i = 0; while (i < n) if (i == 0 or A[i-1] <= A[i]) i++;
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- Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY3 occurrences in the array with value x. What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.Describe an efecient in-place algorithm called Partition-Even-Odd(A) that partitions an array A in even and odd numbers. The algorithm must terminate with A containing all its even elements preceding all its odd elements. For example, for input A = [7, 17, 74, 21, 7, 9, 26, 10], the result might be A = [74, 10, 26, 17, 7, 21, 9, 7]. Partition-Even-Odd must be an in-place algorithm. What does this mean about your algorithm? (a) Write the pseudo-code for Partition-Even-Odd. (b) Characterize the complexity of Partition-Even-Odd. Brie y justify your answer. (c) Formalize the correctness of the partition problem as stated above, and prove that Partition-Even- Odd is correct using a loop-invariant.You have an array of n real numbers and another integer s. Find out whether the array contains two elements whose sum is s. (For example, for the array 5, 9, 1, 3 and s = 6, the answer is yes, but for the same array and s = 7, the answer is no.) Design an algorithm for this problem with a better than quadratic time efficiency.
- Given 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 algorithmsWrite an algorithm that returns the index of the first item that is less than its predecessor in an array s[1],….,s[n].Python: Let A be an array of size n ≥ 2 containing integers from 1 to n − 1, inclusive, with exactly one repeated. Describe a fast algorithm for finding the integer in A that is repeated.
- Write out the algorithm (pseudocode) to find K in the ordered array by the method that compares K to every fifth entry until K itself or an entry larger than K is found, and then, in the latter case, searches for K among the preceding four. How many comparisons does your algorithm do in the worst case?Given an array of positive and negative integers, write the main ideas of an algorithm to segregate them without changing the relative order of elements. The output should contain all positive numbers follow negative numbers while maintaining the same relative ordering. Example: Input: [9, -3, 5, -2, -8, -6, 1, 3] Output: [-3, -2, -8, -6, 9, 5, 1, 3] Determine the running time complexity of this algorithmLet B be an array that is of size n >= 6 containing integers from 1 to n-5, inclusive, with exactly five repeated. Describe an O(n) algorithm for finding the five integers in B that are repeated.
- Given an array of integers arr, sort the array by performing a series of pancake flips. In one pancake flip we do the following steps: Choose an integer k where 1 <= k <= arr.length. Reverse the sub-array arr[0...k-1] (0-indexed). For example, if arr = [3,2,1,4] and we performed a pancake flip choosing k = 3, we reverse the sub-array [3,2,1], so arr = [1,2,3,4] after the pancake flip at k = 3. Print out the k-values corresponding to a sequence of pancake flips that sort arr. Example 1: Input: arr = [3,2,4,1] Output: 4, 2, 4, 3 Explanation: We perform 4 pancake flips, with k values 4, 2, 4, and 3. Starting state: arr = [3, 2, 4, 1]. After 1st flip (k = 4): arr = [1, 4, 2, 3] After 2nd flip (k = 2): arr = [4, 1, 2, 3] After 3rd flip (k = 4): arr = [3, 2, 1, 4] After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted. Another potential solution is: Output = 3, 4, 2, 3, 1, 2, 1, 1 with a similar explanation. All potential solutions that solve the problem are…Given an array, find the total number of inversions of it. If (i < j) and (A[i] > A[j]), then pair (i, j) is called an inversion of an array A. We need to count all such pairs in the array. For example, Input: A[] = [1, 9, 6, 4, 5] Output: The inversion count is 5 There are 5 inversions in the array: (9, 6), (9, 4), (9, 5), (6, 4), (6, 5)What is time complexity for this Bubble Sort algorithm in seconds/minutes? def bubbleSort(array): length = len(array) for i in range(length-1): for j in range(0, length-i-1): if array[j] > array[j+1] : array[j], array[j+1] = array[j+1], array[j] arr = [56,7,1,9,0,4,34,100,67] print ("Elements of array before sorting:") for i in range(len(arr)): print ("%d" %arr[i]), bubbleSort(arr) print ("Elements of array after sorting:") for i in range(len(arr)): print ("%d" %arr[i])