Arrays

An optimized O(N) single-pass algorithm to sort an array into a wave-like pattern.

In this blog post, we'll delve into the world of two-dimensional arrays, a vital data structure in programming. You'll learn what 2D arrays are, how to initialize and traverse them, and their common uses in real-world applications like matrix operations, image processing, and game boards. We'll also tackle classic algorithmic challenges involving 2D arrays, such as rotating a matrix and finding the largest sum subgrid. By the end, you'll have a solid understanding of how to effectively use 2D arrays to solve complex problems in your programming projects.

Kadane's Algorithm is an efficient technique used to find the maximum sum of a contiguous subarray within a one-dimensional array of integers. It is particularly useful in scenarios where the input array may contain both positive and negative numbers. By leveraging a dynamic programming approach, Kadane's Algorithm can identify the maximum sum in linear time, making it optimal for large datasets.

The Product of Array Except Self problem requires calculating the product of all elements in an array except for the element at the current index. The challenge is to perform this without using division and in O(n) time complexity.

Bubble Sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller elements 'bubble' to the top of the list. Although the algorithm is simple, it is too slow and impractical for most problems even when compared to insertion sort. It can be practical if the input is usually in sort order but may occasionally have some out-of-order elements nearly in position.

An array is a collection of items stored at contiguous memory locations. It is a data structure that stores a fixed-size sequential collection of elements of the same type. An array is used to store a collection of data, but it is often more useful to think of an array as a collection of variables of the same type.

Insertion Sort is a simple sorting algorithm that builds the final sorted array one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.

In this blog post, we'll explore Kadane's Algorithm, a dynamic programming algorithm used to find the Maximum Sum Subarray in an array.

Merge Sort is a divide-and-conquer sorting algorithm that divides the array into smaller subarrays, sorts them recursively, and then merges them back together in sorted order. It is a stable and efficient algorithm with $O(n log n)$ time complexity in all cases.

Selection Sort is an in-place comparison sorting algorithm that divides the input list into two parts: the sublist of items already sorted and the sublist of items remaining to be sorted. It repeatedly finds the minimum element from the unsorted part and puts it at the beginning of the unsorted part. The algorithm maintains two subarrays in a given array. The subarray which is already sorted and the remaining subarray which is unsorted. In every iteration of selection sort, the minimum element from the unsorted subarray is picked and moved to the sorted subarray.

Shell Sort is a generalization of insertion sort that allows the exchange of far-apart elements. It uses a gap sequence to progressively reduce the gap and efficiently sort the array. It offers improved performance compared to simple sorting algorithms with O(n log n) to O(n log² n) time complexity.

Thsi page containes Bucket Sort, with codes in python, java and c++

Circular Sort (often called Cycle Sort) is an in-place sorting algorithm that minimizes memory writes by placing elements in their exact positions.

Counting Sort is an efficient sorting algorithm used for sorting a collection of integers when the range of the integers (k) is not significantly greater than the number of integers (n) in the collection. It works well when the integers are within a known, fixed range.

Cyclic Sort is an O(n) in-place sorting algorithm specifically designed for arrays containing numbers in a given continuous range (e.g., 1 to N).

Heap Sort is an efficient comparison-based sorting algorithm based on a binary heap data structure. It sorts by building a max-heap from the data and repeatedly extracting the maximum element.

An optimized O(N) single-pass solution to check if an array is monotonic.

Quick Sort is a highly efficient and commonly used sorting algorithm that employs a divide-and-conquer strategy. It is well-suited for large datasets and typically outperforms other algorithms like insertion sort and bubble sort.

This page explains Radix sort, with code implementations and resources for further learning.

An optimization technique used to reduce time complexity from O(N²) to O(N) for array or string subarrays.