Time Complexities of all Sorting Algorithms

To put the data to some good use, there are times when a programmer needs to sort the given data. In such cases, Time Complexities of all sorting algorithms are used. 

Algorithms in programming are used to make every process more efficient and faster. When it comes to sorting algorithms, there are multiple algorithms available that you can use to sort the given array. 

This includes bubble sort, merge sort, quick sort, and selection sort. However, which algorithm you need to use depends highly on the time and space complexity of that algorithm. 

It is important for any developer to learn the time and space complexities of all the sorting algorithms to get through a coding round easily as this information can help you a lot while solving a particular ümraniye escort problem. 

Dig deeper to know what are time and space complexities and how you can calculate the same for all the sorting algorithms. 

Understanding Time Complexities

Time complexity refers to the total time that an algorithm takes to complete the process in terms of input characteristics. 

In simpler words, the time and space complexity of a sorting algorithm is simply an approximation of the number of elementary processes which will be executed throughout the complete code. Here, we assume that every elementary operation consumes a fixed amount of time to complete the process. 

To express the time complexity, the following notations are used:

• Omega notation: This notation is utilised to express an algorithm’s lower bound running time. 
• Big Oh Notation, O: This notation is utilised to express an algorithm’s upper bound running time. 
• Theta notation: This notation is a combination of big oh notation and omega notation. This notation is utilised to express the asymptotic behaviour of the running time of an algorithm. 

Usually, the time complexity of a sorting algorithm majorly depends on the type of input. Therefore, we use the worst-case time complexity because it is not possible to predict the variation in input. 

Which sorting algorithm has the best asymptotic runtime complexity?

The best asymptotic time complexity of sorting is O(n log n), which means that for any given instance of the problem, it will take less time than the problem has space to solve.

This happens because the height of a heap is constant and so when we add more items to our heap, we make it harder for them all to fit on top of each other. 

The number of comparisons needed increases exponentially with increasing size (number of elements) in this way. However, if enough room exists then we can use quick-sort instead which takes constant time per operation (O(1)).

In addition to these two algorithms both having similar runtime complexities there are also many others with similar performance characteristics such as insertion sort and merge sort

Understanding Space Complexity

The space complexity of the given algorithm determines the amount of memory a specific algorithm will take to complete the process. In simple words, you can say that space complexity is defined as the extra space required to run a program on a system. 

Space and Time Complexity Of Sorting Algorithms

Now that you are familiar with what time and space complexity are, let’s understand the space and time complexity of sorting algorithms. 

• Bubble Sort

Time Complexity

• Best Case: The best case complexity of bubble sort is calculated as O(n). This case occurs when the whole array is already sorted and no swapping is required in the array. 
• Average Case: The average case complexity of bubble sort is calculated as O(n2). This case occurs when the swapping is done for half of the elements i.e, n2/4. 
• Worst Case: The worst-case complexity of bubble sort is O(n2). Such a case occurs when the whole array is reverse sorted. In that case, swapping is done for n*(n-1) /2.

Space Complexity

The space complexity of bubble sort is calculated as O(1) because we are using a constant space throughout the whole process. 

• Selection Sort

Time Complexity

When it comes to selection sort, the best case, worst case and average case complexity are calculated as O(n2). 

Here, in the beginning, iteration, (n-1) comparisons are carried out and (n-2) comparisons are carried out in the second iteration. 

In this way, the total number of iterations will be n* (n-1) /2. 

Space Complexity

In this algorithm, there is no extra data structure being used. This is why the space complexity of the selection sort is calculated as O(1). 

• Insertion Sort

Time Complexity

• Best Case:  In the case of insertion sort, the best case complexity is calculated as O(n). This is the case when the given array is already sorted. 
• Average Case: Here, the average case complexity is calculated as O(n2/4) = O(n2). 
• Worst Case: The worst case complexity of insertion sort is O(n2). This case occurs when you are given an array that is reversely sorted. 

Space Complexity

In this sorting algorithm as well, we are not using any additional space. Therefore, the space complexity of this algorithm is calculated as O(1). 

• Merge Sort

Time Complexity

When it comes to merge sort, the worst case, best case and average case time complexity are calculated as O(n logn). Now that merge sort executes the same operations on the given array of any size, the time complexity remains the same throughout. 

Space Complexity

When it comes to merge sort, an auxiliary or additional space is required to store the array of size n. Therefore, the space complexity is calculated as O(n). 

• Quick Sort

Time Complexity

• Worst Case: The worst-case complexity of quicksort is calculated as O(n2). This case occurs when we already have a sorted array and we have chosen the leftmost element as the pivot or in case the given array is sorted in the reverse order. 
• Best and average case: The best and average case complexity of the quicksort is calculated as O(n logn). This case occurs when we pick the correct median element. 

Space Complexity

In quicksort, the worst-case space complexity is calculated as O(n). This case occurs when we choose the smallest or largest element as the pivot in every call. 

Other than this, the best-case space complexity of quicksort is calculated as O(log n). This case occurs when the chosen pivot position partitions the array in the middle each time. 

• Heap Sort

Time Complexity

The best case, worst case and average case time complexities of heap sort are calculated as O(n log n). This is because heap sort will take the same time to sort a given array of any size. 

Space Complexity

In heap sort, no additional space is used and hence, the space complexity is calculated as O(1). 

Advantages of using Heap sort algorithm

With a heap sort, the entire array is split into two sections: the sorted region and the unsorted region. It transfers the elements from the array’s unsorted portion to the sorted portion one at a time.

The Heap sort algorithm is popular due to its effectiveness. The list of items to be sorted is converted into a binary tree with heap properties in a heap data structure as part of the heap sort process. Each node in a binary tree has a maximum of two descendants.

 When none of a node’s descendants have values greater than the node itself, the node has the heap property. The heap’s biggest component is taken out and added to the sorted list. 

The remaining sub-tree is once more reduced to a heap. Up until no elements are left, this process is repeated. The final sorted list of items is created by successively removing the root node following each rebuilding of the heap.

Conclusion

Understanding the space and time complexity of sorting algorithms is crucial for any programmer to ensure that they choose the right algorithm for the given array. Make sure to go through all the complexities of all the sorting algorithms mentioned to crack your next interview with ease.