Insert current node in sorted way in sorted or result list. location to insert new elements, and therefore performs log2(n) The resulting array after k iterations has the property where the first k + 1 entries are sorted ("+1" because the first entry is skipped). The recursion just replaces the outer loop, calling itself and storing successively smaller values of n on the stack until n equals 0, where the function then returns up the call chain to execute the code after each recursive call starting with n equal to 1, with n increasing by 1 as each instance of the function returns to the prior instance. Space Complexity: Merge sort, being recursive takes up the space complexity of O (n) hence it cannot be preferred . Thank you for this awesome lecture. If you preorder a special airline meal (e.g. The worst-case (and average-case) complexity of the insertion sort algorithm is O(n). With a worst-case complexity of O(n^2), bubble sort is very slow compared to other sorting algorithms like quicksort. Intuitively, think of using Binary Search as a micro-optimization with Insertion Sort. In each iteration the first remaining entry of the input is removed, and inserted into the result at the correct position, thus extending the result: with each element greater than x copied to the right as it is compared against x. Asking for help, clarification, or responding to other answers. What's the difference between a power rail and a signal line? Get this book -> Problems on Array: For Interviews and Competitive Programming, Reading time: 15 minutes | Coding time: 5 minutes. The overall performance would then be dominated by the algorithm used to sort each bucket, for example () insertion sort or ( ()) comparison sort algorithms, such as merge sort. The best case input is an array that is already sorted. For most distributions, the average case is going to be close to the average of the best- and worst-case - that is, (O + )/2 = O/2 + /2. Speed Up Machine Learning Models with Accelerated WEKA, Merge Sort Explained: A Data Scientists Algorithm Guide, GPU-Accelerated Hierarchical DBSCAN with RAPIDS cuML Lets Get Back To The Future, Python Pandas Tutorial Beginner's Guide to GPU Accelerated DataFrames for Pandas Users, Top Video Streaming and Conferencing Sessions at NVIDIA GTC 2023, Top Cybersecurity Sessions at NVIDIA GTC 2023, Top Conversational AI Sessions at NVIDIA GTC 2023, Top AI Video Analytics Sessions at NVIDIA GTC 2023, Top Data Science Sessions at NVIDIA GTC 2023. Direct link to Jayanth's post No sure why following cod, Posted 7 years ago. In insertion sort, the average number of comparisons required to place the 7th element into its correct position is ____ c) Insertion Sort How to prove that the supernatural or paranormal doesn't exist? Consider the code given below, which runs insertion sort: Which condition will correctly implement the while loop? comparisons in the worst case, which is O(n log n). Thus, the total number of comparisons = n*(n-1) = n 2 In this case, the worst-case complexity will be O(n 2). @mattecapu Insertion Sort is a heavily study algorithm and has a known worse case of O(n^2). Insertion sort takes maximum time to sort if elements are sorted in reverse order. This doesnt relinquish the requirement for Data Scientists to study algorithm development and data structures. It repeats until no input elements remain. We could see in the Pseudocode that there are precisely 7 operations under this algorithm. Insertion sort is an in-place algorithm, meaning it requires no extra space. a) Bubble Sort then using binary insertion sort may yield better performance. t j will be 1 for each element as while condition will be checked once and fail because A[i] is not greater than key. Time Complexity of Quick sort. The outer for loop continues iterating through the array until all elements are in their correct positions and the array is fully sorted. Binary Insertion Sort - Take this array => {4, 5 , 3 , 2, 1}. You can do this because you know the left pieces are already in order (you can only do binary search if pieces are in order!). The insertionSort function has a mistake in the insert statement (Check the values of arguments that you are passing into it). Direct link to Miriam BT's post I don't understand how O , Posted 7 years ago. Time Complexity with Insertion Sort. for example with string keys stored by reference or with human It can be different for other data structures. