a) Design an efficient algorithm to solve this problem , and analyze its complexity  [Important instruction: Create an arbitrary list of 10 lectures starting times and their corresponding ending times to provide full explanation of how your proposed  algorithm should work step by step]  b) Implement your efficient algorithm using Python

The following equation can be used to compute values of y as a function of x: y=be¯ªsin(bx) (0.0012x¹ −0.15x³ +0.075x² +2.5x) where a and b are parameters. (a) Write Python code to compute a vector y for a = 2, b = 5, and x as a vector with values from 0 to π/2 in increments Ax= π/40. (b) Compute the vector z = y² with element-by-element-wise operations. (c) Combine x, y, and zinto a 3-column matrix W.(Hint use np. hstack function) (d) Generate a plot of y and z versus x. Include a title, axis labels, and a legend. For the y versus x curve, format a solid blue line. For the z versus x curve, choose a magenta dashed line. Include grid lines.

Exercise 3. For each of the following program fragments give a (.) estimation of the running time as a function of n. (a) sum = 0; (b) (c) (d) (e) for (int i = 0; i< n * n; i++) { for(int j = 0; j < n/2; j++) sum++; } sum = 0; for (int i sum++; +; } for (int j } sum = for = } = 0; j < n/2; j++) { sum++; } 0; (int i = 0; i< n * n; i++) { for (int j = 0; j < n * n; j++) sum++ sum = 0; for (int i = 0; i

For each problem, please provide i. Describe the worst-case input (the input that would cause the largest running time) Summation used to calculate number of steps for the worst case Explanation of how the code relates to the summation ii. iii. a. (loops require discussing number of iterations and steps per iteration) b. (recursion requires a diagram) A O bound iv.

The following equation can be used to compute values of y as a function of x: y=be¯ªsin(bx) (0.0012x¹ −0.15x³ +0.075x² +2.5x) where a and b are parameters. (a) Write Python code to compute a vector y for a = 2, b = 5, and x as a vector with values from 0 to π/2 in increments Ax= π/40. (b) Compute the vector z = y² with element-by-element-wise operations. (c) Combine x, y, and zinto a 3-column matrix W.(Hint use np. hstack function) (d) Generate a plot of y and z versus x. Include a title, axis labels, and a legend. For the y versus x curve, format a solid blue line. For the z versus x curve, choose a magenta dashed line. Include grid lines.

2. R(N) is the running time of strange_sum when called on a List of length N. Since this is recursive code, your answer to iii should include a diagram of the recursion tree. a. Answer for li being an ArrayList b. Answer for li being a LinkedList static int strange_sum(List li) { return strange_sum_helper(li, 0, li.size() - 1); static int strange_sum_helper (List arr, int left, int right) { if (right - left < 0) return 0; else if (right else { int mid = (left + right) / 2; return strange_sum_helper(arr, left, mid) left 0) return arr.get(left); == + strange_sum_helper(arr, mid + 1, right); } }

Please do it in python

ii.Building on your decomposition for part c.i., develop an algorithm for solving the problem. Include this algorithm in your solution document, and also write down your PI and the individual number that you have obtained via Steps 1–3 from your PI H5737055

3. Write a C++ program that implements the following three algorithms and times for various values of n. The program should display a table of the run times of each algorithm for various values of n. //Algorithm C sum = n * (n + 1) / 2 //Algorithm A sum = 0; for (i = 1 to n) sum = sum + 1 //Algorithm B sum = 0; 1 to n) for (i { for (j = 1 to i) sum = sum + 1 }

Express the Euclidean Algorithm in pseudo-code, then convert your pseudocode to a Python Program. "The Euclidean algorithm finds the greatest common divisor of two positive integers X and Y by the following process:  As long as the value of neither X nor Y is zero, assign the larger the remainder of dividing the larger by the smaller.  The greatest common divisor, if it exists, will be the remaining non-zero value."