Example: L = {w over E = = {a, b} | |w| < 3}, list the members of L and what is the cardinality of L. L = {A, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb}. Cardinality of L = |L| = 15. Problem#1: Consider E = {a, b} а. Li -Σ0 υ ΣU Σ 2. b. L2 = {w over E||w| > 2 and |w| < 5 and |w| is odd }. c. L3 {w over E||w[ > 2 and |w| < 5 and |w| is even }. %3D
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Give the strings of each language of the following problems in ascending order of word length.
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- 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."Equatable and Comparable" in the Swift Programming: The Big Nerd Ranch Guide (2nd Ed.) e-book: Point’s current conformance to Comparable yields some confusing results. let c = Point(x: 3, y: 4) let d = Point(x: 2, y: 5) let cGreaterThanD = (c > d) // false let cLessThanD = (c < d) // false let cEqualToD = (c == d) // false As the above example demonstrates, the trouble arises in comparing two points when one point’s x and y properties are not both larger than the other point’s. In actuality, it is not reasonable to compare two points in this manner. Fix this problem by changing Point’s conformance to Comparable. Calculate each point’s Euclidean distance from the origin instead of comparing x and y values. This implementation should return true for a < b when a is closer to the origin than b. Use the formula shown in below Figure 25.1 to calculate a point’s Euclidean distance. Figure 25.1 Euclidean distance Euclidean distancePlease solve max 30 minutes thank u Boolean Satisfaction Problem Boolean Satisfiability Problem (SAT) (https://en.wikipedia.org/wiki/Boolean_satisfiability_problem) is one of the most important problems in Computer Science. SAT is a problem that has NP-Complete complexity, where the only way to solve the problem is to try all the possibilities and check which one is correct. [LO 1, LO 2, LO 3 & LO 4,] Briefly explain how you use Strongly Connected Component (SCC) to solve the special case of the Boolean Satisfiability Problem, namely 2-SAT (https://en.wikipedia. org/wiki/2-SAT) . This solution has linear complexity. NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design methods
- A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.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]
- Suppose you have been given a map of 6 cities connected with each other via different paths. Your job is to visit every city just once covering the minimum distance possible. Solve this problem using Genetic Algorithm. You can start at any point and end at any point. Just make sure that all the cities have been covered. 1. Encode the problem and create an initial population of 3 different chromosomes 2. Choose any one parent from your above solution and identify the following:i. Gene ii. Chromosome 3. Think of an appropriate fitness function to this problem and give proper justification. 4. Use the fitness function to calculate the fitness level of all the chromosomes in your population. Select the fittest 2 chromosomes based on the fitness function. 5. Perform crossover that you have been taught in the class on the selected parents. Now based on the offspring, for this problem do you think that is the best way to perform crossover? If not, explain why. 6. Perform mutation that you…Q1. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it.4. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a) ∃x N(x) b) ∀x N(x) c) ˺∃x N(x) d) ∃x ˺N(x) e) ˺∀x N(x) f ) ∀x ˺N(x)
- Suppose (X[mX]+Y [mY ]) > 0. What can you infer about each of the four subproblems (namely, (X1, Y1), (X1, Y2), (X2, Y1), and (X2, Y2))? Clearly identify the ones that do not have to solved anymore, and those that still have to be solved. Briefly justify.If the first number in a sequence is a positive integer, x Let ao= x, an is defined as follows if an is even, then an+1 = an/2 if an is odd, then an+1 =3 *an+ 1 Then there exists an integer k, such that ak =1 For example, if: 75, then k = 14 and the numbers in the sequence are: 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1. The largest number in the sequence is 340 and it is a position 4 in the sequence (assuming 75 is at position 1) Design and implement a complete C++ program that will • read a series of integers (greater than 0) from a file and for each integer display (to the screen) − the integer − the number of steps it takes to reach 1 − the largest value in the sequence and its positionRecall 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.