From 6ed6fda2be9c2343422047aec0c49ccf24100916 Mon Sep 17 00:00:00 2001
From: syedjafer <syedjafer1997@gmail.com>
Date: Thu, 13 Oct 2022 21:28:17 +0530
Subject: [PATCH 1/3] binary insertion sort

---
 Maths/CollatzSequence.js               |  2 +-
 Sorts/BinaryInsertionSort.js           | 60 ++++++++++++++++++++++++++
 Sorts/test/BinaryInsertionSort.test.js |  8 ++++
 3 files changed, 69 insertions(+), 1 deletion(-)
 create mode 100644 Sorts/BinaryInsertionSort.js
 create mode 100644 Sorts/test/BinaryInsertionSort.test.js

diff --git a/Maths/CollatzSequence.js b/Maths/CollatzSequence.js
index d8ead61cc2..4a3566b216 100644
--- a/Maths/CollatzSequence.js
+++ b/Maths/CollatzSequence.js
@@ -26,5 +26,5 @@ export function collatz (n) {
     steps.push(n)
   }
 
-  return { result: n, steps: steps }
+  return { result: n, steps }
 }
diff --git a/Sorts/BinaryInsertionSort.js b/Sorts/BinaryInsertionSort.js
new file mode 100644
index 0000000000..b522fa63a9
--- /dev/null
+++ b/Sorts/BinaryInsertionSort.js
@@ -0,0 +1,60 @@
+/**
+ * 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).
+ *
+ */
+
+/**
+ * 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
+ */
+function binarySearch (array, key, start, end) {
+  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 binarySearch(array, key, mid + 1, end)
+  } else if (array[mid] > key) {
+    return binarySearch(array, key, start, mid - 1)
+  } else {
+    return mid
+  }
+}
+
+/**
+   * Binary Insertion Sort
+   *
+   * @param {Array} list List to be sorted.
+   * @return {Array} The sorted list.
+   */
+export function binaryInsertionSort (array) {
+  const totalLength = array.length
+  for (let itr = 1; itr < totalLength; itr += 1) {
+    const key = array[itr]
+    const indexPosition = binarySearch(array, key, 0, itr - 1)
+    array.splice(itr, 1)
+    array.splice(indexPosition, 0, key)
+  }
+  return array
+}
diff --git a/Sorts/test/BinaryInsertionSort.test.js b/Sorts/test/BinaryInsertionSort.test.js
new file mode 100644
index 0000000000..84abe6a7ce
--- /dev/null
+++ b/Sorts/test/BinaryInsertionSort.test.js
@@ -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])
+  })
+})

From 954624aa90ee185e5d26da6b309b132e90efaaf6 Mon Sep 17 00:00:00 2001
From: syedjafer <syedjafer1997@gmail.com>
Date: Thu, 13 Oct 2022 22:11:21 +0530
Subject: [PATCH 2/3] Resolved Comments

---
 Sorts/BinaryInsertionSort.js | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/Sorts/BinaryInsertionSort.js b/Sorts/BinaryInsertionSort.js
index b522fa63a9..3326404e40 100644
--- a/Sorts/BinaryInsertionSort.js
+++ b/Sorts/BinaryInsertionSort.js
@@ -43,17 +43,17 @@ function binarySearch (array, key, start, end) {
 }
 
 /**
-   * Binary Insertion Sort
-   *
-   * @param {Array} list List to be sorted.
-   * @return {Array} The sorted list.
-   */
+ * Binary Insertion Sort
+ *
+ * @param {Array} list List to be sorted.
+ * @return {Array} The sorted list.
+ */
 export function binaryInsertionSort (array) {
   const totalLength = array.length
-  for (let itr = 1; itr < totalLength; itr += 1) {
-    const key = array[itr]
-    const indexPosition = binarySearch(array, key, 0, itr - 1)
-    array.splice(itr, 1)
+  for (let i = 1; i < totalLength; i += 1) {
+    const key = array[i]
+    const indexPosition = binarySearch(array, key, 0, i - 1)
+    array.splice(i, 1)
     array.splice(indexPosition, 0, key)
   }
   return array

From 128f43585b537d27229b576797c248b87211f991 Mon Sep 17 00:00:00 2001
From: syedjafer <syedjafer1997@gmail.com>
Date: Sun, 16 Oct 2022 06:30:41 +0530
Subject: [PATCH 3/3] Resolving Commits

---
 Maths/CollatzSequence.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Maths/CollatzSequence.js b/Maths/CollatzSequence.js
index 4a3566b216..d8ead61cc2 100644
--- a/Maths/CollatzSequence.js
+++ b/Maths/CollatzSequence.js
@@ -26,5 +26,5 @@ export function collatz (n) {
     steps.push(n)
   }
 
-  return { result: n, steps }
+  return { result: n, steps: steps }
 }