Posted on : June 13, 2025 By Tech World Times Development and Testing  Rate this post Sorting helps organize data in a specific order. It is used in search, reports, and efficient storage. Different sorting algorithms offer different performance. In this article, we will explain the Time Complexity of Sorting Algorithms in simple words. We will cover Python, Java, and C++ examples. 1. What Is Time Complexity? Time complexity tells how fast an algorithm runs. It measures the number of steps as input grows. It is written in Big-O notation. For example, O(n²) means steps grow with the square of inputs. 2. Types of Time Complexity Here are common types: O(1): Constant time O(n): Linear time O(n log n): Log-linear time O(n²): Quadratic time We will now apply these to sorting. 3. Bubble Sort Bubble Sort compares two numbers and swaps them if needed. It repeats until the list is sorted. Time Complexity: Best Case: O(n) (if already sorted) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef bubble_sort(arr): n = len(arr) for i in range(n): for j in range(n - i - 1): if arr[j] > arr[j+1]: arr[j], arr[j+1] = arr[j+1], arr[j] Java Example: javaCopyEditvoid bubbleSort(int arr[]) { int n = arr.length; for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) { int temp = arr[j]; arr[j] = arr[j+1]; arr[j+1] = temp; } } C++ Example: cppCopyEditvoid bubbleSort(int arr[], int n) { for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(arr[j], arr[j+1]); } 4. Selection Sort This sort picks the smallest number and places it at the front. Time Complexity: Best Case: O(n²) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef selection_sort(arr): for i in range(len(arr)): min_idx = i for j in range(i+1, len(arr)): if arr[j] < arr[min_idx]: min_idx = j arr[i], arr[min_idx] = arr[min_idx], arr[i] 5. Insertion Sort This algorithm builds the final list one item at a time. Time Complexity: Best Case: O(n) Average Case: O(n²) Worst Case: O(n²) Java Example: javaCopyEditvoid insertionSort(int arr[]) { for (int i = 1; i < arr.length; i++) { int key = arr[i]; int j = i - 1; while (j >= 0 && arr[j] > key) { arr[j + 1] = arr[j]; j = j - 1; } arr[j + 1] = key; } } 6. Merge Sort Merge Sort splits the array into halves and merges them back in order. Time Complexity of Sorting Algorithms like Merge Sort is usually better. Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n log n) Python Example: pythonCopyEditdef merge_sort(arr): if len(arr) > 1: mid = len(arr) // 2 left = arr[:mid] right = arr[mid:] merge_sort(left) merge_sort(right) i = j = k = 0 while i < len(left) and j < len(right): if left[i] < right[j]: arr[k] = left[i] i += 1 else: arr[k] = right[j] j += 1 k += 1 arr[k:] = left[i:] + right[j:] 7. Quick Sort Quick Sort picks a pivot and places smaller numbers before it. Time Complexity: Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n²) C++ Example: cppCopyEditint 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], arr[j]); } } swap(arr[i+1], arr[high]); return i + 1; } void quickSort(int arr[], int low, int high) { if (low < high) { int pi = partition(arr, low, high); quickSort(arr, low, pi - 1); quickSort(arr, pi + 1, high); } } 8. Built-in Sort Methods Languages have built-in sort functions. These are well-optimized. Python: sorted() or list.sort() uses TimSort Time Complexity: O(n log n) Java: Arrays.sort() uses Dual-Pivot QuickSort Time Complexity: O(n log n) C++: std::sort() uses IntroSort Time Complexity: O(n log n) These are better for most real-world tasks. 9. Time Complexity Comparison Table AlgorithmBestAverageWorstStableBubble SortO(n)O(n²)O(n²)YesSelection SortO(n²)O(n²)O(n²)NoInsertion SortO(n)O(n²)O(n²)YesMerge SortO(n log n)O(n log n)O(n log n)YesQuick SortO(n log n)O(n log n)O(n²)NoTimSort (Python)O(n)O(n log n)O(n log n)YesIntroSort (C++)O(n log n)O(n log n)O(n log n)No 10. How to Choose the Right Algorithm? Use Merge Sort for large stable data. Use Quick Sort for faster average speed. Use Insertion Sort for small or nearly sorted lists. Use built-in sort functions unless you need control. Conclusion The Time Complexity of Sorting Algorithms helps us pick the right tool. Bubble, Selection, and Insertion Sort are simple but slow. Merge and Quick Sort are faster and used often. Built-in functions are highly optimized. Python, Java, and C++ each have their strengths. Understand your problem and input size. Then pick the sorting method. This ensures better speed and performance in your code. Tech World TimesTech World Times (TWT), a global collective focusing on the latest tech news and trends in blockchain, Fintech, Development & Testing, AI and Startups. If you are looking for the guest post then contact at techworldtimes@gmail.com