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Hello, I'm doing a Data Structure project and I don't know how to answer this, could you help me?
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- 2.a Σ : {c,A,G,T}, L = { w : w = CAG™T™C, m = j + n }. For example, CAGTTC E L; CTAGTC ¢ L because the symbols are not in the order specified by the characteristic function; CAGTT ¢ L because it does not end with c; and CAGGTTC € L because the number of T's do not equal the number of A's plus the number of G's. Prove that L¢ RLs using the RL pumping theorem.Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AGiven the following PDA M, the correct statements are: b, e; bbb a,b; e q0 L(M)= {b³nan: n ≥ 0} L(M) = {bna³n: n>0} OL(M)= {a³nbn:n>0} OL(M)= {anb³n: n>0} a,b; & 91
- Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.If F1(A, B, C, D) = Sum(0, 1, 3, 8, 9, 14, 15) and d=Sum(4, 5, 11, 12, 13), the F1 =initialize s'; evaluate (s'); while (!end_of_iterations){ s=pick_random_neighbor(s'); evaluate (s); if (s better s') s'=s; } Notes: use 1-flip neighborhood • s': current best solution candidate s : solution candidate currently being considered What to do: 1. Write a program in C/C++. 2. The program must read the knapsack data from the given file. 3. The program must implement the given heuristic.
- L₂ = {a"b"a"b" |n,m≥>0} L₁ = {1"0"1"0" |n, m≥ 0}Quadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…Bus timetables specify to the second the exact arrival and departure time of each bus on each stop. You need to pay for the full fare of every bus you ride and different bus lines charge different fees , but they are flat fees (independent of distance travelled on the line) A travel plan is a sequence of stop-time pairs where stop is a location of a bus stop and time is when we arrive at that stop. The plan is feasible if for any two consecutive pairs (a, t) and (b, t′) in the plan there exists a bus that departs after t and arrives at b at exactly t′. That is, a travel plan does not allow us to walk between stops. Assuming that no two buses arrive at the same time at the same stop, a feasible plan uniquely identifies the bus lines that we need to take to realize the plan. The cost of the plan is the sum of the fares we need to pay. Your task is to design an efficient algorithm that given a departure time t, an arrival time t′, an origin stop a and a destination stop b, finds the…
- Given the following NDFSM M, the correct statements are: q0 8 b a q1 94 a b a a q2 q5 a 93 L(M) = {w € {a, b}*: w contains aaa or bab or w| is even). OL(M) = {w € {a, b}*: w contains aaa or bab or w| is odd}. L(M) = {w € {a,b}*: The 2nd to the last character of w is a or|w| is even}. L(M) = {w = {a, b}*: The 2nd to the last character of w is a or |w| is odd}.Q5. Below is the code for power function that computes x". Write the recurrence relation for this function. Solve the recurrence relation using master method (for dividing functions) long power(int x, int n) { if(n==0) return 1; if(x=0) return 0; if(n 1) return x; if(n%2 = 0) // n is even else } return power(x*x, n/2); return x * power(x*x, n/2);sum = 0; for (int i = 1; i< n; i = sum++ || 2*i)