Is selection sort stable. Is Selection Sort Algorithm in-place? Bubble Sort is stable and may perform slightly better in practice, while Selection Sort is not stable. Now we need to find the index of the Aug 28, 2022 · Since selection sort is an inplace sorting algorithm, it has a space complexity of O(1) as it requires one temporal variable used for swapping values. Adaptive: The performance of Selection Sort can be adaptive in certain scenarios. in the given input, (1, 5) comes before (1, 2). Thus, it sorts the array in half the time of the normal selection sort, because it places two elements per pass instead of one. Initialize minimum value min_idx to location 0. In-place means that the input and output occupy the same memory storage space. But it can be made stable if rather than swapping, the m …View the full answer This means that the algorithm becomes very slow as the size of the input array grows. It performs exactly n exchanges. Question: Implement the selection sort in (C++). It can be implemented as a stable sort and requires O (n2) time to sort n items, making it inefficient to use on large lists. Is Selection sort algorithm stable ? The default implementation is not stable. (b) Selection Sort—It is an unstable sorting algorithm. Selection sort has a worst case time complexity of O(nlogn). Out of comparison based techniques, bubble sort, insertion sort and merge sort are stable techniques. It is not stable, meaning it does not preserve the relative order of equal keys. Note: Selection sort is an unstable sort i. To prove that an array is sorted, you just have to prove that there is the same order between all the successive numbers. When using selecting sort it swaps n times at most. it is adaptive on few unique distributions, with a higher constant factor on distinct inputs. Preserving Relative Order: Selection Sort is a stable sorting algorithm, meaning it preserves the relative order of equal elements. Generalization (I am a kind of ) in-place sort . What makes selection sort unstable is that the step of swapping a pair of elements could possibly change the relative order of another pair of elements that have equal keys. You can see that (1, 5) comes before (1, 2) in the sorted order, which was the original order i. Binary search has O (1) space complexity. However, a small constant extra space used for variables is allowed. In case of linked list is sorted, and, instead of swaps, minimal element is linked to the unsorted part, selection sort is stable. The algorithm has a time complexity of O (n^2), where n is the number of elements in the array. 그러면 3. For example, starting with: (4,1)(1,0)(4,0) Selection sort will produce. So, among the given choices, merge sort is the most appropriate answer. *Stable - doesn\'t change the relative. There is no copying of input to output, and the input ceases to May 15, 2020 · In-place sorting can be stable or unstable: a stable sort retains the order of elements with the same key, from the original unsorted list to the final, sorted, list; There are some phenomenal online sorting demonstrations: see the Sorting Algorithm Animations website; here is a great animation site; 15 sorts in 6 minutes video Mar 21, 2023 · The selection sort is not a stable algorithm. order of elements with equal keys. Sorting is Mar 16, 2024 · Insertion Sort has the best-case time complexity of O(n) when the input array is already sorted, which is not possible for Bubble Sort and Selection Sort. for i = 1 Insertion sort is very similar to selection sort. Google Classroom. Apr 27, 2011 · There is no other condition that has essential differences from this one. Brute-force means that the algorithm looks for an options in a straightforward manner, considering them all. Complexity May 7, 2024 · Merge sort is a sorting algorithm that follows the divide-and-conquer approach. e. On the other hand, selection sort is not stable, as it can change the relative order of equal elements during the swapping process. Here’s the best way to solve it. 8. The order of equal elements may change during the sorting process. What is the best case, worst-case and average-case scenario for the selection sort? Justify your answer. Here stock prices are integer keys, and stock names are their associated information. Selection sort loops over indices in the array; for each index, selection sort calls indexOfMinimum and swap. Show transcribed image text. Others such as Quicksort, Heapsort and Selection Sort are unstable. This algorithm gets its name from the way it iterates through the array: it selects the current smallest element, and swaps it into place. Example. As with a bubble sort, after the first pass, the largest Sep 2, 2012 · This technique is more often used with "sorting" data-structures such as trees or priority queues where inherently stable alternatives are more tricky (depending on the context). Selection sort performs minimum number of swaps to sort the array. Here is a list of Non-Adaptive sorting algorithms: Selection sort ; Merge sort ; Heap