algoha

Where algorithms grow naturally

Chapter One

The Sorting Garden

In the tropical garden of algoha, arrays sort themselves like seeds finding their place in the soil. Each element rises to its proper height, comparing itself to its neighbors, swapping positions with the patience of a palm tree growing toward the sun.

The result is always the same: order from chaos, beauty from randomness. Watch the bars rearrange -- sunset-colored bamboo stalks finding their natural order among the fronds.

Bubble sort: O(n²) comparisons, infinite beauty
Chapter Two

Recursive Tides

The ocean does not solve problems in one stroke. It breaks each wave into smaller waves, each foam into smaller foam, until the problem is so small that it solves itself. This is recursion: the art of dividing until conquering is trivial, then combining the solutions as the tide returns.

Like the nautilus shell, each chamber contains within it the blueprint of the whole. The call stack deepens, then unwinds, leaving behind the answer.

Divide and conquer: nature's oldest algorithm
Chapter Three

Island Hopping

Graph traversal is island hopping across an archipelago. Each node is an island, each edge a bridge or boat route between them. Breadth-first search explores the nearest islands first, like ripples spreading from a dropped stone. Depth-first search sails to the farthest horizon before backtracking.

In the algoha archipelago, every island is reachable -- you just need to choose your path wisely.

BFS: explore outward. DFS: explore inward.
The Grove

The Binary Tree

Watch it grow, node by node, from root to canopy

Every node is a fruit. Every branch finds the light.

The best algorithms, like the best islands, are the ones you never want to leave.

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