Let denote the nth Fibonacci number. Construct a sequence of ratios of the form , n = 1, 2, . . . , 30. Does the sequence appear to be converging? Compute the golden ratio . Is the sequence converging to this ratio? (Complete each of the tasks using both the for- and while-loop)
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- Suppose I have 50 strings. At every step, I randomly pick 2 ends of strings(they could be the ends of the same string) and tie them together. At each step, I couldmake either a longer string or a loop.a) What is the expected number of steps it takes me to turn all the strings into loops?b) What is the expected number of loops? (Express this as a sum)Instrument FrequencyCounter to use Stopwatch and StdDraw to make a plot where the x-axis is the number of calls on get() or put() and the y-axis is the total running time, with a point plotted of the cumulative time after each call. Run your program for Tale of Two Cities using SequentialSearchST and again using BinarySearchST and discuss the results. Note : Sharp jumps in the curve may be explained by caching, which is beyond the scope of this question.ALGO(A)x = A[0]p = -1r = nwhile (True) { do { p = p + 1 } while (A[p] < x) do { r = r - 1 } while (A[r] > x) if (p >= r ){ return r } exchange A[p] and A[r]} From the above algorithm, we have to state whether the following statements are True or False(With explanation) (A) At the end of each iteration of the while loop of Line 4, each index of A smaller than p contains an integer smaller than x. (B) At the end of each iteration of the while loop of Line 4, each index of A larger than r contains an integer larger than or equal to x. (C) When ALGO terminates, the integer at index r is x.
- Loops, C++ Write a program whose input is two integers, and whose output is the first integer and subsequent increments of 5 as long as the value is less than or equal to the second integer. Ex: If the input is: -15 10 the output is: -15 -10 -5 0 5 10 Ex: If the second integer is less than the first as in: 20 5 the output is: Second integer can't be less than the first. For coding simplicity, output a space after every integer, including the last.This function takes a string, text, and returns number of spaces in that string. Identify the loop exit condition, the loop post-condition, and the loop invariant at the end of each iteration of the loop, which shows the algorithm's correctness. def count_spaces (text): count = 0 i = 0 while i < len(text): if text[i] == ' ' : count += 1 i += 1 return countConsider the following code segment. What is the value of i and sum2 after the for loop completes? int sum2 = 0, i = 0; for (int i = 0; i < 5; i++) sum2 = sum2 + i; cout << "Sum is: " << sum2 << " i is: " << i << endl;
- Write an algorithm (pseudo code) for a program that display a person name x times. Use For loop, while loop, and Do-while loop.# Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):What is the termination condition (i.e. value of beta) for the following While loop? while (beta > 0 && beta < 10) { cout << beta << endl; cin >> beta; } explain please
- Do a trace on the for loop below, and show each iteration of the loop in the tracing table until the loop finishes. Each row in the table corresponds to one iteration of the for loop. int j=3, k=2; for(int i = 12; i >7; i--){ k = k + j - - * i ; } The tracing table is here: i i > 7 j k1. Write pseudocode that, given two positive integers x and y, follows this procedureand outputs the resulting value. Part of the loop invariant is that the variableholds the current left value, r the current right value, and s the sum of all previousright values that will be included in the final answer. Break the algorithm withinthe loop into two steps. In the first step, if is odd, it decreases by one. In the secondstep (now even) is divided by two. These steps must update r and s as neededgiven a variable t that is associated with a tuple whose elements are numbers, write some statements that use a while loop to count the number of times the first element of the tuple appears in the rest of the tuple, and associate the number with the variable repeats. using Python.