Add Jump Search algorithm.

Author: trekhleb

README.md

@@ -84,6 +84,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
 * **Searches**
   * `B` [Linear Search](src/algorithms/search/linear-search)
+  * `B` [Jump Search](src/algorithms/search/jump-search)
   * `B` [Binary Search](src/algorithms/search/binary-search)
 * **Sorting**
   * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
@@ -129,6 +130,7 @@ of algorithms. It is an abstraction higher than the notion of an algorithm, just
 algorithm is an abstraction higher than a computer program.
 
 * **Brute Force** - look at all the possibilities and selects the best solution
+  * `B` [Linear Search](src/algorithms/search/linear-search)
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
 * **Greedy** - choose the best option at the current time, without any consideration for the future

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

@@ -12,6 +12,11 @@ in the array.
 
 ![Binary Search](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg)
 
+## Complexity
+
+**Time Complexity**: `O(log(n))` - since we split search area by two for every
+next iteration.
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)

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

@@ -1,6 +1,8 @@
 import Comparator from '../../../utils/comparator/Comparator';
 
 /**
+ * Binary search implementation.
+ *
  * @param {*[]} sortedArray
  * @param {*} seekElement
  * @param {function(a, b)} [comparatorCallback]

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

@@ -0,0 +1,27 @@
+# Jump Search
+
+Like Binary Search, **Jump Search** (or **Block Search**) is a searching algorithm 
+for sorted arrays. The basic idea is to check fewer elements (than linear search) 
+by jumping ahead by fixed steps or skipping some elements in place of searching all 
+elements.
+
+For example, suppose we have an array `arr[]` of size `n` and block (to be jumped)
+of size `m`. Then we search at the indexes `arr[0]`, `arr[m]`, `arr[2 * m]`, ..., `arr[k * m]` and 
+so on. Once we find the interval `arr[k * m] < x < arr[(k+1) * m]`, we perform a 
+linear search operation from the index `k * m` to find the element `x`.
+
+**What is the optimal block size to be skipped?**
+In the worst case, we have to do `n/m` jumps and if the last checked value is 
+greater than the element to be searched for, we perform `m - 1` comparisons more 
+for linear search. Therefore the total number of comparisons in the worst case 
+will be `((n/m) + m - 1)`. The value of the function `((n/m) + m - 1)` will be 
+minimum when `m = √n`. Therefore, the best step size is `m = √n`.
+
+## Complexity
+
+**Time complexity**: `O(√n)` - because we do search by blocks of size `√n`.
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Jump_search)
+- [GeeksForGeeks](https://www.geeksforgeeks.org/jump-search/)

src/algorithms/search/jump-search/__test__/jumpSearch.test.js

@@ -0,0 +1,20 @@
+import jumpSearch from '../jumpSearch';
+
+describe('jumpSearch', () => {
+  it('should search for an element in sorted array', () => {
+    expect(jumpSearch([], 1)).toBe(-1);
+    expect(jumpSearch([1], 2)).toBe(-1);
+    expect(jumpSearch([1], 1)).toBe(0);
+    expect(jumpSearch([1, 2], 1)).toBe(0);
+    expect(jumpSearch([1, 2], 1)).toBe(0);
+    expect(jumpSearch([1, 1, 1], 1)).toBe(0);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 2)).toBe(1);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 0)).toBe(-1);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 0)).toBe(-1);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 7)).toBe(-1);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 5)).toBe(2);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 20)).toBe(4);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 30)).toBe(7);
+    expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 48)).toBe(8);
+  });
+});

src/algorithms/search/jump-search/jumpSearch.js

@@ -0,0 +1,51 @@
+import Comparator from '../../../utils/comparator/Comparator';
+
+/**
+ * Jump (block) search implementation.
+ *
+ * @param {*[]} sortedArray.
+ * @param {*} seekElement
+ * @param {function(a, b)} [comparatorCallback]
+ * @return {number}
+ */
+export default function jumpSearch(sortedArray, seekElement, comparatorCallback) {
+  const comparator = new Comparator(comparatorCallback);
+  const arraySize = sortedArray.length;
+
+  if (!arraySize) {
+    // We can't find anything in empty array.
+    return -1;
+  }
+
+  // Calculate optimal jump size.
+  // Total number of comparisons in the worst case will be ((arraySize/jumpSize) + jumpSize - 1).
+  // The value of the function ((arraySize/jumpSize) + jumpSize - 1) will be minimum
+  // when jumpSize = √array.length.
+  const jumpSize = Math.floor(Math.sqrt(arraySize));
+
+  // Find the block where the seekElement belong to.
+  let blockStart = 0;
+  let blockEnd = jumpSize;
+  while (comparator.greaterThan(seekElement, sortedArray[Math.min(blockEnd, arraySize) - 1])) {
+    // Jump to the next block.
+    blockStart = blockEnd;
+    blockEnd += jumpSize;
+
+    // If our next block is out of array then we couldn't found the element.
+    if (blockStart > arraySize) {
+      return -1;
+    }
+  }
+
+  // Do linear search for seekElement in subarray starting from blockStart.
+  let currentIndex = blockStart;
+  while (currentIndex < Math.min(blockEnd, arraySize)) {
+    if (comparator.equal(sortedArray[currentIndex], seekElement)) {
+      return currentIndex;
+    }
+
+    currentIndex += 1;
+  }
+
+  return -1;
+}

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

@@ -8,6 +8,11 @@ comparisons, where `n` is the length of the list.
 
 ![Linear Search](https://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif)
 
+## Complexity
+
+**Time Complexity**: `O(n)` - since in worst case we're checking each element
+exactly once.
+
 ## References
 - [Wikipedia](https://en.wikipedia.org/wiki/Linear_search)
 - [TutorialsPoint](https://www.tutorialspoint.com/data_structures_algorithms/linear_search_algorithm.htm)

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

@@ -1,6 +1,8 @@
 import Comparator from '../../../utils/comparator/Comparator';
 
 /**
+ * Linear search implementation.
+ *
  * @param {*[]} array
  * @param {*} seekElement
  * @param {function(a, b)} [comparatorCallback]