywhere: GPS navigation, network routing, even game AI.

The algorithm works by maintaining a priority queue of nodes to explore, always expanding the least costly option until the destination is reached. It’s efficient, elegant, and incredibly practical.

Here's a sketch in Python using a heap (priority queue):

import heapq

def dijkstra(graph, start):
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    pq = [(0, start)]

    while pq:
        current_distance, node = heapq.heappop(pq)
        if current_distance > distances[node]:
            continue
        for neighbor, weight in graph[node].items():
            distance = current_distance + weight
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(pq, (distance, neighbor))
    return distances

This little piece of genius is why your phone can tell you the fastest way home.

---

Why Algorithms Matter

Looking at these ten, a pattern emerges: algorithms aren’t just abstract math puzzles. They’re insights into how to solve problems more effectively. They:

• Turn messy reality (like the web, traffic, or noise) into structured solutions.
• Balance elegance with practicality.
• Push the boundaries of what’s possible when hardware evolves (like with quantum computing).

And sometimes, like with Bogosort, they just make us laugh.

---

Conclusion

Algorithms are the hidden engines of the modern world. They power everything from the way we find the fastest driving route to how we encrypt our bank details. Understanding them isn’t just an academic exercise—it’s a way of seeing how human creativity meets mathematical rigor to solve problems at scale.

If you’re learning to code, start with classics like Binary Search and Merge Sort. If you’re more advanced, dive into Paxos or Wave Function Collapse and see how clever constraints create emergent beauty.

The takeaway? Every algorithm is a story about how humans solve problems—sometimes elegant, sometimes messy, but always fascinating.

Want more deep dives like this? Subscribe to the newsletter and let’s keep exploring the hidden patterns that run our digital lives.

---