sort. It does not adapt to the data in any way (notice that the four animations above run in lock step), so its runtime is always quadratic. In simple terms, we can say that the process of merge sort is to divide the array into two halves, sort Enhanced with AI, our expert help has broken down your problem into an easy-to-learn solution you can count on. Now for the second loop suppose if all the elements are same then each time the loop would be running from i to 0 , adding both first and second loop the inside loops would be running for n times ,so the worst Aug 1, 2022 · A non-adaptive sorting algorithm tries to force all the items into sorted order. It’s efficient for small datasets and nearly sorted data. Basically in selection sort, swap that occurs at the end of each iteration can change the relative order of items having the same value. it might search for an element via Sep 18, 2023 · As we know, selection sort algorithm takes the minimum on every pass on the array, and place it at its correct position. Formally stability may be defined as, how the algorithm treats equal elements. A stable algorithm produces first output. 3. That is, it have no look-ahead. Though, we can achieve stability in the selection sort using a similar method to the insertion sort. Jul 26, 2017 · 2,1,3(b),3(a) As we can see that order of the elements 3 (a) and 3 (b) is reversed from the original order and remaining part of the heapsort will only sort the first two elements and therefore, the elements 3 (a) and 3 (b) will remain intact at their positions. Mar 13, 2024 · No, selection sort is not a stable sorting algorithm. After 1st iteration array = [2, 7, 5, 3b, 3a, 9] Now, you can see that the order of 3a and 3b are interchanged. Double-selection sort. Use the middle element as the pivot. Jun 28, 2023 · Several common sorting algorithms are stable by nature, such as Merge Sort , Timsort , Counting Sort , Insertion Sort, and Bubble Sort. (b) Selection Sort—There is no best case the time complexity is \(O(n^2)\) in all cases. The swap() function swaps its arguments. If the dataset is partially sorted or nearly sorted, the number of comparisons may be reduced, making it more Jan 10, 2024 · The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at the beginning. Is it possible to implement selection sort for linked lists with the same Θ(n2) efficiency as the array version? 8. Sep 3, 2022 · 0. Selection sort can be implemented as a stable sort if, rather than swapping in step 2, the minimum value is inserted into the first position and the intervening values shifted up. Apr 23, 2022 · Insertion sort is an in-place, stable sorting technique that maintains two sub lists i. Jan 29, 2023 · Bubble sorting is a sorting algorithm where we check two elements and swap them at their correct positions. Nov 11, 2017 · 1. Copyright © 2000–2019, Robert Sedgewick and Kevin Wayne. Selection Sort requires two nested for loops to complete itself, one for loop is in the function Sep 22, 2013 · The sort is stable. Apr 2, 2024 · Question 3. Bubble sort is a simple and well-known sorting algorithm. Insertion sort is unstable and online. Apr 4, 2013 · Step 1: take the next unsorted element from the unsorted list then. Sort the list E, X, A, M, P, L, Ein alphabetical order by selection sort. Selection sort works as-. Since 4 is the smallest value, the index of the smallest value is 3. This is the reason that heapsort is not stable. Bingo Sort is a variant of Selection Sort that swaps equal elements into their correct place. 2 2' 1. (another word, explain with word the selection sort for a given list is a) sorted, b) randomly sorted, c) reversed sorted) Oct 8, 2023 · Bubble Sort is easy to understand but inefficient for large datasets. Apr 17, 2024 · Selection sort is a simple and efficient sorting algorithm that repeatedly selects the smallest (or largest) element and swaps it with the first element of the unsorted part. Selection sort, however, may change the order of elements with equal keys due to the way it repeatedly selects the minimum (or Is selection, for example, stable? The most straightforward answer is that Selection Sort is unstable because it swaps non-adjacent elements. The algorithm works by maintaining two subarrays in a given array: We would like to show you a description here but the site won’t allow us. T is the underlying element type. However it can be made stable. Dec 28, 2022 · A sorting algorithm is said to be stable if it maintains the relative order of records in the case of equality of keys. Step 2: put it in the right place in the sorted list. The first inner loop from i to n, that is for first time it runs n-1 time then n-2 then n-3 1 . But it can also work as a stable sort when it is implemented using linked list. Bubble Sort. Selection sort has a worst case time complexity of O(n). And you will end up with the result as array = [2, 3b, 3a, 5, 7, 9] Which clearly Oct 5, 2009 · A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input array to be sorted. It works on the idea of