Given n integers {a₁, az, ..., an}, let S = a₁ + a2 + + an. Suppose that S is even. Design an algorithm that finds a subset of these n integers whose sum is S/2.
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- A finite sequence of symbols from a given alphabet will be called a string over the alphabet. A string that consists of a sequence a1, a2, a3, a4, … … … … , an of symbols will be denoted by the juxtaposition a1 a2 a3 a4 … … … … an. Given the strings: u = a2bab2and v = bab2, Evaluate the following operations for strings: (i) ԑu(ii) u + v(iii) u(u| v)(iv) v | (v | u)You are given nn points in the plane: (x1,y1),(x2,y2),...,(xn,yn). On the page , in English, give an algorithm that determines if there is a circle on which all of the points lie. In English, write your algorithm to determine if there is a circle on which points(x_1, y_1), (x_2, y_2), . . ., (x_n, y_n) lie. Algorithm:If your first name starts with a letter from A-J inclusively: Perform an experimental analysis of the two algorithms prefixAverage1 and prefixAverage2, from lesson examples. Optionally, visualize their running times as a function of the input size with a log-log chart. Use either Java or Python graphical capabilities for visualization. Hint: Choose representative values of the input size n, similar to StringExperiment.java from class examples. class PrefixAverage { /** Returns an array a such that, for all j, a[j] equals * the average of x[0], ..., x[j]. * A[j] = (X[0] + X[1] + … + X[j])/(j+1) * * ******************************************************/ // inner loop size will be 1, 2, 3, ..., n (based on j=0,1,2,...,n-1) // we know that 1+2+3+...+ n-1+n = n(n+1)/2 // so, the running time os O(n^2) public static double[] prefixAverage1(double[] x) { int n = x.length; double[] a = new double[n]; // filled with zeros by default for (int j=0; j < n; j++)…
- The Fibonacci series is an infinite sequence of natural numbers, starting from 0 and 1, from which the terms are generated from the sum of the previous sequence elements. a0=0, a1=1, a2=a0+a1, ... , an+1=an+an-1 Implement an algorithm in Java that get n from console and that print the first n terms of the Fibonacci series.Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n? (2) There is a decision procedure for the problem. If your answer is true, try to describe the procedure in English or pseudocode for learning purposes. Group of answer choices True FalseThere is a cube and an ant is performing a random walk on its vertices,every step it will start from one vertex and walk to another along the connected edge, it willrandomly select any of the 3 adjoining vertices with equal probability. If it starts at one vertex,what is the expected number of steps it needs to reach the diagonally opposite vertex? Write a c++ program for the same
- Write an algorithm that inputs a number n followed by an array of n numbers and outputs the number of values of i, with i between 1 and n-1 such that ai < ai +1. {i| i is a natural number and 1 <= i <= n-1 and ai < ai +1} *The output is the cardinality of the set Can be written in pseudocodeJava Programming Consider a set of n intervals I1,...,In, each given as an integer tuple (si,fi) with si<fi, such that the ith interval starts at si and ends at fi. We want to determine the maximum number of nonoverlapping intervals. More formally, we want to determine the size of a largest subset S⊆{1,...,n} such that for i, j∈S, with i≠j we have fj≤si or fi≤sj. Note that the intervals [1,2] and [2,3] are not considered to be overlapping. Input The first line of input consists of an integer n∈{1,...,105}, the number of intervals. Each of the following n lines consists of two space-separated integers ss and ff, indicating an interval starting at s and ending at f, with 0≤s<f≤109. requirements: CPU Time limit: 4 seconds Memory limit: 1024 MB Output Output a single integer, the largest number of nonoverlapping intervals.Computer Science There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S. 5 3 4 9 4 X 3 6 1 9 X 4 1 2 3 5 - Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.
- Pseudo-random numbers Randomly generating numbers is a crucial subroutine of many algorithms in computer sci- ence. Because computers execute deterministic code, it is not possible (without external influence) to generate truly random numbers. Hence, computers actually generate psuedo- random numbers. The linear congruential method is a simple method for generating pseudo-random numbers. Let m be a positive integer and a be an integer 2 < a <m, and c be an integer 0 ≤ c<m. A linear congruential method uses the following recurrence relation to define a sequence of pseudo-random numbers: In+1=a+c mod m (a) Use the linear congruence method with a = 8, c=5, and m = 14, to compute the first 15 pseudo-random numbers when co= 1. That is, compute zo,X1, X 14- (b) From part (a) we should notice that, with m = 14, the sequence does not contain all 14 numbers in the set Z14. In particular because the sequence is periodic. Using m = 8, determine the value of a which does give all 8…Consider the following problem: given a list of integers N and an individual integer n, is there any element of N that is a factor of n? (1) There is a semi-decision procedure for the problem. If your answer is true, try to describe the procedure in English or pseudocode for learning purposes. Group of answer choices True FalseLet's consider a long, quiet country road with houses scattered very sparsely along it. (Picture the road as a long line segment with an eastern endpoint and a western endpoint.) Further let’s suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations. Give an efficient algorithm that achieves this goal using as few base stations as possible. Prove its correctness and explain its time complexity.