Algorithm Vision
Sorting AlgorithmsIntermediate

Shell Sort

An optimization of insertion sort that allows exchange of elements that are far apart. Uses a gap sequence that decreases to 1, enabling the algorithm to move elements closer to their final positions faster. Named after Donald Shell who invented it in 1959.

#sorting#gap-sequence#insertion-sort-variant#in-place

Complexity Analysis

Time (Average)

O(n^1.25)

Expected case performance

Space

O(1)

Memory requirements

Time (Best)

O(n log n)

Best case performance

Time (Worst)

O(n²)

Worst case performance

Input Array

Implementation

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Bubble Sort

Beginner

The most basic sorting algorithm that repeatedly compares adjacent elements and swaps them if they are in wrong order. Like bubbles rising to the surface, larger values gradually move to the end of the array. Best suited for small datasets or educational purposes to understand sorting fundamentals.

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Selection Sort

Beginner

Finds the smallest element and moves it to the front repeatedly. Each iteration "selects" the minimum from remaining elements and places it after the sorted portion. Simple to implement with minimal memory usage, but always takes O(n²) time regardless of input.

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Quick Sort

Intermediate

A highly efficient sorting algorithm that selects a pivot element and partitions the array with smaller values on the left and larger on the right. Averages O(n log n) and is the most widely used sorting method in practice. Forms the foundation of built-in sort functions in most programming languages.

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Shell Sort - Algorithm Vision