repeatedly finding the smallest element and placing it at its correct sorted position. Bubble sort performs maximum number of swaps to sort the array. It swaps it with the second element of the unordered list. Selection Sort and Insertion Sort both have the same space complexity of O(1), while Bubble Sort also has a space complexity of O(1). "Quicksort is not stable since it exchanges nonadjacent elements. but when using bubble sort, it swaps almost n* (n-1). But it can be achived using stable selection sort. 1. Selection sort is a stable sorting algorithm. Nov 2, 2022 · Insertion Sort—It is a stable sorting algorithm. Selection and quick sort are not stable sorts. Sort an Array - Level up your coding skills and quickly land a job. Selection sort is not stable. However, selection sort has the property of minimizing the number of swaps. 7. For large arrays, selection sort can take a long time to complete. The section b[k. Bubble sort is a stable sorting algorithm, meaning it preserves the relative order of equal elements. True or False? (a) Nov 23, 2021 · Sorting algorithms are either recursive (for example – quick sort) or non-recursive (for example – selection sort, and insertion sort), and there are some algorithms which use both (for example – merge sort). Explanation: Quick sort, heap sort, and insertion sort are in-place sorting algorithms, whereas an additional space of O(n) is required in order to merge two sorted arrays. See code examples, explanations and answers from experts and users. After running selection sort, we get the sorted order [1, 2b, 2a]. As a result, sorted elements in ascending order are-. Selection sort is not adaptive. Looking at the loop of the implementation of Swap b[k] with Selection Sort is stable Selection Sort is not stable Think of the behaviour of every pass through the inner for loop of Selection Sort if two records are equal, with the greatest value in the array. Algorithm: for i=1 to n  swap a [i ] with smallest of a [i],,a [n]  a) Test it. In the selection loop, the last occurence of the maximum value will always be selected. The index_of_maximum_key() function performs a linear search of its array argument from index 0 to index last for the key with maximum value and returns its index. Bubble sort belongs to O (n2) sorting algorithms, which makes it quite inefficient for sorting large data volumes. Second output can only be produced by Apr 21, 2022 · selection sort. ) 7. Is the selection sort stable or not? Selection sort is not a stable sorting algorithm. The most pertinent example being: Given [2, 2, 1], the '2' values will not retain their initial order in the output sorted array. 42. The most straightforward example: Given [2, 2, 1,], the’2′ values will not remain in their original order. Selection Sort: Repeatedly selects the minimum element from the unsorted portion of the list and places it at the beginning of the sorted portion. Let us see an example of sorting an array to make the idea of selection sort clearer. For instance, we can use extra space to maintain stability in Quicksort. Aug 29, 2022 · One strict definition is. age, height, position in the alphabet, etc. Merge sort is not a whole lot harder These different approaches lead to differences in their stability. Selection sort is unstable as it may change the order of elements with the same value. The Selection class provides static methods for sorting an array using selection sort. On the contrary, the selection sort carries out the selection and positioning of the required elements. Jan 20, 2023 · 2) The selection sort algorithm is stable? This selection sort algorithm is not stable. But appearances are deceptive. sortで安定したソートを実現したい場合は、比較 Jul 14, 2023 · The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted subarray and putting it at the beginning of the sorted subarray. n-1]. Is selection sort stable? (The definition of a stable sorting algorithm was given in Section 1. The insertion sort usually performs the insert operation. Selection sort is noted for its simplicity, and also has performance advantages over more complicated algorithms in certain situations. It has performance advantages over more complicated algorithms in certain situations, particularly where the auxiliary memory is limited. Stable means the order of input elements is unchanged except where change is required to satisfy the requirements. Because by swapping two elements in the second sub-step of the algorithm, it can happen that certain elements in the unsorted part no longer have Jan 26, 2023 · Bingo Sort. This process continues until the entire array is sorted. The final result is. Iterate from the first to the last and put elements into the two lists. Selection sort is unstable because in selection sort, minimum element is found and then put in its proper position by switching with the element that is in the position of the minimum element. Let A [] be an array, and let ‘<‘ be a strict weak ordering on the elements of A []. Selection sort selects the maximum element from the data and keeps replacing it with the elements from the end for maintaining an ascending order. A stable sorting algorithm maintains the relative order Stable? No. To understand this, let's consider an example: array = [3a, 7, 5, 3b, 2, 9] where 3a = 3b. This is because the condition says a[i] >= a[max] rather than a[i] > a[max]. Neither algorithm is adaptive, and they both have a space complexity of O (1). The number of swaps is O (n) . Mar 13, 2024 · Not stable: Quick Sort is not a stable sorting algorithm, meaning the relative order of equal elements may not be preserved. 