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Complete guide to sorting algorithms — Bubble, Selection, Insertion, Merge, Quick, and Heap sort with Java code, complexity analysis, and visual step-throughs.
Comparison of Sorting Algorithms
| Algorithm | Best | Average | Worst | Space | Stable | In-place |
|---|---|---|---|---|---|---|
| Bubble Sort | O(n) | O(n²) | O(n²) | O(1) | ✅ | ✅ |
| Selection Sort | O(n²) | O(n²) | O(n²) | O(1) | ❌ | ✅ |
| Insertion Sort | O(n) | O(n²) | O(n²) | O(1) | ✅ | ✅ |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) | ✅ | ❌ |
| Quick Sort | O(n log n) | O(n log n) | O(n²) | O(log n) | ❌ | ✅ |
| Heap Sort | O(n log n) | O(n log n) | O(n log n) | O(1) | ❌ | ✅ |
Merge Sort ⭐
Divide array in half, sort each half, merge sorted halves.
Example
[38, 27, 43, 3, 9, 82, 10]
Split
[38, 27, 43, 3] [9, 82, 10]
Split Split
[38, 27] [43, 3] [9, 82] [10]
Split Split Split
[38][27] [43][3] [9][82] [10]
Merge Merge Merge
[27, 38] [3, 43] [9, 82] [10]
Merge Merge
[3, 27, 38, 43] [9, 10, 82]
Merge
[3, 9, 10, 27, 38, 43, 82]
Example
public static void mergeSort(int[] arr, int left, int right) {
if (left < right) {
int mid = left + (right - left) / 2;
mergeSort(arr, left, mid); // Sort left half
mergeSort(arr, mid + 1, right); // Sort right half
merge(arr, left, mid, right); // Merge sorted halves
}
}
private static void merge(int[] arr, int left, int mid, int right) {
int n1 = mid - left + 1;
int n2 = right - mid;
int[] leftArr = new int[n1];
int[] rightArr = new int[n2];
System.arraycopy(arr, left, leftArr, 0, n1);
System.arraycopy(arr, mid + 1, rightArr, 0, n2);
int i = 0, j = 0, k = left;
while (i < n1 && j < n2) {
if (leftArr[i] <= rightArr[j]) {
arr[k++] = leftArr[i++];
} else {
arr[k++] = rightArr[j++];
}
}
while (i < n1) arr[k++] = leftArr[i++];
while (j < n2) arr[k++] = rightArr[j++];
}
Time: O(n log n) always | Space: O(n) | Stable: Yes
Quick Sort ⭐
Pick a pivot, partition array so elements < pivot are left, > pivot are right.
| Partition | [3, 1, 0, 2] [7] [8, 10] |
| Recurse | [0, 1, 2, 3] [7] [8, 10] |
| Result | [0, 1, 2, 3, 7, 8, 10] |
Example
public static void quickSort(int[] arr, int low, int high) {
if (low < high) {
int pivotIndex = partition(arr, low, high);
quickSort(arr, low, pivotIndex - 1);
quickSort(arr, pivotIndex + 1, high);
}
}
private static int partition(int[] arr, int low, int high) {
int pivot = arr[high]; // Choose last element as pivot
int i = low - 1; // Index of smaller element boundary
for (int j = low; j < high; j++) {
if (arr[j] <= pivot) {
i++;
swap(arr, i, j);
}
}
swap(arr, i + 1, high); // Place pivot in correct position
return i + 1;
}
private static void swap(int[] arr, int i, int j) {
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
Time: O(n log n) avg, O(n²) worst | Space: O(log n) | Stable: No
When to Use Which
| Scenario | Best Algorithm | Why |
|---|---|---|
| Small array (n < 50) | Insertion Sort | Low overhead, good cache performance |
| General purpose | Merge Sort | Guaranteed O(n log n), stable |
| In-place needed | Quick Sort | O(1) extra space (O(log n) stack) |
| Nearly sorted data | Insertion Sort | O(n) for nearly sorted |
| Stability required | Merge Sort | Preserves equal element order |
| Memory constrained | Heap Sort | O(1) space, O(n log n) guaranteed |
Interview Questions
Q1: Why is QuickSort generally faster than MergeSort in practice?
Answer: QuickSort has better cache locality (works on contiguous memory), lower constant factors, and requires less memory (in-place). MergeSort has guaranteed O(n log n) but needs O(n) extra space and has more memory allocation overhead.
Q2: What does "stable" mean in sorting?
Answer: A stable sort preserves the relative order of elements with equal keys. If you sort students by grade and two have grade 'A', a stable sort keeps them in their original order. Merge Sort and Insertion Sort are stable; QuickSort and Heap Sort are not.
Q3: What is the worst case for QuickSort and how to avoid it?
Answer: Worst case O(n²) occurs when pivot is always the smallest/largest element (already sorted array with last-element pivot). Avoid with: random pivot selection, median-of-three, or IntroSort (switches to HeapSort when recursion is too deep).
Q4: How does Java's Arrays.sort() work?
Answer: For primitives: Dual-Pivot Quicksort (two pivots, three partitions). For objects: TimSort (hybrid merge sort + insertion sort, stable). TimSort exploits existing order in data (runs).
Q5: Can you sort in O(n) time?
Answer: Yes, for restricted inputs: Counting Sort (integers in known range), Radix Sort (fixed-length numbers/strings), Bucket Sort (uniformly distributed data). These are non-comparison sorts and break the O(n log n) comparison-based lower bound.
Exam Focus
Revise definitions, diagrams, examples, and short-answer points for Sorting Algorithms in Java.
Interview Use
Prepare one clear explanation, one practical example, and one common mistake for this Java Master Course topic.
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