docs: quicksort readme cleanup

Author: kaitinghh

src/main/java/algorithms/sorting/quickSort/hoares/README.md

@@ -5,21 +5,23 @@ Note that the usual Hoare's QuickSort differs slightly from lecture implementati
 
 This version of QuickSort assumes the **absence of duplicates** in our array.
 
+## Background
+
 QuickSort is a sorting algorithm based on the divide-and-conquer strategy. It works by selecting a pivot element from
 the array and rearranging the elements such that all elements less than the pivot are on its left, and
 all elements greater than the pivot are on its right. This effectively partitions the array into two parts. The same
 process is then applied recursively to the two partitions until the entire array is sorted.
 
-Implementation Invariant:
+## Implementation Invariant:
 
 The pivot is in the correct position, with elements to its left being < it, and elements to its right being > it.
 
 ![Lecture Hoare's QuickSort](../../../../../../../docs/assets/images/LectureHoares.jpeg)
 Example Credits: Prof Seth/Lecture Slides
 
 ## Complexity Analysis
-
-Complexity Analysis: (this analysis is based on fixed index pivot selection)
+* This analysis is based on fixed index pivot selection.
+* The complexity analysis for Hoare's quicksort is the same as that of Lomuto's quicksort. 
 
 Time:
 

src/main/java/algorithms/sorting/quickSort/lomuto/README.md

@@ -23,7 +23,8 @@ then swap the pivot back to its correct position. Below is an illustration:
 The pivot is in the correct position, with elements to its left being <= it, and elements to its right being > it.
 
 ## Complexity Analysis:
-Time:
+* The complexity analysis for Lomuto's quicksort is the same as that of Hoare's quicksort.
+  Time:
 - Expected worst case (poor choice of pivot): O(n^2)
 - Expected average case: O(nlogn)
 - Expected best case (balanced pivot): O(nlogn)

src/main/java/algorithms/sorting/quickSort/paranoid/README.md

@@ -1,11 +1,11 @@
 # Paranoid QuickSort
 
-### Background 
+## Background 
 Paranoid Quicksort is the naive quicksort with an additional check to guarantee a good pivot.
 
 ![ParanoidQuickSort](../../../../../../../docs/assets/images/ParanoidQuickSort.jpeg)
 
-### Complexity Analysis:
+## Complexity Analysis:
 Time: (this analysis assumes the absence of many duplicates in our array)
 - Expected worst case: O(nlogn)
 - Expected average case: O(nlogn)

src/main/java/algorithms/sorting/quickSort/threeWayPartitioning/README.md

@@ -1,6 +1,6 @@
 # Three-Way Partitioning
 
-### Background
+## Background
 Three-way partitioning is used in QuickSort to tackle the scenario where there are many duplicate elements in the
 array being sorted.
 
@@ -10,11 +10,11 @@ and swaps with duplicate elements, making the sorting process more efficient.
 
 ![ThreeWayPartitioning](../../../../../../../docs/assets/images/ThreeWayPartitioning.jpeg)
 
-### Implementation Invariant:
+## Implementation Invariant:
 The pivot and any element numerically equal to the pivot will be in the correct positions in the array. Elements
 to their left are < them and elements to their right are > than them.
 
-### Complexity Analysis:
+## Complexity Analysis:
 Time:
 - Worst case: O(nlogn)
 - Average case: O(nlogn)