Let G = ({S,A},{0,1},P,S) where P:S-OS, S-A, .A - 1A, A- 1. Then L(G) = {0m1"|m > 0, n 2 1} :Select one True False أخل اختياري
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- Define a sequence c0, c1, c2, … of pictures recursively as follows:For all integers i ≥ 1 Initial Conditions, c0 = an upright equilateral triangle ?. Recurrence Relation, ci = in centre of each upright equilateral triangle in ci-1, draw an upside down equilateral triangle ? such that its corners touch the edges of the upright one. Draw the first 4 iterations, starting with c0. You may want to draw c3 large. Each should be a separate drawing.Get your work checked by an IA/TA/Instructor. Count the total # of triangles for each iteration in a).Note: Triangles can be of any orientation.Only count the individual triangles. Do not count a triangle which has triangles inside it. Determine T(0), the # of triangles in the 0th term. Determine the recurrence relation, T(n), that gives the # of triangles in the nth term, for n ≥ 1.Recall that histograms are used for constructing load-balanced range partitions. Suppose you have a histogram where values are between 1 and 100, and are partitioned into 10 ranges, 1–10, 11–20,...,91–100, with frequencies 15, 5, 20, 10, 10, 5, 5, 20, 5, and 5, respectively. Give a load-balanced range partitioning function to divide the values into 5 partitions. Write an algorithm for computing a balanced range partition with p partitions, given a histogram of frequency distributions containing n ranges.Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.
- PYTHON DATASET given x = np.array([i*np.pi/180 for i in range(60,300,4)]) np.random.seed(10) #Setting seed for reproducibility y = 4*x + 7 + np.random.normal(0,3,len(x)) Write a function inspired by sklearn’s polynomial preprocessing: (https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html) your function should have: degree and include bias parameters only. For this assignment, assume that input is a 1-dimensional numpy array. For example, if an input sample is np.array([a, b]), the degree-2 polynomial features with "include_bias=True" are [1, a, b, a2, b2].Consider the set F = {1, −1, i, −i} with an operation ✕ defined by the table. ✕ 1 −1 i −i 1 1 −1 i −i −1 −1 1 −i i i i −i −1 1 −i −i i 1 −1 a ✕ b means find the entry in row a and column b; for example, −1 ✕ (−i) = i (the entry in row −1 and column −i). Find each of the following. (a) −1 ✕ i (b) i ✕ i (c) −i ✕ i (d) −i ✕ 1 (e) 1 ✕ i (f) −i ✕ −iComputer Science Given 2 arrays X[1...n] and Y[1...m], provide time analysis in term n and m successor (X[1...n]. Y[1...m]): set sucessor[1...m] to infinitive for each 1<= i <=n: for each 1<= j <=m: if Y[j] < X[i] and X[i] < successor[j]: successor[j] = X[i] return successor
- If you can make an optimal solution for a problem by making optimal solutions for its subproblems, then the problem has the quality in question. a) Subproblems that overlap; b) best substructure; c) memory; d) greedyModeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…The problem states that there are five philosophers sitting around a circular table. The philosophers must alternatively think and eat. Each philosopher has a bowl of food in front of them, and they require a fork in each hand to eat. However, there are only five forks available. You need to design a solution where each philosopher can eat their food without causing a deadlock.
- point p is on line l if and only if point l∗is on line p∗.1. Using the property above, prove the following properties:(a) If n points p1, ..., pnare on a common line l, then p∗1, p∗2, ..., p∗nintersect at a common point l∗.(b) If n lines l1, ..., lnintersect at a common point p, then l∗1, l∗2, ..., l∗nare on a common line p∗.2. If we have a line segment s connecting two points p1 and p2, describe a region s∗corresponding to thedual of s in terms of p∗1 and p∗2. (No rigorous proof is needed.)3. If a line l intersects the line segment s, prove that l∗is in the region s∗.Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) T[i, j] = ( T[i − 1, j] or T[i, j − ci]) b) T[i, j] = ( T[i − 1, j] and T[i, j − ci ]) c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − ci ]) d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − cj ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) T[1, K + 1] b) T[n, K] c) T[n, 0] d) T[n, K + 1]Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) ?[?, ?] = ( ?[? − 1, ?] ?? ?[?, ? − ?? ]) b) ?[?, ?] = ( ?[? − 1, ?] ??? ?[?, ? − ?? ]) c) ?[?, ?] = ( ?[? − 1, ?] ?? ?[? − 1, ? − ?? ]) d) ?[?, ?] = ( ?[? − 1, ?] ??? ?[? − 1, ? − ?? ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) ?[1, ? + 1] b) ?[?, ?] c) ?[?, 0] d) ?[?, ? + 1]