Development and Testing  Rate this post Sorting is a basic task in programming. It arranges data in order. There are many sorting algorithms. Selection Sort is one of the simplest sorting methods. It is easy to understand and code. But it is not the fastest. In this guide, we will explain the Selection Sort Time Complexity. We will cover best, worst, and average cases. What Is Selection Sort? Selection Sort works by selecting the smallest element from the list. It places it in the correct position. It repeats this process for all elements. One by one, it moves the smallest values to the front. Let’s see an example: Input: [5, 3, 8, 2]Step 1: Smallest is 2 → swap with 5 → [2, 3, 8, 5]Step 2: Smallest in remaining is 3 → already correctStep 3: Smallest in remaining is 5 → swap with 8 → [2, 3, 5, 8] Now the list is sorted.How Selection Sort Works Selection Sort uses two loops. The outer loop moves one index at a time. The inner loop finds the smallest element. After each pass, the smallest value is moved to the front. The position is fixed. Selection Sort does not care if the list is sorted or not. It always does the same steps. Selection Sort Algorithm Here is the basic algorithm: Start from the first element Find the smallest in the rest of the list Swap it with the current element Repeat for each element This repeats until all elements are sorted. Selection Sort Code (Java Example) javaCopyEditpublic class SelectionSort { public static void sort(int[] arr) { int n = arr.length; for (int i = 0; i < n - 1; i++) { int min = i; for (int j = i + 1; j < n; j++) { if (arr[j] < arr[min]) { min = j; } } int temp = arr[min]; arr[min] = arr[i]; arr[i] = temp; } } } This code uses two loops. The outer loop runs n-1 times. The inner loop finds the minimum. Selection Sort Time Complexity Now let’s understand the main topic. Let’s analyze Selection Sort Time Complexity in three cases. 1. Best Case Even if the array is already sorted, Selection Sort checks all elements. It keeps comparing and swapping. Time Complexity: O(n²) Reason: Inner loop runs fully, regardless of the order Example Input: [1, 2, 3, 4, 5] Even here, every comparison still happens. Only fewer swaps occur, but comparisons remain the same. 2. Worst Case This happens when the array is in reverse order. But Selection Sort does not optimize for this. Time Complexity: O(n²) Reason: Still needs full comparisons Example Input: [5, 4, 3, 2, 1] Even in reverse, the steps are the same. It compares and finds the smallest element every time. 3. Average Case This is when elements are randomly placed. It is the most common scenario in real-world problems. Time Complexity: O(n²) Reason: Still compares each element in the inner loop Example Input: [3, 1, 4, 2, 5] Selection Sort does not change behavior based on input order. So the complexity remains the same. Why Is It Always O(n²)? Selection Sort compares all pairs of elements. The number of comparisons does not change. Total comparisons = n × (n – 1) / 2 That’s why the time complexity is always O(n²).It does not reduce steps in any case. It does not take advantage of sorted elements. Space Complexity Selection Sort does not need extra space. It sorts in place. Space Complexity: O(1) Only a few variables are used No extra arrays or memory needed This is one good point of the Selection Sort. Comparison with Other Algorithms Let’s compare Selection Sort with other basic sorts: AlgorithmBest CaseAverage CaseWorst CaseSpaceSelection SortO(n²)O(n²)O(n²)O(1)Bubble SortO(n)O(n²)O(n²)O(1)Insertion SortO(n)O(n²)O(n²)O(1)Merge SortO(n log n)O(n log n)O(n log n)O(n)Quick SortO(n log n)O(n log n)O(n²)O(log n) As you see, Selection Sort is slower than Merge Sort and Quick Sort. Advantages of Selection Sort Very simple and easy to understand Works well with small datasets Needs very little memory Good for learning purposes Disadvantages of Selection Sort Slow on large datasets Always takes the same time, even if sorted Not efficient for real-world use When to Use Selection Sort Use Selection Sort when: You are working with a very small dataset You want to teach or learn sorting logic You want stable, low-memory sorting Avoid it for: Large datasets Performance-sensitive programs Conclusion Selection Sort Time Complexity is simple to understand. But it is not efficient for big problems. It always takes O(n²) time, no matter the case. That is the same for best, worst, and average inputs. Still, it is useful in some cases. It’s great for learning sorting basics. It uses very little memory. If you’re working with small arrays, Selection Sort is fine. For large data, use better algorithms. Understanding its time complexity helps you choose the right algorithm. 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