3) How many maximum steps require in the selection sort algorithm? In the worst case of the selection sort algorithm, we might perform maximum n (size of an Aug 11, 2022 · Selection code in Java. It deals with how the algorithm treats comparable items with equal sort keys. 43. Greedy and brute force describe different traits of the algorithm. This is because the order might be jumbled when swapping, as such: Whether or not you need stability depends on your use-case. But selection sort typically makes many more comparisons than insertion sort, so insertion sort is usually preferable for sorting small inputs. This implementation of selection sort in not stable. Insertion sort is stable, online but not suited well for large number of elements. 8. In order to do this, a selection sort looks for the largest value as it makes a pass and, after completing the pass, places it in the proper location. Mar 10, 2024 · Stable Algorithm: Selection Sort is a stable sorting algorithm. since the element with the minimum key is 1, you'll have to push it to the lowest position of the array by swapping 1 with 2: The code you posted seems to be a stable sort. Examples: First example: 7 8 5 4 9 2. If you are using a stable sort, then you first sort the entire list by name and then sort the entire list by gender. it does so by finding the minimum, and then scanning through the array again to swap any elements that are equal to it to the front. Selection Sort is one of the simplest sorting algorithms. (algorithm) Definition: A sort algorithm that repeatedly searches remaining items to find the least one and moves it to its final location. For example, consider sorting the list [2a, 2b, 1] where 2a and 2b both have the value of 2. I had a bit of fun and practically reverse engineered Sep 21, 2019 · Insertion sort is a stable sorting algorithm. Its Time complexity in the Best case is O (N^2) Its Time complexity in the Best case is O (N) 3. It performs maximum (n – 1) swaps on a list of size n. The compare time and other running time can be ignored. Double selection sort works by finding both the smallest and largest elements in the unsorted region and then swapping both into place: smallest at the beginning, largest at the end. And some sorting algorithms are not, like Heap Sort, Quick Sort, etc. Complexity Analysis of Selection Sort. Question: Which of the following statements is correct? (Choose all correct answers) Binary search time complexity is O (n log n) Selection sort is stable. Which of the following statements is correct with respect to insertion sort ? *Online - can sort a list at runtime. it is easy, and it has the obvious benefit of having the fewest swaps of any algorithm. It swaps it with the first element of the unordered list. However, this modification either requires a data structure that supports efficient insertions or deletions, such as a linked list, or it leads to performing Θ ( n 2 Apr 5, 2013 · Selection sort is generally an unstable sorting algorithm. The stability of quicksort depends on partitioning strategy. The following function defines selection sort of an array A of size n. 6. However, Selection sort can be made stable if instead of swapping, the minimum element is Oct 28, 2012 · Selection sort can be implemented as a stable sort. Some sorting algorithms are stable by nature like Insertion sort, Merge Sort, Bubble Sort, etc. Insertion Sort makes O (N^2) comparisons ( every element is compared to every other element). Advantages of non-adaptive sorting algorithms: In case of non-adaptive sorting, the time complexity remains unaffected by the order of elements. It finds the second smallest element (5). . Here's how it works: Find the smallest element in the array and swap it with the first element. 