Q5. (Section 1.4.) Write the complexity categories of the following functions: The function f(x) = 3n² +10n log n+1000n+4 log n+9999 а. Answer: (please write your answer here, add required space if needed) The function f(x) = (log n)? + 2n + 4n + log n + 50 b. Answer: (please write your answer here, add required space if needed) The function f(x) = n + n² + 2" + nº %3D Answer: (please write your answer here, add required space if needed)

Q5. (Section 1.4.) Write the complexity categories of the following functions: The function f(x) = 3n² +10n log n+1000n+4 log n+9999 а. Answer: (please write your answer here, add required space if needed) The function f(x) = (log n)? + 2n + 4n + log n + 50 b. Answer: (please write your answer here, add required space if needed) The function f(x) = n + n² + 2" + nº %3D Answer: (please write your answer here, add required space if needed)

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 7SA

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Question 19. The following function f uses recursion: def f(n): if n 0 a <- a +i+ (1-1) return a c) def f(n): arr [0] <- 0 arr[1] <- 1 if n <= 1 return arr [n] else for i in 2..n arr [i] <- arr[i-1] + arr[i-2] return arr [n] d) def f(n): arr[0..n] <- [0, .., n) if n <= 1 return arr [n] else a <- 0 for i in 0..n a <- a + arr [i] return a
Midterm Practice Problems 1. Use recursion to write a function count_ones that returns how many Is there are in a number n when represented in decimal (base 10). For example, 1231 has two 1s. You can assume that n is nonnegative and at most 9 digits long. Do not use global (or static) variables. In main perform at least three tests of count_ones and use assert to check that the returned value is correct. Your function should have the following prototype: // count_ones (n) returns the number of is in the decimal representation of n // requires: 0 <= n < 10^9 int count_ones (int n);
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Question#1: Let P and Q be integers and suppose F (P, Q) is recursively defined by: F(int P, int Q) if (P == 0) return Q else return F(P- 1, P + Q) Find and Trace F(8,1)
1. Consider the following recursive function: def foo(n): if (n == 0): return 0 return n + foo(n - 1)a. What is foo(5) b. What is foo(10) c. Suppose that n + foo(n - 1) is changed to n * foo(n - 1). What is foo(5) now? d. What happens if foo(-1) is called?
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Question 1. Consider the following difference equation: With ro := 130, set rn := 0.0001 - 0,0194r1 + 1.6909r-1 (n = 1, 2, 3, ...). Question 1.1. Implement a non-recursive function in Python 3 according to the following specification. Include your implementation in your submission. Function specification: Function name: Input parameters: n: a non -negative integer Return The value of r. Question 1.2. Use matplotlib to make a scatter plot of the the first 21 elements in the solution of the difference equation. That is, make a scatter plot of the dataset {(J.r,) : 1 = 0,1, 2, 3,..., 20). Using the "set-ylim" function on your matplotlib axes, set the bounds of the y-axis to be the interval (0,200].
Python only** Use recursive function* Define countBetween with 2 parameters Use def to define countBetween with 2 parameters thas two parameters: a starting number and an ending number, and counts up (i.e., prints consecutive integers) from the starting number to the ending number. If the numbers are the same, it just prints that number; if the ending number is lower than the starting number, it prints nothing. Do not use any kind of loop Within the definition of countBetween with 2 parameters, do not use any kind of loop. Call countBetween Within the definition of countBetween with 2 parameters, call countBetween in at least one place. Python only** Use recursive function* Define countThereAndBack with 2 parameters Use def to define countThereAndBack with 2 parameters after reaching the ending number, it also counts back down to the starting number. It accepts the same two parameters defining starting and ending numbers it should print nothing if the starting number is…
Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…