The following pseudocode is supposed to take an array of numbers as input and return their sum. Prove the correctness via loop invariant. In other words, state the loop invariant and prove it using Initialization (Base case), Maintenance (Inductive Step), and Termination (Conclusion). Input: A[1 n] ... 1. sum = 0 = 1 to A.length A[j] 2. for j 3. sum = sum +
Q: Consider the following algorithm segment. Assume that n is a positive integer. for i := 1 ton for…
A: 1 a) b
Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…
A: Answer: I have given answer in the handwritten format.
Q: A palindrome is a sequence that is the same as its reverse. For example, the word "RACECAR" is a…
A: dp[i, j] — minimum number of operations to convert substring s[i..j] into palindrome. Below are the…
Q: for i: = 1 to 4n S:= 0 for j:= 1 to i - 1 s:= s+j• (i - j+ 1) next j r:= s? next i (a) What is the…
A: LINE 1 - for i := 1 to 2nLINE 2 - s := 0LINE 3 - for j := 1 to…
Q: Question 3: What is the time complexity of following code. Show the time complexity of each…
A: The answer is given below:-
Q: What is the worse-case complexity scenario for the following snippets of code? Please show the…
A: Complexity – The time complexity of the nested loops is O(N^2), as the outer loop depends on the…
Q: A certain computer algorithm executes twice as many operations when it is run with an input of size…
A: Answer
Q: A certain computer algorithm executes twice as many operations when it is run with an input of size…
A: In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of…
Q: Two algorithms A, B sort the same problem. When you go through each algorithm and break them down…
A: Below is the explanation
Q: Consider the following algorithm segment. Assume that n is a positive integer. for i:=1 to 4n S := 0…
A: (A) outer for loop iterate 4n times. So the statement "s=0" executes 4n times. for each value of…
Q: Code in Python Given two sorted arrays nums1 and nums2 of size m and n respectively, return the…
A: Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Algorithm: 1. Provide the…
Q: Write a program to implement the dot product operation for given two input arrays. The program will…
A: Program Approach: Import the necessary header files for the standard I/O operations. Declare a…
Q: An artificial intelligence system was design to forecast the financial trading market and predict…
A: All the answers are given below :
Q: Write a program to shift all the zero present in the array in the alternative order, For example.…
A: PROGRAM CODE: #include <iostream> // include header file for input output stream…
Q: Find the complexity of the program.
A: Since there are nested loop we compute the complexity as follows: Starting with the outer loop, it…
Q: Suppose we are given an n x n square grid, some of whose squares are colored black and the rest…
A: This problem , we can compare with n-queen problem , both have much similarities with each other. So…
Q: The Computer Science club is sponsoring a jigsaw puzzle contest. Jigsaw puzzles are assembled by…
A: Given that, The Computer Science club is sponsoring a jigsaw puzzle contest. Jigsaw puzzles are…
Q: Solve using JAVA only Given a square chess board of size N, solve the N queens problem.…
A: The Java Code for the given problem is provided below: We are using multi-dimensional array to…
Q: number of operations
A: Explanation: m=0; for( i = 1 to n) for( j = i+1 to n) m= max(ai,aj,m) Then here,…
Q: what is the time complexity of this 2 nested for loop for(int i = 0; i < num.length; i++)…
A: Here have to determine time complexity of given code snippet.
Q: The following method of computing a is due to Archimedes: 1. Let A = 1 and N =6 2. Repeat 10 times,…
A: code : % Draw the unit circle clf; t=linespace90,2*pi,200); plot(cos(t),sin(t),'b--); axis equal…
Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…
A: For each i, the statements are executed once. As i runs from j to n this…
Q: Using only one 2-D array (table) with equal odd sizes for its rows and columns, write a complete…
A: The above question is solved in step 2 :-
Q: 1. Consider the following two loops: / Loop A for (i - 1; i n; i+4) for (j - 1; j« 10000; j++) sum -…
A: 1. In the Loop A, outer for loop is executing n times and each time the inner for loop is executing…
Q: rs and outputs them in reverse order of how they were entered. For example, if the user enters 39,…
A: Step 1: Accept the string of three integers separated by comma from the user. Step 2: Create the…
Q: Suppose that two matrices A and B with dimension n x n are stored on a 2D mesh of n2 processors such…
A: Here is the C-style pseudocode for an asychronous algorithm
Q: Consider the following algorithm. (It doesn't do anything, but it sure wastes a bunch of time doing…
A: a) lower bound on the number of iterations of Loop 1 For the base case scenario, the loop control…
Q: Code in Python Given two sorted arrays nums1 and nums2 of size m and n respectively, return the…
A: Algorithm: Start Read array1 and array2 If array1 and array2 are in sorted order, calculate…
Q: You are given an array A[1, ., n] in which the elements A[2] to A[n] are already sorted, i.e., A[2,…
A: Algorithm with proper pseudocode
Q: A formula for finding the greatest common divisor (GCD) of two numbers was formulated by the…
A: Given : Values of a and b. Output : GCD of a and b using recursive function.
