### Sorting and Searching

Binary search is one of the fundamental algorithms in computer science. In order to Here is some code to go with the description: binary_search(A Java has a built-in jogglerwiki.info_search method for arrays and jogglerwiki.info Framework has. Recursive binary search is an implementation of the binary search algorithm Write a query to find all staff (Staff number, Eirst name, Last Name) who work at. Binary Search in Java without using Recursion - Iterative algorithm .. how to persist objects and relationships in Neo4j's NoSQL data store.

The same basic approach is effective for many important problems, as you will learn if you take a course on algorithm design. A problem A reduces to a problem B if we can use a solution to B to solve A. For example, consider the problem of determining whether the elements in an array are all different. This problem reduces to sorting because we can sort the array, the make a linear pass through the sorted array to check whether any entry is equal to the next if not, the elements are all different.

We accomplish this by two sorts. Our first step is to sort the strings on standard input. In this case, we are not so much interested in the fact that the strings are put into sorted order, but in the fact that sorting brings equal strings together.

If the input is to be or not to be to then the result of the sort is be be not or to to to with equal strings like the three occurrences of to brought together in the array. Now, with equal strings all together in the array, we can make a single pass through the array to compute all the frequencies. Next, we sort the Counter objects. We can do so in client code without any special arrangements because Counter implements the Comparable interface.

The application highlighted in FrequencyCount. Exercises Write a filter Dedup. Creative Exercises This list of exercises is intended to give you experience in developing fast solutions to typical problems.

Think about using binary search, mergesort, or devising your own divide-and-conquer algorithm. Implement and test your algorithm. Write a linear-time filter IntegerSort. For example, presented with the input sequence 98 2 3 1 0 0 0 3 98 98 2 2 2 0 0 0 2 your program should print the output sequence 0 0 0 0 0 0 1 2 2 2 2 2 3 3 98 98 98 Three sum.

Given an array of n integers, design an algorithm to determine whether any three of them sum to 0. The order of growth of the running time of your program should be n2 log n. Develop a program that solves the problem in quadratic time. Write a recursive program Quick. First, pick a random element v as the partitioning element. Next, partition the array into a left subarray containing all elements less than v, followed by a middle subarray containing all elements equal to v, followed by a right subarray containing all elements greater than v.

Finally, recursively sort the left and right subarrays. Write a program to read in a list of domain names from standard input, and print the reverse domain names in sorted order. For example, the reverse domain of cs. This computation is useful for web log analysis. To do so, create a data type Domain. Local minimum in an array. Web Exercises Union of intervals. Given N intervals on the real line, determine the length of their union in O N log N time. For example the union of the four intervals [1, 3], [2, 4.

Suppose you have a coffee can which contains an unknown number of black beans and an unknown number of white beans. Repeat the following process until exactly one bean remains: Select two beans from the can at random. If they are both the same color, throw them both out, but insert another black bean. If they are different colors, throw the black one away, but return the white one.

Prove that this process terminates with exactly one bean left. What can you deduce about the color of the last bean as a function of the initial number of black and white beans? To initiate an illegal spam campaign, you have a list of email addresses from various domains the part of the email address that follows the symbol.

To better forge the return addresses, you want to send the email from another user at the same domain. For example, you might want to forge an email from nobody princeton. How would you process the email list to make this an efficient task? Given an array of N elements, not necessarily in ascending order, devised an algorithm to find the kth largest one.

It should run in O N time on random inputs. Given two permutations, Kendall's tau distance is the number of pairs out of position. Useful in top-k lists, social choice and voting theory, comparing genes using expression profiles, and ranking search engine results.

Given N points on a circle, centered at the origin, design an algorithm that determines whether there are two points that are antipodal, i. Your algorithm should run in time proportional to N log N.

Repeat the previous question, but assume the points are given in clockwise order. Your algorithm should run in time proportional to N. Given an array a[] of N distinct integers positive or negative in ascending order. 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? Given two arrays of N bit integers, design an algorithm to print out all elements that appear in both lists.

The output should be in sorted order. Your algorithm should run in N log N.

## Binary Searching in Java Without Recursion

Repeat the above exercise but assume the first array has M integers and the second has N integers where M is much less than N. Give an algorithm that runs in N log M time. Design a O N log N algorithm to read in a list of words and print out all anagrams.

For example, the strings "comedian" and "demoniac" are anagrams of each other. Assume there are N words and each word contains at most 20 letters. Given a list of N points in the plane, find all subset of 3 or more points that are collinear.

Given a list of N points in the plane in general position no three are collinearfind a new point p that is not collinear with any pair of the N original points.

Search in a sorted, rotated list. Given a sorted list of N integers that has been rotated an unknown number of positions, e. Each user ranks N songs in order of preference. Given a preference list, find the user with the closest preferences.

Measure "closest" according to the number of inversions. Devise an N log N algorithm for the problem. Throwing cats from an N-story building.

### java - How to use recursion in creating a binary search algorithm - Stack Overflow

Suppose that you have an N story building and a bunch of cats. Suppose also that a cat dies if it is thrown off floor F or higher, and lives otherwise. Devise a strategy to determine the floor F, while killing O log N cats. Throwing cats from a building.

Repeat the previous exercise, but devise a strategy that kills O log F cats. Throwing two cats from an N-story building. Repeat the previous question, but now assume you only have two cats. Now your goal is to minimize the number of throws. This application might occur in practice if search hits cat surviving fall are much cheaper than misses cat dying. Throwing two cats from a building. The algorithm exhibits a logarithmic order of growth because it essentially divides the problem domain in half with each pass, hence its time complexity is O logN in both average and worst case.

Important points of Binary Search Algorithm 1 The Binary search algorithm, both iterative and recursive requires a sorted array. You can sort the array in your method, or can ask the client to sort that. You should not use binary search algorithm with a linear data structure like linked list.

It's always better to use library method because it is well tested and generally provides better performance. This is also one of the advice I learned from Effective Java.

Implementation of Binary Search Algorithm in Java Here is our sample Java program to implement binary search algorithm using recursion in Java.

The algorithm is naturally recursive because in every step it divides the input in half and then applies the same algorithm in the remaining half. We have a public binarySearch int[] input, int target method which accepts an integer array and a target value to search in the array. This method then calls another helper method which performs the binary search algorithm using recursion.

This helper method is private and not visible to clients because it also accepts some additional variables in terms of start and end points to search in the array. This is why I have a public method which is part of API and accept input and target value from a client and this private method is part of implementation hence not visible to the client.

- Insertion sort.
- Your Answer
- JAVA EXAMPLE PROGRAMS

This binarySearch is the overloaded version of the previous one because it's method signature is different. It returns the index of the target value if found in array and -1 if the value doesn't exist in the array. In each step, this recursive method first checks if low is greater than high or not i. This is the base case of the recursive binary search algorithm. If this condition is not met then it calculates the midpoint and checks if the value at midpoint matches with the target value, if yes then we have found the position of target value and method completes by returning the index of the target value.

If the value is not found then a recursive call is made to the relevant half e. By the way, if you have trouble understanding how a recursive algorithm works, I suggest you to first read Grokking Algorithms By Aditya Bhargavahe explained recursion really well using nice diagrams.

Along with Linear search, this is two of the essential search algorithms you learn in your computer science class.

The binary search tree data structure take advantage of this algorithm and arrange data in hierarchical structure, so that you can search any node in O logN time. Though, you must remember that in order to use binary search, you need a sorted list or array, so, you also need to consider cost of sorting when you consider using binary search algorithm in real world.