Where is sorting used

The most noteworthy of these considerations are:. To get the amount of time required to sort an array of 'n' elements by a particular method, the normal approach is to analyze the method to find the number of comparisons or exchanges required by it.

Most of the sorting techniques are data sensitive, and so the metrics for them depends on the order in which they appear in an input array. Hence, the result of these cases is often a formula giving the average time required for a particular sort of size 'n. JavaScript Tutorials jQuery Tutorials. Sorting Techniques. Table of Contents. What is sorting? Categories of Sorting. Grade data type. Write a program Grade. It should implement the Comparable interface using the natural ordering on grades by GPA.

Student data type. Write an data type Student. Each student should have a login String , a section number integer , and a grade Grade. Case insensitive order. Write a code fragment to read in a sequence of strings and sort them in ascending order, ignoring case.

Implement your own version of the comparator String. Implement a comparator that sorts string in descending order instead of ascending order. It returns a Comparator that imposes the reverse of the natural ordering of objects that implement the Comparable interface.

Sorting strings from non-English alphabets. Write a program to sort strings according to non-English alphabets, for accents, umlauts, and pre-composed character like ch in Spanish. Hint: Use Java's java. Collator API. Arrays; import java. The following problem arises in supply chain management. You have a bunch of jobs to schedule on a single machine. Give example. Job j requires p[j] units of processing time. Job j has a positive weight w[j] which represents its relative importance - think of it as the inventory cost of storing the raw materials for job j for 1 unit of time.

The goal is to sequence the jobs so as to minimize the sum of the weighted completion times of each job. Write a program SmithsRule. Hint: Use Smith's rule : schedule the jobs in order of their ratio of processing time to weight.

This greedy rule turns out to be optimal. Rhyming words. For your poetry class, you would like to tabulate a list of rhyming words. A crude way to accomplish this task is as follows: Read in a dictionary of words into an array of strings. Reverse the letters in each word, e. Sort the resulting array of words. Reverse the letters in each word back to their original state. Now the word confound will be next to words like astound and compound.

Write a program Rhymer. Now repeat, but use a customized Comparator that sorts lexicographically from right-to-left. Give an O N log N algorithm for computing the mode value that occurs most frequently of a sequence of N integers.

Closest 1d pair. Given a sequence of N real numbers, find the pair of integers that are closest in value. Give a O N log N algorithm. Farthest 1d pair. Given a sequence of N real numbers, find the pair of integers that are farthest apart in value. Give a O N algorithm. Sorting with many duplicates. Suppose you have a sequence of N elements, with at most log N distinct ones.

Describe how to sort them in O N log log N time. Nearly sorted. Given an array of N elements, each which is at most k positions from its target position, devise an algorithm that sorts in O N log k time.

Sorting a linked list. Given a singly linked list of N elements, how could you sort it in guaranteed O N log N time, stably, and with O 1 extra space? Goofysort Jim Huggins.

Argue that Goofy. What is the best-case running time of as a function of the number of items to be sorted N? What is the worst-case running time of as a function of the number of items to be sorted N? Feel-good interval. Given an array of N nonnegative integers representing a person's emotional value on each day , the happiness in an interval is the sum of the values in that interval multiplied by the smallest integer in that interval.

Design an O N log N divide-and-conquer algorithm to find the happiest interval. Here's a mergesort style solution. Divide the elements in the middle: a[l.. Here's a greedy solution: If the optimal interval containing a[m] contains one element, it is simply a[m]. Repeat, etc. Return the best interval of any size constructed by this process. Equality detector. Assume the only operation on the elements you can perform is equality testing. Design an algorithm that performs O N log N equality tests to find a representative element if it exists.