3. The selection sort improves on the bubble sort by making only one exchange for every pass through the list. E. Or otherwise stated, that every number in the array is at least as much as its predecessor. It has size -k. So the outer loop runns n-1 times. It is used in practice once in a blue moon and its main application is to make an introduction to the sorting algorithms. As elements bubble to the correct position in the sorted area of the array, the original relative order of equal elements are maintained. Dec 28, 2018 · This demo shows the effect of using a stable (insertion sort) and unstable sorting (selection sort) algorithm to sort a small table of data. Dec 4, 2013 · 3. Find the number of comparisons and number of swap. If the length of the array is n , there are n indices in the array. Sort {5, 1, 12, -5, 16, 2, 12, 14} using selection sort. Stable sorting algorithms maintain the relative order of equal elements in the sorted output. And obviously reading time is less than writing time even in memory. Selection sort would swap the value at index 3 with the value at index 0, giving [4, 19, 18, 13, 10]. Is “Selection sort” stable? Justify your answer. If, rather than swapping in step 2, the minimum value is inserted into the first position (that is, all intervening items moved down), the algorithm is stable. b) Is selection sort stable? Implement the selection sort in ( C + +). In this article, we will learn to write a C program to implement selection sort. The swapping process in selection sort is not guaranteed to preserve the original ordering of equivalent items. ] can be written as b[k. It uses Θ(1) extra memory (not including the input array). It has O(n 2) complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort. 5. Selection Sort is not a stable sorting algorithm, because it swaps non-adjacent elements. That is, there's no guarantee that selection sort will change the relative order of equal items. Since each execution of the body of the loop runs two lines of code, you might think that 2 n lines of code are executed May 16, 2022 · Selection sort, also known as in-place comparison sort, is a simple sorting algorithm. As in selection sort, after k passes through the array, the first k elements are in sorted order. Insertion sort is said to be stable while selection sort is not a stable algorithm. Then the first 5 and the 3 are swapped, which places the first 5 after the second 5. Q: Is selection sort stable? A: No, selection sort is not stable. Question 9: What happens if all the items being sorted have the same value? Answer: If all the items being sorted have the same value, Quick Sort’s performance degrades to its worst-case time complexity of O(n^2). . The run time is Θ (n²), where n is the number of elements. One of the steps is easier for one algorithm and vice versa. To see this, suppose b[k. Selection sort is an in-place comparison sort. Bubble, insertion and merge sort are stable sorts. Sorting 방법에 따른 stable sort 여부 정리. A stable sort applied to a sequence of equal elements will not change their order. Basic Principle of Selection Sort. Insertion Sort: Builds the final sorted array one item at a time. Selection sort, like bubble sort, is a comparison-based in-place sorting algorithm. So in every pass, we keep track of both maximum and minimum and array becomes sorted from both ends. Jun 25, 2020 · Selection Sort appears stable at first glance: If the unsorted part contains several elements with the same key, the first should be appended to the sorted part first. This is the best place to expand your knowledge and get prepared for your next interview. Sort key — A key used to determine the ordering of items in a collection, e. Not stable: Selection sort is not a stable sorting algorithm. Expert-verified. This sorting algorithm is not stable. , integers, floating-point numbers, strings, etc) of an array (or a list) in a certain order (increasing, non-decreasing (increasing or flat), decreasing, non-increasing (decreasing or flat), lexicographical, etc). The original ordering of elements 2a and 2b was not preserved Analysis of selection sort. Number of Comparisons and Swaps. Q: Can selection sort be used for large arrays? A: While selection sort is not the most efficient algorithm for large arrays, it can still be used. Selection sort has O (n) comparisons. For instance, when sorting the array. For sorting alone, you would typically pick insertion sort instead of selection, since it is stable and as easy to implemented. Illustrated for clarity in the diagram below: Both Bubble Sort and Insertion Sort are stable, but Selection is not. The final list will have the ordering you want. It basically selects the smallest element from an unsorted array in each iteration and places that element at the beginning of the unsorted array. g. True or False? (a) Insertion Sort—The best-case time complexity is O(n) when the array is already in ascending order. Execution time of selection sort Let . Greedy means that the algorithm on each step selects some option which is locally the best. e it might change the occurrence of two similar elements in the list while sorting. A stable sort preserves the relative order of equal elements in the sorted output. sorted and unsorted and progresses by comparing each consecutive element and inserting it in the correct order. 