Q: Given an array A with 8 integers (in words), the 8 elements of the array are defined based on your…
A: l=list(map(int,input().split()))su=sum(l)halfsum=su//2sum1=0sum2=0for i in l: if i>=0:…
Q: Consider the following algorithm segment. Assume that n is a positive integer such that n 2 6. for i…
A:
Q: Give a big-O estimate for the number of times a gets updated in the inner loop of the following…
A: 1. a := 0 2. for i := 1 to n 3. for j := n downto 1 4. a := a + i + j…
Q: Consider the following algorinm segment. ASSUME that n Is a positive integer. for i: = 1 to 3n S:= 0…
A: Note: - As per the guidelines we can only answer one specific question at a time. Please resubmit…
Q: Write a GO program to read an positive integer n>4, and then run the Fermat primality test for at…
A: #include <bits/stdc++.h>using namespace std; int power(int x, unsigned int y, int p){ int res…
Q: Design and implement an algorithm using recursion and backtracking to sort an array of integers into…
A: Note: Since the language in the question is not defined so I am using python to implement this…
Q: Write an efficient algorithm for the following problem (either pseudocode or java), and describe…
A: Step 1: Initialize two variables count1 and count2 to store the count of first and second maximum…
Q: An n-bit Gray code is a list of the 2n different n-bit binary numbers such that each entry in the…
A: N-bit Gray code, and how does it work: This n-bit grey code time series is a series of 2n numbers…
Q: You want to design an algorithm, called minMax(A,p,r), that takes an array of integers and indexes…
A: Below is the minmax algorithm using divide and conquer technique:
Q: Print the square that consists of NxN cells filled with numbers from 1 to N*N in a spiral mode(see…
A: Given: Print the squares that consist of NxN cells filled with number form 1 to N*N in a spiral…
Q: Figure 5.17 CPE performance for different degrees of loop unrolling. Only integer addition and…
A: The solution of the above question is here given below:- Before unrolling: #include…
Q: 4.11 Exercise: Suppose Algorithm A takes 3n³+5n²+100n time and Algorithm B takes 4n³ time…
A: The Java code to check if g(n) will rise above f(n) i.e. g(n) > f(n) for which value of n has…
Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…
A: I like the way you asked the question. First you solved the question yourself and then you asked…
Q: can you please fix the AssertionError in this: (please don't use try and except or break/continue or…
A: The correct Python code along with the screenshot of code and output is given below:
Q: How many times will the innermost loop be iterated when the algorithm segment is implemented and…
A: The pseudocode given:- for k:= 1 to n for j:= k to n for i:= j to n…
Q: Give an informal description of a Turing machine with three tapes,that gets as input the binary…
A: The Turing machine Informally, a Turing machine is a finite automaton equipped with an un- bounded…
Q: Write a program to shift all the zero present in the array in the alternative order, For example.…
A: Note: Here you didn't mention any programming language so we are writing the program in the C++…
Q: Consider the following algorithm segment. Assume that n is a positive integer such that n 2 6. max…
A: Explanation: For Example n=10 Elements are a[0] a[2] a[3] a[4] a[5] a[6] a[7]…
Q: Analyze another algorithm under Divide and Conquer. In your discussion, include the following: 1.…
A: The program is written in Java. Check the program screenshot for the correct indentation. Please…
Q: . Given n > 3 points P₁ = (x₁, y₁), ..., Pn = (Xn, Yn) in the coordinate plane, design an algorithm…
A: Find the convex hull for the given set of points. If the convex hull for the given set of points has…
Step by step
Solved in 2 steps
- 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.Suppose that your implementation of a particular algorithm appears in C++ as for (int pass = 1; pass <= n; pass++) { for (int index = 0; index < n; index++) { for (int count = 1; count < 10; count++) { ... } // end for } // end for } // end for The previous code shows only the repetition in the algorithm, not the computations that occur within the loops. These computations, however, are independent of n. What is the Big O of the algorithm?Suppose that two matrices A and B with dimension n x n are stored on a 2D mesh of n2 processors such that P_(i,j) holds A[I,j] and B[j,i] . Write C-style pseudocode for an asynchronous algorithm that computes the product of A and B in O(n) time. (10 points) (WRITE THE PSEUDOCODE! IF YOU DON'T WRITE PSEUDOCODE, YOU WILL BE WRONG!! C-STYLE ONLY!!!)
- Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n -1 elements of A. write pseudocode for this algorithm , which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n – 1 elements, rather than for all n elements? Give the best-case and worst-case running times of selection sort in Θ-notation.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 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.
- (Write the code in java)Given 2 sorted arrays (in increasing order), find a path through the intersection that produces the maximum sum and return the maximum sum. That is, we can switch from one array to another array only at common elements. If no intersection element is present, we need to take the sum of all elements from the array with greater sum. Sample Input: 6 1 5 10 15 20 25 5 2 4 5 9 15 Sample Output : 81 Explanation : We start from array 2 and take sum till 5 (sum = 11). Then we'll switch to array at element 10 and take till 15. So sum = 36. Now, no elements are left in array after 15, so we'll continue in array 1. Hence the sum is 81.You want to design an algorithm, called minMax(A,p,r), that takes an array of integers and indexes of the first and last elements, and returns the minimum and maximum values in that range. Now write the pseudo code of a divide and conquer (and therefore, recursive) algorithm with the same time complexity (Θ(n)). You can assume that p ≤ r. Also, in your code, you can return two numbers by returning a pair, e.g. “return (a, b)”, and can save the output in a similar way, e.g. “(a, b) = minMax(parameters)”. (Short answer please)Subject - Design & Anal algorithms Please complete all the questions together. Thank you in Advance. Consider the following pseudocode for bubblesort:bubblesort(A, n)for i from 1 to n − 1for j from n to i + 1if A[j] < A[j − 1]swap(A[j], A[j − 1])(a) What is the loop invariant for bubblesort?(b) State briefly a proof of correctness.(c) Derive concisely the worst-case running time of bubblesort as a function of the input array sizen? Show your work!(d) Derive concisely the best-case running time as a function of n. Show your work!
- Suppose we have two arrays, a and b, containing numbers of size n and m, respectively. a and b array; All elements of a and b (only one copy of common elements) in another array c Write the adder program in C and calculate the number of steps and time complexity of the algorithm?Write an efficient algorithm (to the best of your knowledge) for the following problem, briefly describe why it is a correct algorithm, and analyze the time complexity. If you cannot find any polynomial-time algorithm, then give a backtracking algorithm. Problem: Repeated Number Input: An array A[1...3n] of positive integers. Output: If any number in the array appears at least n times, then print such a number. Otherwise, print 'none'. Example: Input: A = [1,3,3,3,1,1]. Here 3n = 6 and n =2. Output: 3. Note that here 1 would also be a valid output. You just need to print one if there are many options. Example: Input: A = [4,3,5,7,9,1]. Here 3n = 6 and n =2. Output: 'none'Write a program in java for the below given problem statement: Given 2 sorted arrays (in increasing order), find a path through the intersection that produces themaximum sum and return the maximum sum. That is, we can switch from one array to another array only atcommon elements. If no intersection element is present, we need to take the sum of all elements from thearray with greater sum.Sample Input:61 5 10 15 20 2552 4 5 9 15Sample Output :81Explanation :We start from array 2 and take sum till 5 (sum = 11). Then we'll switch to array at element 10 and take till15. So sum = 36. Now, no elements are left in array after 15, so we'll continue in array 1. Hence the sum is81.