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. The outer loop runs over all the elements except the first one, because the single-element prefix A[0:1] is trivially sorted, so the invariant that the first i entries are sorted is true from the start. Let vector A have length n. For simplicity, let's use the entry indexing i { 1,., n }. Therefore overall time complexity of the insertion sort is O(n + f(n)) where f(n) is inversion count. Can I tell police to wait and call a lawyer when served with a search warrant? . When we do a sort in ascending order and the array is ordered in descending order then we will have the worst-case scenario. Insertion Sort Explanation:https://youtu.be/myXXZhhYjGoBubble Sort Analysis:https://youtu.be/CYD9p1K51iwBinary Search Analysis:https://youtu.be/hA8xu9vVZN4 (answer by "templatetypedef")", Animated Sorting Algorithms: Insertion Sort, https://en.wikipedia.org/w/index.php?title=Insertion_sort&oldid=1135199530, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0. We push the first k elements in the stack and pop() them out so and add them at the end of the queue. So each time we insert an element into the sorted portion, we'll need to swap it with each of the elements already in the sorted array to get it all the way to the start. In the data realm, the structured organization of elements within a dataset enables the efficient traversing and quick lookup of specific elements or groups. . The worst case happens when the array is reverse sorted. Cost for step 5 will be n-1 and cost for step 6 and 7 will be . Which of the following is correct with regard to insertion sort? The simplest worst case input is an array sorted in reverse order. A variant named binary merge sort uses a binary insertion sort to sort groups of 32 elements, followed by a final sort using merge sort. In general the number of compares in insertion sort is at max the number of inversions plus the array size - 1. But since it will take O(n) for one element to be placed at its correct position, n elements will take n * O(n) or O(n2) time for being placed at their right places. We can reduce it to O(logi) by using binary search. Identifying library subroutines suitable for the dataset requires an understanding of various sorting algorithms preferred data structure types. The simplest worst case input is an array sorted in reverse order. The worst case occurs when the array is sorted in reverse order. How do you get out of a corner when plotting yourself into a corner, Movie with vikings/warriors fighting an alien that looks like a wolf with tentacles, The difference between the phonemes /p/ and /b/ in Japanese. You are confusing two different notions. which when further simplified has dominating factor of n2 and gives T(n) = C * ( n 2) or O( n2 ), Let's assume that tj = (j-1)/2 to calculate the average case Why is Binary Search preferred over Ternary Search? How to earn money online as a Programmer? As demonstrated in this article, its a simple algorithm to grasp and apply in many languages. It does not make the code any shorter, it also doesn't reduce the execution time, but it increases the additional memory consumption from O(1) to O(N) (at the deepest level of recursion the stack contains N references to the A array, each with accompanying value of variable n from N down to 1). Why are trials on "Law & Order" in the New York Supreme Court? Should I just look to mathematical proofs to find this answer? Fibonacci Heap Deletion, Extract min and Decrease key, Bell Numbers (Number of ways to Partition a Set), Tree Traversals (Inorder, Preorder and Postorder), merge sort based algorithm to count inversions. Sanfoundry Global Education & Learning Series Data Structures & Algorithms. Which algorithm has lowest worst case time complexity? Hence the name, insertion sort. So i suppose that it quantifies the number of traversals required. c) insertion sort is stable and it does not sort In-place Presumably, O >= as n goes to infinity. To sort an array of size N in ascending order: Time Complexity: O(N^2)Auxiliary Space: O(1). STORY: Kolmogorov N^2 Conjecture Disproved, STORY: man who refused $1M for his discovery, List of 100+ Dynamic Programming Problems, Generating IP Addresses [Backtracking String problem], Longest Consecutive Subsequence [3 solutions], Cheatsheet for Selection Algorithms (selecting K-th largest element), Complexity analysis of Sieve of Eratosthenes, Time & Space Complexity of Tower of Hanoi Problem, Largest sub-array with equal number of 1 and 0, Advantages and Disadvantages of Huffman Coding, Time and Space Complexity of Selection Sort on Linked List, Time and Space Complexity of Merge Sort on Linked List, Time and Space Complexity of Insertion Sort on Linked List, Recurrence Tree Method for Time Complexity, Master theorem for Time Complexity analysis, Time and Space Complexity of Circular Linked List, Time and Space complexity of Binary Search Tree (BST), The worst case time complexity of Insertion sort is, The average case time complexity of Insertion sort is, If at every comparison, we could find a position in sorted array where the element can be inserted, then create space by shifting