Hint : divide-and-conquer. Note: can also do in O N tests. A maxima is a point that is not dominated by any other point in the set. Devise an O n log n algorithm to find all maxima. Application: on x-axis is space efficiency, on y-axis is time efficiency. Maxima are useful algorithms. Hint: sort in ascending order according to x-coordinate; scan from right to left, recording the highest y-value seen so far, and mark these as maxima. Min and max. Given an array of N elements, find the min and max using as few compares as possible.

Brute force: find the max N-1 compares , then find the min of the remaining elements N-2 compares. Solution 1. Solution 2. Divide the elements into pairs and compare two elements in each pair. Put the smallest elements in A and the largest in B. If n is odd, put element n in both A and B. L1 norm. There are N circuit elements in the plane. You need to run a special wire parallel to the x-axis across the circuit.

Each circuit element must be connected to the special wire. Where should you put the special wire? Hint : median minimizes L1 norm. Median given two sorted arrays. Or find the kth overall largest in O log k. Three nearby numbers in an array.

Hint: if a[i] Three nearby numbers in three arrays. Minimum dot product. Given two vectors of the same length, find a permutation of the two vectors such that the dot product of the two vectors is as small as possible. Given an array of N integers, design a linearithmic algorithm to find a pair of integers whose sum is closest to zero. Comments have been included in the implementation below to help you understand the Quick Sort algorithm better.

Merge Sort is a divide-and-conquer algorithm. In each iteration, merge sort divides the input array into two equal subarrays, calls itself recursively for the two subarrays, and finally merges the two sorted halves.

Now that you're familiar with the intuition behind merge sort, let's take a look at its implementation. Counting Sort is an interesting sorting technique primarily because it focuses on the frequency of unique elements between a specific range something along the lines of hashing.

It works by counting the number of elements having distinct key values and then building a sorted array after calculating the position of each unique element in the unsorted sequence.

It stands apart from the algorithms listed above because it literally involves zero comparisons between the input data elements! Given an array of n input integers, return the absolute difference between the maximum and minimum elements of the array in linear time complexity. As you saw earlier, counting sort stands apart because it's not a comparison-based sorting algorithm like Merge Sort or Bubble Sort , thereby reducing its time complexity to linear time. For each digit i where i varies from the least significant digit to the most significant digit of a number, sort input array using count sort algorithm according to the ith digit.

Remember we use count sort because it is a stable sorting algorithm. Thus we observe that radix sort utilizes counting sort as its subroutine throughout its execution. Given two sorted arrays arr1[] and arr2[] of size M and N of distinct elements. Given a value Sum. The problem is to count all pairs from both arrays whose sum is equal to Sum. Note: The pair has an element from each array. Bucket Sort is a comparison-based sorting technique that operates on array elements by dividing them into multiple buckets recursively and then sorting these buckets individually using a separate sorting algorithm altogether.

Finally, the sorted buckets are re-combined to produce the sorted array. We can probe further into the working of bucket sort by assuming that we've already created an array of multiple 'buckets' lists. Elements are now inserted from the unsorted array into these "buckets" based on their properties. These buckets are finally sorted separately using the insertion sort algorithm as explained earlier. Well if you're still unsure about the bucket sort algorithm, go back and review the pseudocode one more time.

You are given two arrays, A and B , of equal size N. Comb sort is quite interesting. In fact, it is an improvement over the bubble sort algorithm. If you've observed earlier, bubble sort compares adjacent elements for every iteration. But for comb sort, the items are compared and swapped by a large gap value. The gap value shrinks by a factor of 1. This shrink factor has been empirically calculated to be 1.

Given an array, find the most frequent element in it. If there are multiple elements that appear maximum number of times, print any one of them. Shell sort algorithm is an improvement over the insertion sort algorithm wherein we resort to diminishing partitions to sort our data.

In each pass, we reduce the gap size to half of its previous value for each pass throughout the array. Thus for each iteration, the array elements are compared by the calculated gap value and swapped if necessary. The idea of shell sort is that it permits the exchange of elements located far from each other. In Shell Sort, we make the array N-sorted for a large value of N.