6, 2, 11, 7, 5. Selection sort can beat insertion sort if the cost of swapping elements is vastly higher than the cost of comparing them, but that doesn't apply to functional lists. Create two lists, one for smaller, the other for larger. It does not preserve the relative order of items with equal keys; Not optimal: Selection sort is not an optimal sorting algorithm Jul 13, 2023 · Selection sort is a sorting algorithm that repeatedly finds the minimum element in the unsorted portion of an array and swaps it with the element at the beginning of the unsorted section. Sep 21, 2022 · A sorting algorithm is stable if equal values do not lose their original order when sorted. Approach. void SelectionSort(T A[], int n) {. By Stability : Sorting algorithm is stable if two elements with equal values appear in the same order in output as it was in the input. A stable sorting algorithm is one where two objects with equal keys appear in the same order in the sorted output as they appear in the input array to be sorted. Expected output for the sorting should be: [(CSCO 1), (MSFT 1), (GOOG 3)] (containing both stock price and its name, and the CSCO stock should appear before MSFT so that it is a stable sort) A counts array will be calculated for sorting this (let's say stock Feb 21, 2024 · 이런식으로 유지된다면 stable sorting이라고 할 수 있다. There are many different sorting algorithms, each has its own advantages and limitations. Potential quiz/exam questions for you to think through: Why is selection sort not Sep 10, 2021 · by codecrucks · Published 10/09/2021 · Updated 08/06/2022. In insertion sort algorithm the elements Jan 23, 2024 · A sorting technique is stable if it does not change the order of elements with the same value. This implementation makes ~ ½ n 2 compares to sort any array of length n, so it is not suitable for sorting large arrays. The point is how to achieve it. Note that you may select multiple statements. Key Differences Between Insertion Sort and Selection Sort. However, its running time is quadratic, making it Sep 14, 2022 · Selection sort is an unstable, in-place sorting algorithm known for its simplicity. STLで提供されているsortは安定しないソートで、stable_sortは安定しているソートである。. It finds the first smallest element (2). Even though we have a variation of merge sort (to do in-place sorting), it is not the default option. A more broad definition is, Jul 19, 2015 · 概要. There is a good example. A stable sorting algorithm ensures that items that are equal to each other These sorting algorithms are usually not stable: quicksort heapsort selection sort Dec 4, 2019 · Selection Sort. Insertion Sort makes O (N^2) swaps Apr 25, 2017 · The proof is about sorting. 2. Dec 28, 2018 · The stability of sorting algorithms is one of the distinguishing properties among them. This feature can be useful in situations where the relative order of equivalent elements needs to be maintained. Jan 23, 2024 · Selection Sort is not stable by default. A sort is said to be stable if the order of equivalent items is preserved. 즉 같은 원소더라도 원래의 순서가 sorting 후에도 유지되면 stable sorting, 유지되지 않으면 unstable sorting이라고 할 수 있다. Also, the results of sorting any particular array with selection sort might indicate that selection sort is stable. Dec 24, 2013 · Learn how selection sort can be implemented as stable or unstable depending on whether it swaps or inserts elements. Last updated: Thu Aug 11 09:04:20 EDT 2022. Bubble sort is stable and adaptive. In Selection Sort, the swapping step might change the For example, if the array initially has values [13, 19, 18, 4, 10], we first need to find the index of the smallest value in the array. When choosing between Bubble Sort and Selection Sort, it is important to consider the specific requirements of the application and the characteristics of the input Oct 23, 2023 · Selection Sort could be adapted to find the minimum or maximum elements efficiently. An in-place algorithm is an algorithm that does not need an extra space and produces an output in the same memory that contains the data by transforming the input ‘in-place’. " This statement relies on the prerequisite that Hoare partitioning is used. 색깔을 잘 보면 이해가 될 것이다. Bubble sort uses more swap times, while selection sort avoids this. Bubble Sort and Insertion Sort are stable sorting Jan 10, 2023 · A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input data set. ] contains (5, 5, 3). However, the fundamental difference between the two algorithms is that insertion sort scans backwards from the current key, while selection sort scans forwards. The Selection Sort ¶. In applications where the cost of swapping items is high, selection sort very well may be the algorithm of choice. Insertion sort : We take the first element of the unsorted list, put it in the sorted list, somewhere. selection sort. The default implementation of selection sort is not stable. Selection sort is an in-place sorting algorithm. Similarly, it continues to sort the given elements. The idea is to take also the maximum on every pass and place it at its correct position. Complexity Sorting is a very classic problem of reordering items (that can be compared, e. sortには同位の場合に、その順番を保障する安定したソートと保障していない安定しないソートの二種類がある。. We can modify unstable sorting algorithms to be stable. It works by recursively dividing the input array into smaller subarrays and sorting those subarrays then merging them back together to obtain the sorted array. wg tw ge zr mi cp an zv hw hf