the elements to right and, Simple and easy to understand implementation, If the input list is sorted beforehand (partially) then insertions sort takes, Chosen over bubble sort and selection sort, although all have worst case time complexity as, Maintains relative order of the input data in case of two equal values (stable). I'm pretty sure this would decrease the number of comparisons, but I'm not exactly sure why. Since number of inversions in sorted array is 0, maximum number of compares in already sorted array is N - 1. Of course there are ways around that, but then we are speaking about a . , Posted 8 years ago. When the input list is empty, the sorted list has the desired result. But then, you've just implemented heap sort. During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array. @MhAcKN You are right to be concerned with details. Insertion sort and quick sort are in place sorting algorithms, as elements are moved around a pivot point, and do not use a separate array. While some divide-and-conquer algorithms such as quicksort and mergesort outperform insertion sort for larger arrays, non-recursive sorting algorithms such as insertion sort or selection sort are generally faster for very small arrays (the exact size varies by environment and implementation, but is typically between 7 and 50 elements). The average case is also quadratic,[4] which makes insertion sort impractical for sorting large arrays. The definition of $\Theta$ that you give is correct, and indeed the running time of insertion sort, in the worst case, is $\Theta(n^2)$, since it has a quadratic running time. d) O(logn) By clearly describing the insertion sort algorithm, accompanied by a step-by-step breakdown of the algorithmic procedures involved. One important thing here is that in spite of these parameters the efficiency of an algorithm also depends upon the nature and size of the input. In the case of running time, the worst-case . Thus, swap 11 and 12. for every nth element, (n-1) number of comparisons are made. This is, by simple algebra, 1 + 2 + 3 + + n - n*.5 = (n(n+1) - n)/2 = n^2 / 2 = O(n^2). Consider an example: arr[]: {12, 11, 13, 5, 6}. To reverse the first K elements of a queue, we can use an auxiliary stack. In worst case, there can be n* (n-1)/2 inversions. Do I need a thermal expansion tank if I already have a pressure tank? a) Heap Sort 1,062. b) Statement 1 is true but statement 2 is false Insertion sort is an example of an incremental algorithm. Analysis of insertion sort. In this article, we have explored the time and space complexity of Insertion Sort along with two optimizations. that doesn't mean that in the beginning the. View Answer. b) insertion sort is unstable and it sorts In-place Average-case analysis Best . Pseudo-polynomial Algorithms; Polynomial Time Approximation Scheme; A Time Complexity Question; Searching Algorithms; Sorting . During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array. To see why this is, let's call O the worst-case and the best-case. I hope this helps. Loop invariants are really simple (but finding the right invariant can be hard): Can we make a blanket statement that insertion sort runs it omega(n) time? Theres only one iteration in this case since the inner loop operation is trivial when the list is already in order. b) Quick Sort The Insertion Sort is an easy-to-implement, stable sort with time complexity of O(n2) in the average and worst case. The while loop executes only if i > j and arr[i] < arr[j]. When given a collection of pre-built algorithms to use, determining which algorithm is best for the situation requires understanding the fundamental algorithms in terms of parameters, performances, restrictions, and robustness. If an element is smaller than its left neighbor, the elements are swapped. The same procedure is followed until we reach the end of the array. Simple implementation: Jon Bentley shows a three-line C version, and a five-line optimized version [1] 2. Then each call to. Efficient algorithms have saved companies millions of dollars and reduced memory and energy consumption when applied to large-scale computational tasks. can the best case be written as big omega of n and worst case be written as big o of n^2 in insertion sort? series of swaps required for each insertion. Algorithms power social media applications, Google search results, banking systems and plenty more. Merge Sort performs the best. With the appropriate tools, training, and time, even the most complicated algorithms are simple to understand when you have enough time, information, and resources. How to handle a hobby that makes income in US. On average (assuming the rank of the (k+1)-st element rank is random), insertion sort will require comparing and shifting half of the previous k elements, meaning that insertion sort will perform about half as many comparisons as selection sort on average. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as n in asymptotic notation).It gives an upper bound on the resources required by the algorithm. Library implementations of Sorting algorithms, Comparison among Bubble Sort, Selection Sort and Insertion Sort, Insertion sort to sort even and odd positioned elements in different orders, Count swaps required to sort an array using Insertion Sort, Difference between Insertion sort and Selection sort, Sorting by combining Insertion Sort and Merge Sort algorithms. . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Statement 2: And these elements are the m smallest elements in the array. We have discussed a merge sort based algorithm to count inversions. In worst case, there can be n*(n-1)/2 inversions. before 4. interaction (such as choosing one of a pair displayed side-by-side), Insertion Sort is more efficient than other types of sorting. Following is a quick revision sheet that you may refer to at the last minute, Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above, Time complexities of different data structures, Akra-Bazzi method for finding the time complexities, Know Your Sorting Algorithm | Set 1 (Sorting Weapons used by Programming Languages), Sorting objects using In-Place sorting algorithm, Different ways of sorting Dictionary by Values and Reverse sorting by values, Sorting integer data from file and calculate execution time, Case-specific sorting of Strings in O(n) time and O(1) space. (n-1+1)((n-1)/2) is the sum of the series of numbers from 1 to n-1. Note that the and-operator in the test must use short-circuit evaluation, otherwise the test might result in an array bounds error, when j=0 and it tries to evaluate A[j-1] > A[j] (i.e. Example: what is time complexity of insertion sort Time Complexity is: If the inversion count is O (n), then the time complexity of insertion sort is O (n). or am i over-thinking? If the inversion count is O(n), then the time complexity of insertion sort is O(n). While insertion sort is useful for many purposes, like with any algorithm, it has its best and worst cases. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Asking for help, clarification, or responding to other answers. Insertion sort: In Insertion sort, the worst-case takes (n 2) time, the worst case of insertion sort is when elements are sorted in reverse order. Best case - The array is already sorted. View Answer, 4. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Worst case time complexity of Insertion Sort algorithm is O(n^2). In this case insertion sort has a linear running time (i.e., O(n)). Yes, you could. The current element is compared to the elements in all preceding positions to the left in each step. insert() , if you want to pass the challenges. The algorithm is still O(n^2) because of the insertions. [We can neglect that N is growing from 1 to the final N while we insert]. Often the trickiest parts are actually the setup. Insertion sort algorithm involves the sorted list created based on an iterative comparison of each element in the list with its adjacent element. However, if you start the comparison at the half way point (like a binary search), then you'll only compare to 4 pieces! Checksum, Complexity Classes & NP Complete Problems, here is complete set of 1000+ Multiple Choice Questions and Answers, Prev - Insertion Sort Multiple Choice Questions and Answers (MCQs) 1, Next - Data Structure Questions and Answers Selection Sort, Certificate of Merit in Data Structure II, Design and Analysis of Algorithms Internship, Recursive Insertion Sort Multiple Choice Questions and Answers (MCQs), Binary Insertion Sort Multiple Choice Questions and Answers (MCQs), Insertion Sort Multiple Choice Questions and Answers (MCQs) 1, Library Sort Multiple Choice Questions and Answers (MCQs), Tree Sort Multiple Choice Questions and Answers (MCQs), Odd-Even Sort Multiple Choice Questions and Answers (MCQs), Strand Sort Multiple Choice Questions and Answers (MCQs), Merge Sort Multiple Choice Questions and Answers (MCQs), Comb Sort Multiple Choice Questions and Answers (MCQs), Cocktail Sort Multiple Choice Questions and Answers (MCQs), Design & Analysis of Algorithms MCQ Questions. Direct link to Cameron's post Yes, you could. Shell made substantial improvements to the algorithm; the modified version is called Shell sort. Shell sort has distinctly improved running times in practical work, with two simple variants requiring O(n3/2) and O(n4/3) running time. Average case: O(n2) When the array elements are in random order, the average running time is O(n2 / 4) = O(n2). Time complexity in each case can be described in the following table: To avoid having to make a series of swaps for each insertion, the input