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) tim
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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
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- The algorithm below is to determine if two given sequences A and B both containing n integers have identical values. It returns a Boolean value “True” if the two arrays have identical values and “False” if otherwise. Two sequences A and B are considered having identical values if every element of sequence A is equal to its corresponding element in sequence B (that is, A[0] is equal to B[0], A[1] is equal to B[1], etc.). Any problem with this algorithm? a. Incorrect as the statement that increases the variable LoopCount is wrong placed in the While-loop. b. Correct but inefficient c. Incorrect as it just based on the last number in the sequence. d. Correct e. InefficientSuppose you are given a vector x. Write first a pseudo-code or algorithm that would print out the sum of all the entries in x. You will probably want to use a some kind of for loop construction to achieve this. 1: for i = start : finish do 2: statements 3: end for Now use the start:increment:finish notation, and modify your procedure slightly, to print out the sum of the odd elements in the array (that is, the elements in entries 1, 3, 5, and so on). Implement and test your algorithm with an arbitrary array of real numbers using Python.PYTHON Given an array consisting of N integers returns the maximum sum of two numbers who’s digits add up to an equal sum. If there are no two numbers who’s digital shave an equal sum, the function should return -1 write an efficient algorithm of the following assumption: N is an integer within the range [1..200.000]
- Design an algorithm that takes an array containing n distinct natural numbers. A number k ≤ n and calculates the sum of the k largest numbers in the array. For example, if the array is {3, 7, 5, 12, 6} and k = 3, then the algorithm should return 25 (12+7+6). You may freely use standard data structure/s and algorithms from the course in your solutionYou should design and implement an algorithm to order an array of n integers in a way that finally even elements come after odd ones. The algorithm must run in O(n) time and use O(1) space (in addition to the array itself). The program must read its all input into an array and after that sort it in place. Eventually it must print the resulting array and the number of comparison operations performed. The array can be sorted at any order provided that the even elements come after the odd ones.Problem2: A square matrix can be represented by a two-dimensionalarray with N rows and N columns. You may assume a maximum size of 50 rows and 50 columns. 1. Write an algorithm MakeEmpty(n), which sets the first n rows and n columns to zero. 2. Write an algorithm Add(M1, M2, M3), which adds two matrices M1 and M2 together to produce matrix M3. 3. Write an algorithm Subtract(M1, M2, M3), which subtracts matrix M2 from matrix M1 to produce matrix M3. 4. Write an algorithm Copy(M1, M2), which copies matrix M1 into matrix M2.
- // Input: array A[0, ..., n-1] minval :=A[0] maxval :=A[0] for i = 1 to n-1 do end for a. b. C. if A[i] < minval then minval :=A[i] end if if A[i] < maxval then maxval:=A[i] end if What does the algorithm do? What is the basic operations? What is the efficiency class of the algorithm?1. Estimate in terms of n, the worst case time complexity of each of the following pseudo-code snippets: a. ALGORITHM sum(n) sum -0 for i 0 to n do for j +0 to n*n do sum Esum + 1 return sumYou are now running the insertion sort algorithm on your computer. Assume that at the start of iteration j=4 of the for loop, the array A is A=3,6,8,4,9,2,7,10, and that the for loop is iteration j=4. The array A should be written at the beginning of iteration j=5 of the for loop.
- Suppose you are given a 6 * 6 matrix filled with 0 and 1. All rows and all columns have the even number of 1s. Let the user flip one cell (i.e., flip from 1 to 0 or from 0 to 1) and write a program to find which cell was flipped. Your program should prompt the user to enter a 6 * 6 array with 0 and 1 and find the first row r and first column c where the parity is violated (i.e., the number of 1’s is not even). The flipped cell is at (r, c).Given a group of characters a circular array A[ ]. It is required for each one to print the index of the first bigger character on its right. Print -1 if no one is bigger than it. Example 1: (refer to the figure below) A[]={L,B,Q,F,T,M} Output: 2 2 4 4 -1 2 Explanation of example 1: The given array A[] of character is as follows: A[index] A[0] A[1] A[2] A[3] | A[4] A[5] Content L В Q F M Example 2: A[]={J,P,S,D,N} Output: • Regarding "L", the first bigger character on its right is "Q" (i.e., A[2]), and hence 2 is printed. • Regarding “B" has also the same "Q" on her right, and hence 2 is printed again and so on. ... 1 2 -1 4 1 Describe how a brute-force approach algorithm would solve the above problem and explain its complexity Design a more efficient algorithm to solve this problem. [The efficiency of your algorithm is the main driver of solution], and analyze the complexity of your solution. Develop a python code to implement your efficient algorithm. Prepare a brief report comparing…1. Design an algorithm to find the weighted sum of four test scores (https://en.wikipedia.org/wiki/Weight_function). Assume that the weights have been accurately calculated in advance such that their sum equals one. Your algorithm must-read in the four test scores and four corresponding weights in the following order: score1 weight1 score2 weight2 score3 weight3 score4 weight4 Write your algorithm such that it can be run with any set of data values. However, you can test your algorithm on the following sample data to verify that the result is 70: 90 0.10 80 0.20 70 0.30 60 0.40 2. Write an algorithm that prompts the user for the radius, in inches, and price of a pizza, and then reads in those values. Finally, have the algorithm compute and output the pizza’s cost per square inch. 3. Sports exercise advisor algorithm. In this algorithm you will start out with a temperature value in Celsius, so you do not need to ask the user for it. First, convert the temperature to Fahrenheit.…