Insertion Sort Algorithm

README.md

@@ -8,6 +8,7 @@ This repository is one where we document the implementations and usage of differ
 - [Sort Algorithms](./src/com/sketch/sort/)
   - [Quick Sort](./src/com/sketch/sort/quicksort/QuickSort.md)
   - [Selection Sort](./src/com/sketch/sort/selectionsort/SelectionSort.md)
+  - [Insertion Sort](./src/com/sketch/sort/insertionsort/InsertionSort.md)
 
 ## Contributions
 This repository is open-source and available to everyone to wants to learn DSA or wants to contibute to documenting other algorithms.

src/com/sketch/Main.java

@@ -1,24 +1,30 @@
 package com.sketch;
 
-import com.sketch.sort.quicksort.QuickSort;
+import com.sketch.sort.insertionsort.InsertionSort;
 
 import java.util.Arrays;
 import java.util.Random;
 
 public class Main {
     public static void main(String[] args){
-        int[] unsortedArray = new int[100];
+        int[] unsortedArray = new int[10000];
         Random random = new Random();
         for(int i = 0; i < unsortedArray.length; i++){
-            unsortedArray[i] = random.nextInt(20);
+            unsortedArray[i] = random.nextInt(50);
         }
 
         int[] unsortedArrayResult = new int[unsortedArray.length];
         System.arraycopy(unsortedArray, 0, unsortedArrayResult, 0, unsortedArray.length);
 
-        QuickSort.sort(unsortedArrayResult, 0, unsortedArrayResult.length - 1);
+        long startTime = System.nanoTime();
 
-        System.out.println("Actual Value Index: " + Arrays.toString(unsortedArray));
-        System.out.println("Actual Value Index: " + Arrays.toString(unsortedArrayResult));
+        InsertionSort.sort(unsortedArrayResult);
+
+        long endTime = System.nanoTime();
+        double duration = (endTime - startTime) / 1_000_000.0;
+
+        System.out.println("Default Array: " + Arrays.toString(unsortedArray));
+        System.out.println("Sorted Array: " + Arrays.toString(unsortedArrayResult));
+        System.out.println("Execution Time: " + duration + "ms");
     }
 }

src/com/sketch/sort/insertionsort/InsertionSort.java

@@ -0,0 +1,15 @@
+package com.sketch.sort.insertionsort;
+
+public class InsertionSort {
+    public static void sort(int[] array){
+        for(int i = 1; i < array.length; i++){
+            int currentValue = array[i];
+            int j = i - 1;
+            while (j >= 0 && array[j] > currentValue){
+                array[j + 1] = array[j];
+                j--;
+            }
+            array[j + 1] = currentValue;
+        }
+    }
+}

src/com/sketch/sort/insertionsort/InsertionSort.md

@@ -0,0 +1,60 @@
+# Insertion Sort
+
+Insertion Sort is a simple, comparison-based algorithm that builds a sorted list one element at a time.
+It works similarly to the way most people instinctively sort a hand of playing cards - by picking up one card at a time and inserting it into its correct position relative to the cards already held.
+
+The algorithm is classified as an in-place and stable sorting algorithm =, meaning it requires no additional memory proportional to the input size,
+and it preserves the relative order of elements with equal keys.
+
+![img.png](img.png)
+
+Insertion Sort divides the input list into two conceptual parts:
+- A sorted portion on the left, and
+- An unsorted portion on the right.
+
+At the start, the sorted portion contains only the first element, since a single element is trivially sorted.
+The algorithm then proceeds through the following steps for each remaining element:
+- The current element is picked from the unsorted portion - *this is called the key*.
+- The key is compared against the elements in the sorted portion, moving from right to left.
+- Any sorted element that is greater than the key is shifted one position to the right to make room.
+- Once the correct position is found, the key is inserted there.
+- This process repeats until all elements have been moved from the unsorted portion into the sorted portion.
+
+By the time the algorithm reaches the last element, the entire list i guaranteed to be sorted.
+
+## Interesting facts
+- Insertion Sort is one of the few sorting algorithms that can sort a list as it receives it - it is an online algorithm, meaning it does not need all elements to be present before it begins sorting.
+- Unlike Bubble Sort and [Selection Sort](../selectionsort/SelectionSort.md), Insertion Sort performs very well on nearly sorted data, achieving close to linear time (O(n)) is such cases.
+- The algorithm is naturally adaptive - its performance improves the more sorted the input already is.
+- Insertion Sort is stable, meaning two elements with equal values will retain their original relative order after sorting.
+- It is widely used in education settings as an introduction to sorting due to its intuitive, step-by-step nature.
+
+## Complexity Analysis
+- Time Complexity
+  - Best Case: O(n)
+  - Average Case: O(n^2)
+  - Worst Case: O(n^2)
+- Auxiliary Space:
+  - Best Case: O(1)
+  - Average Case: O(1)
+  - Worst Case: O(1)
+
+## Advantages
+- Simple to understand and implement, making it ideal for learning and teaching sorting concepts.
+- Very efficient on small datasets, often outperforming more complex algorithms like [Quick Sort](../quicksort/QuickSort.md) or Merge Sort at small sizes.
+- Performs exceptionally well o nearly sorter or partially sorted data due to its adaptive nature.
+- In-place sorting requires no extra memory allocation, making it memory efficient.
+- Stable sort preserves the original order of equal elements, which is important in certain use cases such as sorting records with multiple fields.
+- Online algorithm - can sort data as it arrives without needing the full dataset upfront.
+
+## Disadvantages
+- Inefficient on large datasets due to its O(n^2) average and worst-case time complexity.
+- Performance degrades significantly when the data is in reverse order, as every element must shift past all previously sorted elements.
+- Not suitable as a general-purpose sorting algorithm for large-scale applications where performance is critical.
+- Compared to divide-and-conquer algorithms like Merge Sort or [Quick Sort](../quicksort/QuickSort.md), ir does not scale well as input size grows.
+
+## Applications
+- Used as a subroutine in Bucket Sort
+- Can be useful when array is already almost sorted
+- Since Insertion sort is suitable for small sized arrays, it is used in Hybrid Sorting algorithms along with other efficient algorithms like [Quick Sort](../quicksort/QuickSort.md) and Merge Sort. When the subarray size becomes small, we switch to insertion sort in these recursive algorithms.
+- Embedded Systems: In low-memory environments such as micro-controllers, Insertion Sort's in-place O(1) space requirement makes it a practical choice.