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- For this given code, please help me create a recursive case for transpose of matrix using the cache oblivious algorithm. for ( size_t i=0; i<n; i += block ) { for ( size_t j=0; j<n; j++ ) { for ( size_t b = 0; b < block && i + b < n; ++b){ b[ j*n + i ] = a[ i*n + j ]; } } else { recursMatTranspose ( n, n, a, 0, 0, b, 0, 0 ); //recursive case using cache-oblivious algo } }Question 17. Sorting a data set is an important sub-problem in data science. Given the size n of a data set, which statements are correct? a) Bubble Sort has worst-case run-time complexity O(n).b) Bubble Sort has worst-case run-time complexity O(n log N).c) Bubble Sort has worst-case run-time complexity O(n2).d) Merge Sort has worst-case run-time complexity O(n).e) Merge Sort has worst-case run-time complexity O(n log N).f) Merge Sort has worst-case run-time complexity O(n2).g) Quick Sort has worst-case run-time complexity O(n).h) Quick Sort has worst-case run-time complexity O(n log N).i) Quick Sort has worst-case run-time complexity O(n2).Demonstrate the output of the 1st and 2nd iteration of the given data [8, 0, 4, 2, 1, 9, 7, 5, 6, 3] in A. Quick sort B. Analyze the computational complexity of all the above algorithms in terms of big-O notation?
- Let M(m,n) denote the number of comparisons required to merge two sorted lists of sizes m and n. a) Derive an "information theoretic" lower bound on M(m,n). b) Find an interesting relation between M(m,n) and the analogous function S defined for sorting. Use this relation to derive a lower bound for M(m,n) in terms of S. (Hint: Start with an upper bound on S(m+n).Given a sequence of integers, e.g., \[ 9,-1,45,6,8,21,34,5,55,65,543,18,90,122,132,0,66,100,-12,17 \] design an algorithm/method to re-arrange the order of the data items (i.e., form a new sequence of the integers) so that when the data items are inserted sequentially into an initially empty BST, the newly created BST will be a balanced BST. a) Design the algorithm (in pseudo code) and analyse your algorithm. b) Write a Python function/method to implement your algorithm. c) Write a program that calls the above function, thereby demonstrating your algorithm by (i). Print the re-arranged data items (i.e., a new sequence) generated by the algorithm, and (ii). Build a BST using the newly generated data sequence as input (that is, insert the data items, oneby-one, into an initially empty BST). Print the tree shape of the BST. (Note: The program should use at least two datasets to demonstrate the algorithm, one of which is the dataset given above).Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106 Write the whole code in python language Attach the code outputs also and explain the implementation.
- Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 32nlogn steps. For which values of n does insertion sort beat merge sort? Group of answer choices: 1. n < 1024 2. n > 1024 3. n < 16 4. n > 16 5. Merge sort is always better since O(nlogn) is better than O(n^2)A sorting algorithm is in O(n2) in the worst case. It takes 5 seconds to sort 10,000records, i.e. n = 10,000.(i) What is the predicted time for the algorithm to sort 20,000 records?(ii) Suppose that you are presented with a machine that is 49 times as fast.How many records will you be able to process on the new machine in 5seconds?
- Write pseudo code for it & what conditions) what else should change in Semigroup computation on a PRAM algorithm? to avoid the final broadcasting phase which essentially doubles the execution time of the semigroup computation algorithm in the EREW PRAM, it has been suggested that we replace the indices j + s in the algorithm with j + s mod p (i.e., allow the computations to wrap around). And under what conditions would this method yield correct results in all processors? (Write pseudo code for it)Given and nxn matrix filled with either 0 or 1 your task is to turn as few 0 as possible into 1 such that every index meets the requirement that its neighbour (i+1,i-1,j+1,j-1) sum is even. return minimum no of zero you need to convert into 1, return -1 if no soltuion possible constraints : 1<=tc<=10 1<=n<=10 input: tc = 2 n = 3 1 1 1 1 1 1 0 0 0 n = 3 0 0 0 1 0 0 0 0 0 output : for first tc : -1 for second : 3Consider the LCS problem discussed in class. Suppose we only want to compute the length of the LCS of x[1..m] and y[1..n] (i.e. we do not care about the actual subsequence itself). This means we do not need to “traceback” to find the LCS. In this setting, show how the algorithm can be altered so that it only needs min(m,n) + O(1) space rather than m · n space (note that it must be min(m,n) and not O(min(m, n))).