feat: add binary insertion sort algorithm

DIRECTORY.md

@@ -3,11 +3,43 @@
   * [Xor Cipher](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/ciphers/xor_cipher.ts)
 
 ## Data Structures
-  * [Array Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/array_queue.ts)
-  * [Linked Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/linked_queue.ts)
-  * [Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue.ts)
-  * [Stack](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack.ts)
-  * [Stack Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack_queue.ts)
+  * List
+    * [Doubly Linked List](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/doubly_linked_list.ts)
+    * [Linked List](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/linked_list.ts)
+    * [Singly Linked List](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/singly_linked_list.ts)
+    * Test
+      * [Doubly Linked List.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/test/doubly_linked_list.test.ts)
+      * [Linked List](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/test/linked_list.ts)
+      * [Singly Linked List.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/list/test/singly_linked_list.test.ts)
+  * Map
+    * [Hash Map](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/map/hash_map.ts)
+    * [Map](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/map/map.ts)
+    * Test
+      * [Hash Map.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/map/test/hash_map.test.ts)
+  * Queue
+    * [Array Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/array_queue.ts)
+    * [Linked Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/linked_queue.ts)
+    * [Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/queue.ts)
+    * [Stack Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/stack_queue.ts)
+    * Test
+      * [Array Queue.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/test/array_queue.test.ts)
+      * [Linked Queue.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/test/linked_queue.test.ts)
+      * [Queue](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/test/queue.ts)
+      * [Stack Queue.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/queue/test/stack_queue.test.ts)
+  * Set
+    * [Hash Map Set](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/set/hash_map_set.ts)
+    * [Map Set](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/set/map_set.ts)
+    * [Set](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/set/set.ts)
+  * Stack
+    * [Linked List Stack](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack/linked_list_stack.ts)
+    * [Stack](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack/stack.ts)
+    * Test
+      * [Linked List Stack.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack/test/linked_list_stack.test.ts)
+      * [Stack.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/stack/test/stack.test.ts)
+  * Tree
+    * [Binary Search Tree](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/tree/binary_search_tree.ts)
+    * Test
+      * [Binary Search Tree.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/data_structures/tree/test/binary_search_tree.test.ts)
 
 ## Dynamic Programming
   * [Knapsack](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/dynamic_programming/knapsack.ts)
@@ -18,9 +50,11 @@
   * [Armstrong Number](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/armstrong_number.ts)
   * [Binary Convert](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/binary_convert.ts)
   * [Calculate Mean](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/calculate_mean.ts)
+  * [Calculatemedian](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/calculatemedian.ts)
   * [Degrees To Radians](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/degrees_to_radians.ts)
   * [Digit Sum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/digit_sum.ts)
   * [Factorial](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/factorial.ts)
+  * [Factors](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/factors.ts)
   * [Fibonacci](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/fibonacci.ts)
   * [Find Min](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/find_min.ts)
   * [Greatest Common Factor](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/greatest_common_factor.ts)
@@ -29,8 +63,10 @@
   * [Is Even](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_even.ts)
   * [Is Leap Year](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_leap_year.ts)
   * [Is Odd](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_odd.ts)
+  * [Is Prime](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_prime.ts)
   * [Is Square Free](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_square_free.ts)
   * [Lowest Common Multiple](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/lowest_common_multiple.ts)
+  * [Number Of Digits](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/number_of_digits.ts)
   * [Perfect Square](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/perfect_square.ts)
   * [Pronic Number](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/pronic_number.ts)
   * [Radians To Degrees](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/radians_to_degrees.ts)
@@ -40,6 +76,7 @@
       * [Hexagonal Numbers.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/series/test/hexagonal_numbers.test.ts)
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/sieve_of_eratosthenes.ts)
   * [Signum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/signum.ts)
+  * [Zellers Congruence](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/zellers_congruence.ts)
 
 ## Other
   * [Parse Nested Brackets](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/other/parse_nested_brackets.ts)
@@ -51,8 +88,10 @@
   * [Linear Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/linear_search.ts)
 
 ## Sorts
+  * [Binaryinsertionsort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/binaryinsertionsort.ts)
   * [Bubble Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/bubble_sort.ts)
   * [Gnome Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/gnome_sort.ts)
   * [Insertion Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/insertion_sort.ts)
   * [Merge Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/merge_sort.ts)
   * [Quick Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/quick_sort.ts)
+  * [Selection Sort](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/sorts/selection_sort.ts)

sorts/binaryinsertionsort.ts

@@ -0,0 +1,61 @@
+/**
+ * Pure Implementation of Binary Search Algorithm
+ *
+ * Binary insertion sort is a sorting algorithm similar to insertion sort,
+ * but instead of using linear search to find the position
+ * where the element should be inserted, we use binary search.
+ * Thus, we reduce the number of comparisons for inserting one element from O(N)
+ * (Time complexity in Insertion Sort) to O(log N).
+ *
+ */
+
+/**
+ * @function binarySearch
+ * @description Search the key element in the array from start position to end position.
+ * @param {Array} array Array of numbers.
+ * @param {Number} key Value to be searched
+ * @param {Number} start start index position of array
+ * @param {Number} end end index position of array
+ * @return {Number} Position of the key element
+ */
+const findPosbinarySearch = (array: number[], key: number, start: number, end: number): number => {
+  if (start === end) {
+    if (array[start] > key) {
+      return start;
+    } else {
+      return start + 1;
+    }
+  }
+
+  if (start > end) {
+    return start;
+  }
+
+  const mid = Math.floor((start + end) / 2);
+
+  if (array[mid] < key) {
+    return findPosbinarySearch(array, key, mid + 1, end);
+  } else if (array[mid] > key) {
+    return findPosbinarySearch(array, key, start, mid - 1);
+  } else {
+    return mid;
+  }
+}
+
+/**
+ * @function Binary Insertion Sort
+ * @param {Array} list List to be sorted.
+ * @return {Array} The sorted list.
+ */
+export const binaryInsertionSort = (array: number[]): number[] => {
+  const totalLength = array.length;
+  for (let itr = 1; itr < totalLength; itr += 1) {
+    const key = array[itr];
+    const indexPosition = findPosbinarySearch(array, key, 0, itr - 1);
+    array.splice(itr, 1);
+    array.splice(indexPosition, 0, key);
+  }
+  return array;
+}
+
+console.log(binaryInsertionSort([5,4, 3, 1, 2]))

sorts/test/binaryinsertionsort.test.ts

@@ -0,0 +1,8 @@
+import { binaryInsertionSort } from "../BinaryInsertionSort";
+
+describe("BinaryInsertionSort", () => {
+  it("should sort arrays correctly", () => {
+    expect(binaryInsertionSort([5, 4, 3, 2, 1])).toEqual([1, 2, 3, 4, 5]);
+    expect(binaryInsertionSort([7, 9, 4, 3, 5])).toEqual([3, 4, 5, 7, 9]);
+  });
+});