T(n) = aT (^) + f(n) F(n) = 3 F()+n, use el Teorema Maestro
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use the master theorem
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- QUADRATIC PRIMES This question is adopted from Project Euler Question 27. (https://projecteuler.net/problem=27) The quadratic formula n^2 + n + 41 will produce 40 primes for consecutive integer values 0 <= n <= 39. However, when n = 40, this formula will not generate a prime number. Another interesting quadratic formula n^2 – 79n + 1601 produces 80 prime numbers for consecutive values 0 <= n <= 79. The Question: find a and b such that when -999 <= a <= 999 and -1000 <= b <= 1000, the quadratic form ?^2 + ? × ? + ? produces the maximum number of primes for consecutive values of n, starting with n = 0. Requirement: MUST BE WRITTEN IN C++ - Print the 40 primes generated by formula n 2 + n + 41 - Print the 80 primes generated by formula n 2 – 79n + 1601 - Write a function that takes in an integer and returns whether the given number is prime or not. - Output the value of a, b and how many consecutive values of n (count the starting zero!) can be generated. - Submit…4x1+4x2+6x3+9x4=03x1+3x5=26x2+5x4+7x5=-46x1+8x4+2x5=54x5+7x2+6x3+8x1=-10Represent the set of equations in a matrix equation, Ax=b, where A is a square matrix and x and b are column vectors. Write the line of code to define matrix A for this problem matlab/octave languagePython question Application: Big-O Notation (Q8-11) For each of the time complexities in this segment give the tightest bound in terms of a simple polylogarithmic function using big-O notation. Note: use the ‘^’ symbol to indicate exponents, i.e., write O(n^2) for O(n2). Question 8 (Big-O Notation 1) T(n) = n2+ log n + n Question 9 (Big-O Notation 2) T(n) = n/3 + 4 log n + 2n log(n) Question 10 (Big-O Notation 3) T(n) = 7n5 + 2n Question 11 (Big-O Notation 4) T(n) = (n%5) + 12,000
- You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 10 10 3 9 11 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 567 999 2 999 999 0 6 999 1 999 17 999 999 2 6 0 999 7 999 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 0 8 9 999 999 999 999 999 999 4 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial nearest 1 2 3 4 5 6 7 8 9 16 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.с++ The table of the football championship is given by a square matrix of order n, in which all elements belonging to the main diagonal are equal to zero, and each element not belonging to the main diagonal is equal to 2, 1 or 0 (the number of points scored in the game: 2—win, 1 — draw, 0—loss).Determine the numbers of the teams that passed the championship without defeat. Input: 5 0 1 0 2 2 2 0 1 2 1 0 1 0 2 0 2 2 2 0 1 1 0 2 2 0 Output: 1 3multiplier 3 make_multiplier (3) print (multiplier_2(5)) # Output: 10 print (multiplier_3(5)) 10 15 In [4]: def sum_of_digits (n): if n < 10: else: return n I return n % 10 + sum_of_digits (n // 10) # Example usage: result sum_of_digits (123456222) print("Sum of digits:", result) # Output: 10 In []: Sum of digits: 27 How did it become 27 I want to explain in detail and give different examples to understand the material
- Problem: Given 20 positive integers as input, calculate the number of divisors for each integer and sort the data set from smallest to largest based on the number of divisors. When multiple integers have the same number of divisors then sort them smallest to largest. Examples: Integer value 12 has divisors 1, 2, 3, 4, 6, 12 for a total of 6. Prime numbers only have divisors of 1 and the number itself. The integer 1, the smallest value that will be provided as input, has only a single divisor, itself. Example Execution #1: Enter 20 integer values -> 21 15 10 6 3 1 28 13 5 7 9 29 31 37 17 19 12 43 24 2 Data sorted by number of divisors: 1 2 3 5 7 13 17 19 29 31 37 43 9 6 10 15 21 12 28 24 Example Execution #2 (data does not have to be unique): Enter 20 integer values -> 9 7 5 3 8 6 4 2 9 75 3 8 6 4 2 9 7 5 3 Data sorted by number of divisors: 2 2 3 33 5 5 5 7 7 7 4 4 9 9 9 6 6 8 8An algorithm that requires operations to complete its task on n data elements is said to have a linear runtime. O 2n + 1 O n^2 O 8 O n^2 + 15 O None of the choicesfor b in range (3,7,2): print(b*b) need value