Sorting Algorithms¶
Key sorting algorithms: QuickSort (O(n log n) avg, in-place, unstable), MergeSort (O(n log n) guaranteed, stable, extra space), HeapSort (O(n log n), in-place). Java's Arrays.sort() uses TimSort (merge+insertion) for objects, dual-pivot QuickSort for primitives. Know when to use each and their trade-offs.
Key Concepts¶
Deep Dive: Comparison of Sorting Algorithms
| Algorithm | Best | Average | Worst | Space | Stable |
|---|---|---|---|---|---|
| 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) | ❌ |
| Counting Sort | O(n+k) | O(n+k) | O(n+k) | O(k) | ✅ |
Deep Dive: Quick Sort
public 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 int partition(int[] arr, int low, int high) {
int pivot = arr[high];
int i = low - 1;
for (int j = low; j < high; j++) {
if (arr[j] <= pivot) {
i++;
swap(arr, i, j);
}
}
swap(arr, i + 1, high);
return i + 1;
}
Deep Dive: Merge Sort
public void mergeSort(int[] arr, int left, int right) {
if (left >= right) return;
int mid = left + (right - left) / 2;
mergeSort(arr, left, mid);
mergeSort(arr, mid + 1, right);
merge(arr, left, mid, right);
}
private void merge(int[] arr, int left, int mid, int right) {
int[] temp = new int[right - left + 1];
int i = left, j = mid + 1, k = 0;
while (i <= mid && j <= right) {
if (arr[i] <= arr[j]) temp[k++] = arr[i++];
else temp[k++] = arr[j++];
}
while (i <= mid) temp[k++] = arr[i++];
while (j <= right) temp[k++] = arr[j++];
System.arraycopy(temp, 0, arr, left, temp.length);
}
Common Interview Questions
- Sort an array (implement quicksort or mergesort)
- Sort Colors (Dutch National Flag — 3-way partition)
- Merge Intervals
- Largest Number (custom comparator)
- When would you choose merge sort over quick sort?
- What is a stable sort? Why does it matter?