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Commita327b68

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Add Jump Search algorithm.
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‎README.md

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@@ -84,6 +84,7 @@ a set of rules that precisely define a sequence of operations.
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*`A`[Regular Expression Matching](src/algorithms/string/regular-expression-matching)
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***Searches**
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*`B`[Linear Search](src/algorithms/search/linear-search)
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*`B`[Jump Search](src/algorithms/search/jump-search)
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*`B`[Binary Search](src/algorithms/search/binary-search)
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***Sorting**
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*`B`[Bubble Sort](src/algorithms/sorting/bubble-sort)
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algorithm is an abstraction higher than a computer program.
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***Brute Force** - look at all the possibilities and selects the best solution
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*`B`[Linear Search](src/algorithms/search/linear-search)
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*`A`[Maximum Subarray](src/algorithms/sets/maximum-subarray)
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*`A`[Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
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***Greedy** - choose the best option at the current time, without any consideration for the future

‎src/algorithms/search/binary-search/README.md

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![Binary Search](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg)
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##Complexity
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**Time Complexity**:`O(log(n))` - since we split search area by two for every
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next iteration.
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##References
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-[Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)

‎src/algorithms/search/binary-search/binarySearch.js

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importComparatorfrom'../../../utils/comparator/Comparator';
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/**
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* Binary search implementation.
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*
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*@param {*[]} sortedArray
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*@param {*} seekElement
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*@param {function(a, b)} [comparatorCallback]
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#Jump Search
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Like Binary Search,**Jump Search** (or**Block Search**) is a searching algorithm
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for sorted arrays. The basic idea is to check fewer elements (than linear search)
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by jumping ahead by fixed steps or skipping some elements in place of searching all
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elements.
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For example, suppose we have an array`arr[]` of size`n` and block (to be jumped)
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of size`m`. Then we search at the indexes`arr[0]`,`arr[m]`,`arr[2 * m]`, ...,`arr[k * m]` and
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so on. Once we find the interval`arr[k * m] < x < arr[(k+1) * m]`, we perform a
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linear search operation from the index`k * m` to find the element`x`.
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**What is the optimal block size to be skipped?**
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In the worst case, we have to do`n/m` jumps and if the last checked value is
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greater than the element to be searched for, we perform`m - 1` comparisons more
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for linear search. Therefore the total number of comparisons in the worst case
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will be`((n/m) + m - 1)`. The value of the function`((n/m) + m - 1)` will be
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minimum when`m = √n`. Therefore, the best step size is`m = √n`.
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##Complexity
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**Time complexity**:`O(√n)` - because we do search by blocks of size`√n`.
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##References
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-[Wikipedia](https://en.wikipedia.org/wiki/Jump_search)
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-[GeeksForGeeks](https://www.geeksforgeeks.org/jump-search/)
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importjumpSearchfrom'../jumpSearch';
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describe('jumpSearch',()=>{
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it('should search for an element in sorted array',()=>{
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expect(jumpSearch([],1)).toBe(-1);
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expect(jumpSearch([1],2)).toBe(-1);
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expect(jumpSearch([1],1)).toBe(0);
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expect(jumpSearch([1,2],1)).toBe(0);
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expect(jumpSearch([1,2],1)).toBe(0);
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expect(jumpSearch([1,1,1],1)).toBe(0);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],2)).toBe(1);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],0)).toBe(-1);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],0)).toBe(-1);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],7)).toBe(-1);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],5)).toBe(2);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],20)).toBe(4);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],30)).toBe(7);
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expect(jumpSearch([1,2,5,10,20,21,24,30,48],48)).toBe(8);
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});
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});
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importComparatorfrom'../../../utils/comparator/Comparator';
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/**
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* Jump (block) search implementation.
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*
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*@param {*[]} sortedArray.
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*@param {*} seekElement
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*@param {function(a, b)} [comparatorCallback]
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*@return {number}
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*/
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exportdefaultfunctionjumpSearch(sortedArray,seekElement,comparatorCallback){
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constcomparator=newComparator(comparatorCallback);
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constarraySize=sortedArray.length;
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if(!arraySize){
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// We can't find anything in empty array.
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return-1;
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}
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// Calculate optimal jump size.
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// Total number of comparisons in the worst case will be ((arraySize/jumpSize) + jumpSize - 1).
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// The value of the function ((arraySize/jumpSize) + jumpSize - 1) will be minimum
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// when jumpSize = √array.length.
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constjumpSize=Math.floor(Math.sqrt(arraySize));
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// Find the block where the seekElement belong to.
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letblockStart=0;
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letblockEnd=jumpSize;
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while(comparator.greaterThan(seekElement,sortedArray[Math.min(blockEnd,arraySize)-1])){
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// Jump to the next block.
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blockStart=blockEnd;
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blockEnd+=jumpSize;
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// If our next block is out of array then we couldn't found the element.
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if(blockStart>arraySize){
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return-1;
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}
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}
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// Do linear search for seekElement in subarray starting from blockStart.
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letcurrentIndex=blockStart;
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while(currentIndex<Math.min(blockEnd,arraySize)){
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if(comparator.equal(sortedArray[currentIndex],seekElement)){
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returncurrentIndex;
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}
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currentIndex+=1;
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}
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return-1;
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}

‎src/algorithms/search/linear-search/README.md

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![Linear Search](https://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif)
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##Complexity
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**Time Complexity**:`O(n)` - since in worst case we're checking each element
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exactly once.
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##References
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-[Wikipedia](https://en.wikipedia.org/wiki/Linear_search)
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-[TutorialsPoint](https://www.tutorialspoint.com/data_structures_algorithms/linear_search_algorithm.htm)

‎src/algorithms/search/linear-search/linearSearch.js

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importComparatorfrom'../../../utils/comparator/Comparator';
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/**
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* Linear search implementation.
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*
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*@param {*[]} array
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*@param {*} seekElement
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*@param {function(a, b)} [comparatorCallback]

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