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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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- Q2. Consider the following options for characters in setting a password: Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } Letters = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z } Special characters = { *, &, $, # } Compute the number of passwords possible that satisfy these conditions: Password must be of length 8. Characters can be special characters, digits, or letters. The first character must be a letter. Characters may be repeated.Suppose we have a nice young couple who borrow $700000 from the bank, at an annual interest rate of3.124%. The mortgage is a 30 year loan, so they need to pay it off within 360 months total. Our happycouple decide to set their monthly mortgage payment at $2000 per month. Will they pay off the loan intime or not?Note that the monthly balance will be calculated asbalance = (im × previous balance) - monthly paymentwhere the convert annual interest to a monthly multiplier im is calculated as im = (1 +i)1/12 and i = annualinterest rate.Write a loop for track the total payment in 360 months so that we can evaluate if the couple can pay off theloan. Write in R Please and thank you.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)
- Proof the following statement by definition of big O and big theta: If f(n) = O(g(n)), then f(n) + g(n) = Θ(g(n)).A university assigns student IDs of the form 1, 2, 3, ... such that if n students are currently enrolled, then the next student to enroll will receive and ID of n + 1. Consider the following algorithm that accomplishes this. // Global variable storing number of students currently enrolled current_student_count = 0 // Function that reads the above global variable, calculates new ID, and increments the global count assign_new_id(): count = current_student_count new_id = count + 1 current_student_count = count + 1 return new_id (a) If two different threads run the above code in parallel to enroll two different students, it is possible for the two students to receive the same ID, and for the current_student_count to have a wrong value. Explain how this is possible. (b) Modify the code above so that the problem in (a) does not happen.Answer all 3 must else ?
- You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…Note that for this question, you can in addition use ``land'' for the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬. Given the following three sentences:A) Every mathematician is married to an engineer.B) A bachelor is not married to anyone.C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, whereMn(x): x is a mathematician.Er(x): x is an engineer.Md(x,y): x is married to y.Br(x): x is a bachelor.george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation I such that I models A, but does-not-model C.)c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C).d) Convert A,B, lnot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses…The factorial function f(n) = n! is defined by n! = 1 2 3... n whenever n is a positive integer, and O! = 1. Provide big-O estimates for the factorial function and the logarithm of the factorial function. As an illustration, 1! = 1, 2! = 1 2=2, 3! = 1 23 = 6, and 4! = 1 234=24.Take note of how quickly the function n! expands. Consider the following: 20! = 2,432,902,008,176,640,000.
- Q 1.Consider the following functions f1 and f2:int f1(int n) { if (n == 0) { return 1; } else { return f2(4, f1(n – 1)); }} int f2(int n1, int n2) { if (n1 == 0) { return 0; }else { return n2 + f2(n1 – 1, n2); }} a. Evaluate the value of f1(7)? b. Analyze the computational complexity of the f1 function expressed in terms of big-O notation?In C++ Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 383 -5 -1 the output is: x = 3, y = 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: There is no solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. #include <iostream>using namespace std; int main() { /* Type your code here. */ return 0;}Problem 1: Let P(x, y) denote the statement “Student x has taken class y”, where the domain for x consists of all students in your class, and for y consists of all computer science courses at your school. Express each of the following quantifications in English.1. x y P(x, y)2. x y P(x, y)3. x y P(x, y)4. y x P(x, y)5. y x P(x, y)6. x y P(x, y)