could be stored in a linked list, which allows elements to be spliced into or out of the list in constant time when the position in the list is known. View Answer, 3. The variable n is assigned the length of the array A. The algorithm as a whole still has a running time of O(n2) on average because of the series of swaps required for each insertion. Direct link to Cameron's post Let's call The running ti, 1, comma, 2, comma, 3, comma, dots, comma, n, minus, 1, c, dot, 1, plus, c, dot, 2, plus, c, dot, 3, plus, \@cdots, c, dot, left parenthesis, n, minus, 1, right parenthesis, equals, c, dot, left parenthesis, 1, plus, 2, plus, 3, plus, \@cdots, plus, left parenthesis, n, minus, 1, right parenthesis, right parenthesis, c, dot, left parenthesis, n, minus, 1, plus, 1, right parenthesis, left parenthesis, left parenthesis, n, minus, 1, right parenthesis, slash, 2, right parenthesis, equals, c, n, squared, slash, 2, minus, c, n, slash, 2, \Theta, left parenthesis, n, squared, right parenthesis, c, dot, left parenthesis, n, minus, 1, right parenthesis, \Theta, left parenthesis, n, right parenthesis, 17, dot, c, dot, left parenthesis, n, minus, 1, right parenthesis, O, left parenthesis, n, squared, right parenthesis, I am not able to understand this situation- "say 17, from where it's supposed to be when sorted? The most common variant of insertion sort, which operates on arrays, can be described as follows: Pseudocode of the complete algorithm follows, where the arrays are zero-based:[1]. [5][6], If the cost of comparisons exceeds the cost of swaps, as is the case for example with string keys stored by reference or with human interaction (such as choosing one of a pair displayed side-by-side), then using binary insertion sort may yield better performance. It can also be useful when input array is almost sorted, only few elements are misplaced in complete big array. [1], D.L. (n) 2. the worst case is if you are already sorted for many sorting algorithms and it isn't funny at all, sometimes you are asked to sort user input which happens to already be sorted. We can optimize the searching by using Binary Search, which will improve the searching complexity from O(n) to O(log n) for one element and to n * O(log n) or O(n log n) for n elements. This algorithm sorts an array of items by repeatedly taking an element from the unsorted portion of the array and inserting it into its correct position in the sorted portion of the array. Direct link to ng Gia Ch's post "Using big- notation, we, Posted 2 years ago. Sort array of objects by string property value, Sort (order) data frame rows by multiple columns, Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing, Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition, Fastest way to sort 10 numbers? a) O(nlogn) In contrast, density-based algorithms such as DBSCAN(Density-based spatial clustering of application with Noise) are preferred when dealing with a noisy dataset. Note that this is the average case. Now imagine if you had thousands of pieces (or even millions), this would save you a lot of time. Acidity of alcohols and basicity of amines. whole still has a running time of O(n2) on average because of the However, searching a linked list requires sequentially following the links to the desired position: a linked list does not have random access, so it cannot use a faster method such as binary search. So starting with a list of length 1 and inserting the first item to get a list of length 2, we have average an traversal of .5 (0 or 1) places. Making statements based on opinion; back them up with references or personal experience. Best and Worst Use Cases of Insertion Sort. It is significantly low on efficiency while working on comparatively larger data sets. c) Merge Sort Quick sort-median and Quick sort-random are pretty good; View Answer, 6. vegan) just to try it, does this inconvenience the caterers and staff? How to react to a students panic attack in an oral exam? Does Counterspell prevent from any further spells being cast on a given turn? So its time complexity remains to be O (n log n). However, a disadvantage of insertion sort over selection sort is that it requires more writes due to the fact that, on each iteration, inserting the (k+1)-st element into the sorted portion of the array requires many element swaps to shift all of the following elements, while only a single swap is required for each iteration of selection sort. For example, if the target position of two elements is calculated before they are moved into the proper position, the number of swaps can be reduced by about 25% for random data. Therefore, its paramount that Data Scientists and machine-learning practitioners have an intuition for analyzing, designing, and implementing algorithms. Let's take an example. In this case, on average, a call to, What if you knew that the array was "almost sorted": every element starts out at most some constant number of positions, say 17, from where it's supposed to be when sorted? This results in selection sort making the first k elements the k smallest elements of the unsorted input, while in insertion sort they are simply the first k elements of the input. Therefore total number of while loop iterations (For all values of i) is same as number of inversions. answered Mar 3, 2017 at 6:56. vladich. For example, the array {1, 3, 2, 5} has one inversion (3, 2) and array {5, 4, 3} has inversions (5, 4), (5, 3) and (4, 3). 