How does the bead sort algorithm work?

The bead sort algorithm works by visualising the elements of the list as beads on vertical rods.

Bead sort, also known as gravity sort, is a natural sorting algorithm. It is both a distribution sort and a bin sort. The algorithm visualises the elements of the list as beads on vertical rods, where the height of each rod corresponds to the value of each element. The beads then "fall" down the rods, arranging themselves in sorted order.

To understand how the bead sort algorithm works, imagine an abacus. Each rod on the abacus represents a digit in the number to be sorted. The beads on each rod represent the numbers themselves. When the abacus is flipped, the beads fall down the rods, arranging themselves in order from highest to lowest.

The algorithm begins by placing the beads on the rods according to the input list. Each bead represents a single element of the list, and the height of the rod corresponds to the value of the element. The beads are then allowed to "fall" down the rods. As they fall, they arrange themselves in order from highest to lowest. This is because the beads representing larger numbers will fall further than those representing smaller numbers.

Once all the beads have fallen, the algorithm reads off the new order of the beads. This new order represents the sorted list. The algorithm then returns this sorted list as its output.

Bead sort is a simple and intuitive algorithm, but it is not often used in practice. This is because it requires a large amount of space to execute, and its time complexity is not as good as other sorting algorithms. However, it is a useful tool for teaching the principles of sorting algorithms, and it provides a clear visual representation of how sorting works.