#heap sort

Quicksort Program and Complexity (Big-O)

Quicksort is a comparison sort based on divide and conquer algorithm. Quick sort is more fast in comparison to Merge Sort ot Heap Sort. It’s not required additional space for sorting.

How Quick Sort Works

The idea to implement Quicksort is first divides a large array into two smaller sub-arrays as the low elements and the high elements then recursively sort the sub-arrays.

The above process…

Performance Analysis of Four Different Types of Sorting Algorithms using Different Languages

By Dr. I. Lakshmi"Performance Analysis of Four Different Types of Sorting Algorithms using Different Languages"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018,

URL: http://www.ijtsrd.com/papers/ijtsrd9464.pdf

http://www.ijtsrd.com/computer-science/other/9464/performance-analysis-of-four-different-types-of-sorting-algorithms-using-different-languages/dr-i-lakshmi

peer reviewed journal, call for paper technology, social science journal

Understanding that in what condition, which sorting algorithm should be used.

http://www.knowsh.com Understanding that in what condition, which sorting algorithm should be used. Comparison between :- Quick Sort, Merge Sort, Heap Sort, Introsort, Insertion Sort, Bubble Sort, Selection Sort, Counting Sort, Radix Sort & Bucket Sort. http://knowsh.com/Notes/210295/When-To-Use-Which-Sorting  

Topics

Radix Sorting - bucket sorting

LSD - Least Significant Digit (start from ones digit, move <--)

MSD - Most Significant Digit (start from left digit, move -->)

Use nested buckets - MSD for 3-digit numbers ex:

Start with hundreds-place-digit % 10 bucket

Within that bucket, place in tens-place-digit % 10 bucket

Within that bucket, place in ones-place-digit % 10 bucket

Can mod by different size/number of buckets

Will take O(n) time to place elements - placing in sorted order

Will take O(n) time to retrieve elements in sorted order

Total sort time is O(n) time

Not a comparative sort, since merely placing elements

Can only work with arrays of integers

Good for when you have a set range of integes since sort is very fast

Bad for an infinite/unknown range, since can't set the appropriate number of buckets

Heaps - Binary tree where each parent is smaller than its children

Min Heap - default, what most people assume when talking about Heaps

Max Heap - binary tree where each parent is larger than its children

Often stored as an array where reading in a Breadth First manner

[1,2,3,4,5,6,7]

1 - root

2, 3 -- children of 1

4, 5 -- children of 2

6, 7 -- children of 3

Can reference parents/children by index

Parent of node i is node (i-1)/2

Children of node i are (i*2)+1 & (i*2)+2

O(n) time to place all elememnts

Heap Sort

Percolation - can either percolate up or percolate down

Percolating up - add a new element on the end of the array (become new leaf of tree), then compare it to its parent (using index). If it is smaller than its parent, swap positions. Compare to new parent. Continue this until new element is smaller than its parent (in correct position)

Percolating down - add a new element to the beginning of the array (make it the new root). Of its two children, swap with the smaller of the two (if it's smaller. Check new children, and swap with the smaller of the two if it's still larger. Continue this until it is larger than its children.

Because we're storing a binary tree in an array, it will compact to the top (so no extra-long branches)

Number of levels for n nodes --> log(n)

Hence, will take max O(logn) time to percolate up or percolate down

Because it takes O(logn) time to place 1 element, it will take O(nlogn) time to place all objects into the binary tree. Once placed, elements are in sorted order

Take first element, place at end of array and percolate up. This will take max O(logn) time

O(nlogn) time to sort all elements

In-place algorithm

Not a stable sort

[nextpage title=”Introduction”] Heap Sort is one of the efficient sorting algorithms with a guaranteed worst case running time of O(NlogN). This is an in place sorting algorithm but it does not offer stable sorting.

In place Sorting: A sorting algorithm which sorts the input using very small or no extra space. It means that the input data is overwritten by the resulting output data.

Stable…