complexity of this modified QuickSort algorithm?
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Suppose we have a O(1) time
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- A given implementation of bubble-sort takes on average 1 second to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take? A given implementation of quicksort takes on average 0.1 seconds to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take?Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…Question A: Mapping. The two-sum problem is a popular algorithm problem. Given an array of integers and an integer target, return indices of the two numbers such that they add up to the target. You may assume that each input would have exactly one solution, and you may not use the same element twice. For example, suppose we have an array arr = [1,10,100]. If the target is 11, you should return [0,1] because arr[0] + arr[1] = 1+ 10 = 11. If the target is 101, you should return [0,2] because arr[0] + arr[2] = 1+ 100 = 101. Complete this problem in O(n). Hint: using a hash table.
- Explain the behavior of Quicksort Algorithm when the input array A [1: n] consists of n identical elements.Given an unsorted array. The array has this property that every element in the array is at most k distance from its position in sorted array where k is a positive integer smaller than the size of the array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity? (A) Insertion Sort with time complexity O(kn) (B) Heap Sort with time complexity O(nLogk) (C) Quick Sort with time complexity O(kLogk) (D) Merge Sort with time complexity O(kLogk)Suppose we have an O(n) time algorithm that finds the median of an unsorted array. Now consider a QuickSort implementation where we first find median using the above algorithm, then use median as the pivot. What will be the worst-case time complexity of this modified QuickSort? (A) O(n^2 Logn) (B) O(n^2) (C) O(n Logn Logn) (D) O(nLogn) (E) O(n)
- Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4Given an integer array [A], efficiently find a descending sorted triplet such that: A[i]> A[i]> A[k] and 0 <=i<j <k <n, where n is the array size. For example, Input: A[] = {9, 1, 6, 7, 3, 4, 5) Output: Any one of the following triplets: (9, 7,5) (9, 7, 4) (9, 7, 3) (9, 6, 5) (9, 6, 4) (9, 6, 3) a) Design a brute-force algorithm to solve this problem complexity of your solution b) Design a more efficient algorithm to do the same task with less complexity and analyse the complexity of your solution. c) Develop a python code to implement your efficient algorithm. depend on the correctness of the code, indentation, comments, test-case] d) Prepare a brief report (250 words) comparing the two algorithmsGiven an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1. 1. Can this problem be solved in O(logN)? 2. If so, write the implementation. Mention time and space complexity 3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.
- ) Implement a quicksort based on using a sample of size 2k 1. First, sort the sample, then arrange to have the recursiveroutine partition on the median of the sample and to move the two halves of the rest ofthe sample to each subarray, such that they can be used in the subarrays, without havingto be sorted again. This algorithm is called samplesort.What is the time complexity of the following algorithm? function findLargest(array): largest = array[0] for i = 1 to array.length: if array[i] > largest: largest = array[i] return largest Assume that array.length is n, and that all other operations take constant time. Express your answer in big O notation.Given an integer array A of size N where every element is in the range [0, 9]. When traversing the array, one could move from index į to index (i-1), index (i+1) or index j # į such that A[i]=A[j]. For example, given A = {4, 3, 1, 6, 3, 7, 1}, one can move • From A[0] to A[1] • From A[1] to A[2], A[0] or A[4] (since A[4]=A[1]=3) • From A[2] to A[3], A[1] or A[6] (since A[6]=A[2]=1) From A[3] to A[4], A[2] • And so on. The task is to compute the minimum number of moves to reach to the last index of the array starting from the first index. Examples: Input: A = {1, 2, 3, 4, 1, 5} Output: 2 Explanation: First move from A[0] to A[4] and then from A[4] to A[5]. Input: A = {1, 2, 3, 4, 5, 1} Output: 1 Explanation: Move from A[O] to A[5]. 6. Input: A = {1, 2, 3, 4, 5, 6, 7, 3, 4, 5, 4, 3, 6, 1, 5, 5, 4, 4, 7, 7} Output: 5 Explanation: Move from A[0] to A[13], from A[13] to A[12], from A[12] to A[5], from A[5] to A[6], from A[6] to A[19]. a) Explain how you would represent this problem as a…
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