Given an integer n and an array a of length n, your task is to apply the following mutation to a: Array a mutates into a new array b of length n. For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1]. If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].
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Given an integer n and an array a of length n, your task is to apply the following mutation to a:
Array a mutates into a new array b of length n.
For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1].
If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].
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- Consider an array A of N values (N entered by the user). Write a C program that creates a second array B such that the i-th element of B, i.e., B[i] is equal to A[0] *A[1] * A[2] * ... A[i]; In other words:- B[0] = A[0]- B[1] = A[0] * A[1];- B[2] = A[0] * A[1] * A[2];- B[3] = A[0] * A[1] * A[2] * A[3]- ....etc.For this exercise, we would like to implement two solutions and compare their complexity /performance in terms of computation time.Solution 1: Implement blindly the following algorithms: for each element B[i], compute A[0] *A[1] * A[2] * .... *A[i] and save the result in B[i];To test the solution, create an array A of 1000 elements and initialize each of its elements with arandom value (instead of asking the user to . To do that, use the function rand, which, every timecalled, returns a random number Questions:- How long does your program take to produce the solution?- Analyze the solution above and explain why it is taking long time. What are the mainfactors that affect how long…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)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…
- Let A and B be two arrays of length n, each containing a random permutation of the numbers from 1 to n. An inversion between the two permutations A and B is a pair of values (x, y) where the index of x is less than the index of y in array A, but the index of x is more than the index of y in array B. Design an algorithm which counts the total number of inversions between A and B that runs in O(n log n) time.Given two arrays A and B of equal size N, the task is to find if given arrays are equal or not. Two arrays are said to be equal if both of them contain same set of elements, arrangements (or permutation) of elements may be different though.Note : If there are repetitions, then counts of repeated elements must also be same for two array to be equal. Example 1: Input: N = 5 A[] = {1,2,5,4,0} B[] = {2,4,5,0,1} Output: 1.Given an array A[0 : n−1] of n integers, compute the maximum sum of non-empty consecutive subsequence present in the array. For example, if the input is A = [3, 2, 5, 1, 6], then the output max sum is 17 (the corresponding maximum sum consecutive subsequence is [3, 2, 5, 1, 6]. If the input is A = [−2, 11, −4, 13, −5, −2], then the output max sum is 20 (the corresponding maximum sum consecutive subsequence is [11, −4, 13]. (a) Given input A[0 : n − 1] and n, design a divide-and-conquer algorithm which outputs the maximum sum of non-empty consecutive subsequence in the array. You only need to output the sum value and do not need to output the exact subsequence. [We are expecting a brief justification for the intuitive idea of the algorithm and the pseudocode of the algorithm.] (b) Let T(n) be the runtime of your algorithm when the input size is n. Establish the recurrence relation of T(n) for the algorithm, and then solve the recurrence relation to provide the big-O runtime of the…
- Given an array A[0 : n−1] of n integers, compute the maximum sum of non-empty consecutive subsequence present in the array.For example, if the input is A = [3, 2, 5, 1, 6], then the output max sum is 17 (the corresponding maximum sum consecutive subsequence is [3, 2, 5, 1, 6]. If the input is A = [−2, 11, −4, 13, −5, −2], then the output max sum is 20 (the corresponding maximum sum consecutive subsequence is [11, −4, 13].(a) Given input A[0 : n − 1] and n, design a divide-and-conquer algorithm which outputs the maximum sum of non-empty consecutive subsequence in the array. You only need to output the sum value and do not need to output the exact subsequence. [We are expecting a brief justification for the intuitive idea of the algorithm and the pseudocode of the algorithm.](b) Let T(n) be the runtime of your algorithm when the input size is n. Establish the recurrence relation of T(n) for your algorithm, and then solve the recurrence relation to provide the big-O runtime of your…Write a program that reads an array A of N elements containing only 0's and 1's. Your program should find the position of a 0 and replace it with a 1 to get the longest continuous sequence of 1's. Let this position of 0 be called P. Print P if such a 0 exists and print -1 if the original array A contains only 1's. Assume the array indexing starts from 0.Let A be an array of numbers. In the maximum sub-array problem, your goal is to determine the sub-array A[x . . . y] of consecutive terms for which the sum of the entries is as large as possible. For example, if A = [−2, −3, 4, −1, −2, 1, 5, −3], the maximum sub-array is [4, −1, 2, 1, 5], and the largest possible sum is S = 4 − 1 − 2 + 1 + 5 = 7. Suppose A = [1, 2, −4, 8, 16, −32, 64, 128, −256, 512, 1024, −2048]. Determine S, the largest possible sum of a sub-array of A.
- Take an array of length n where all the numbers are nonnegative and unique. Find the element inthe array possessing the highest value. Split the element into two parts where the first part containsthe next highest value in the array and the second part holds the required additive entity to get thehighest value. Return the array index value. Consider the negative numbers as well.Input: [4, 8, 6, 3, 2]Output: [4, 6, 2, 6, 3, 2]1) Consider an integer array a of length n with indexing starting at 0, where n is a positive integer.If the elements of array a are to be written out in reverse order, which of the following C++ code fragment does NOT do the job? Question options: a. int i=n-1; while (i>=1){cout << a[i] << endl; i = i-1;} cout << a[i] << endl; b. int i=n-1; while (i>=1){cout << a[i] << endl; i = i-1;} c. int i=n-1; while (i>=0){cout << a[i] << endl; i = i-1;} d. int i=n; while (i>0){cout << a[i-1] << endl; i = i-1;} 2) Assume we use 8-bit cell to store floating point numbers, 1 bit for sign, 3 bits for excessed exponent, and 4 bits for significand. What is the decimal value for a cell with bit pattern 0 111 1101 Question options: a. 125 b. 224…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 algorithms