528 5 9. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. Its important to remember why Data Scientists should study data structures and algorithms before going into explanation and implementation. Analysis of Insertion Sort. Direct link to csalvi42's post why wont my code checkout, Posted 8 years ago. In this worst case, it take n iterations of . Sorry for the rudeness. If a more sophisticated data structure (e.g., heap or binary tree) is used, the time required for searching and insertion can be reduced significantly; this is the essence of heap sort and binary tree sort. It is known as the best sorting algorithm in Python. d) (1') The best case run time for insertion sort for a array of N . Then, on average, we'd expect that each element is less than half the elements to its left. The worst case time complexity is when the elements are in a reverse sorted manner. So the worst case time complexity of . acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Sort an array of 0s, 1s and 2s | Dutch National Flag problem, Sort numbers stored on different machines, Check if any two intervals intersects among a given set of intervals, Sort an array according to count of set bits, Sort even-placed elements in increasing and odd-placed in decreasing order, Inversion count in Array using Merge Sort, Find the Minimum length Unsorted Subarray, sorting which makes the complete array sorted, Sort n numbers in range from 0 to n^2 1 in linear time, Sort an array according to the order defined by another array, Find the point where maximum intervals overlap, Find a permutation that causes worst case of Merge Sort, Sort Vector of Pairs in ascending order in C++, Minimum swaps to make two arrays consisting unique elements identical, Permute two arrays such that sum of every pair is greater or equal to K, Bucket Sort To Sort an Array with Negative Numbers, Sort a Matrix in all way increasing order, Convert an Array to reduced form using Vector of pairs, Check if it is possible to sort an array with conditional swapping of adjacent allowed, Find Surpasser Count of each element in array, Count minimum number of subsets (or subsequences) with consecutive numbers, Choose k array elements such that difference of maximum and minimum is minimized, K-th smallest element after removing some integers from natural numbers, Maximum difference between frequency of two elements such that element having greater frequency is also greater, Minimum swaps to reach permuted array with at most 2 positions left swaps allowed, Find whether it is possible to make array elements same using one external number, Sort an array after applying the given equation, Print array of strings in sorted order without copying one string into another, This algorithm is one of the simplest algorithm with simple implementation, Basically, Insertion sort is efficient for small data values. [1][3][3][3][4][4][5] ->[2]<- [11][0][50][47]. Therefore, the running time required for searching is O(n), and the time for sorting is O(n2). ANSWER: Merge sort. Compare the current element (key) to its predecessor. algorithms computational-complexity average sorting. The time complexity is: O(n 2) . Hence, the overall complexity remains O(n2). a) insertion sort is stable and it sorts In-place In this case, worst case complexity occurs. About an argument in Famine, Affluence and Morality. Time complexity of insertion sort when there are O(n) inversions? (numbers are 32 bit). In each step, the key under consideration is underlined. For example, first you should clarify if you want the worst-case complexity for an algorithm or something else (e.g. What Is Insertion Sort Good For? The space complexity is O(1) . O(N2 ) average, worst case: - Selection Sort, Bubblesort, Insertion Sort O(N log N) average case: - Heapsort: In-place, not stable. Euler: A baby on his lap, a cat on his back thats how he wrote his immortal works (origin? View Answer, 7. Input: 15, 9, 30, 10, 1 Before going into the complexity analysis, we will go through the basic knowledge of Insertion Sort. You shouldn't modify functions that they have already completed for you, i.e.
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