feat: Add implementation of jump serach algorithm in typescript (TheAlgorithms#133)

* feat: add jump search

* feat: add jump serach to directory.md

* feat: jumpSearch test fix

Author: BSzmolke

DIRECTORY.md

@@ -49,6 +49,7 @@
 
 ## Search
   * [Binary Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/binary_search.ts)
+  * [Jump Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/jump_search.ts)
   * [Linear Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/linear_search.ts)
 
 ## Sorts

search/jump_search.ts

@@ -0,0 +1,47 @@
+/**
+ * @function jumpSearch
+ * @description Jump search algorithm for a sorted array. 
+ * 
+ * Jump search is a searching algorithm for sorted arrays that checks elements 
+ * by jumping ahead by fixed steps. The optimal step size is the square root of the array length. 
+ * 
+ * The algorithm works as follows:
+ * 1.Start from the first element and jump by step size until finding an element that is greater than or equal to the target value.
+ * 2.Go back one step and perform a linear search from there until finding the target value or reaching the end of the subarray.
+ * 3.If the target value is found, return its index. Otherwise, return -1 to indicate that it is not in the array.
+ * 
+ * @param {number[]} array - sorted list of numbers
+ * @param {number} target - target number to search for
+ * @return {number} - index of the target number in the list, or -1 if not found
+ * @see [JumpSearch](https://www.geeksforgeeks.org/jump-search/)
+ * @example jumpSearch([1,2,3], 2) => 1
+ * @example jumpSearch([4,5,6], 2) => -1
+ */
+
+export const jumpSearch = (array: number[], target: number): number => {
+    if (array.length === 0) return -1;
+
+    // declare pointers for the current and next indexes and step size
+    let currentIdx: number = 0,
+        stepSize: number = Math.floor(Math.sqrt(array.length)),
+        nextIdx: number = stepSize;
+        
+    while (array[nextIdx - 1] < target) {
+        currentIdx = nextIdx;
+        nextIdx += stepSize;
+
+        if (nextIdx >= array.length) {
+            nextIdx = array.length - 1;
+            break;
+        }
+    }
+
+    for (let index = currentIdx; index < nextIdx; index++) {
+        if(array[index] == target)
+        {
+            return index;
+        } 
+    }
+
+    return -1;
+}

search/test/jump_search.test.ts

@@ -0,0 +1,14 @@
+import { jumpSearch } from "../jump_search";
+
+describe("Jump search", () => {
+  test.each([
+    [[], 1, -1],
+    [[1, 2, 3, 4, 5], 4, 3],
+    [[1, 3, 5, 8, 9], 4, -1],
+  ])(
+    "of %o , searching for %o, expected %i",
+    (array: any[], target: any, index: number) => {
+      expect(jumpSearch(array, target)).toStrictEqual(index)
+    },
+  );
+});