Problem Description The hailstone sequence is defined as the integer sequence that results from manipulating a positive integer value n as follows: • If n is even, divide it by 2 (using floor division) • If n is odd, multiply it by 3 and then add 1 Repeat this process until you reach 1. For example, starting with n = 5, we get the sequence 5, 16, 8, 4, 2, 1. If n is 6, we get the sequence 6, 3, 10, 5, 16, 8, 4, 2, 1. If n is 7, we get 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. If n is 8, we get the sequence 8, 4, 2, 1. As far as anyone can tell, this process will eventually reach 1 for any starting value, although mathematicians have been unable to formally prove this property as of yet. a. Write a Python function named hail () that takes a single integer argument. hail() should print out the sequence of numbers generated by applying the process above to the function parameter. This function does not return any value.

[Python Language] Using loops of any kind, lists, or Sets is not allowed. Sloan’s Book Collection Sloan loves reading books. She recently started reading an AI generated series called "Harry Trotter". Sloan is collecting books from the series at her nearest bookstore. Since the series is AI generated, the publishers have produced an infinite collection of the books where each book is identified by a unique integer. The bookstore has exactly one copy of each book. Sloan wants to buy the books in the range [l,r], where l ≤ r. As an example, the range [−3,3] means that Sloan wants to buy the books − 3, − 2, − 1, 0, 1, 2, and 3. Pam also loves the series (or maybe annoying Sloan– who knows, really), and he manages to sneak into the bookstore very early to buy all of the books in the range [d,u], where d ≤ u. When Sloan later visits, sadly she will not find those books there anymore. For example, if Sloan tries to buy books [−2,3] and Pam has bought books [0,2], Sloan would only receive...

# NumberFun.py # using multiple functions. # copy/paste this program to run it first, you are supposed to use Google Chrome as Internet Browser for this course. # 1. calculate sum of the first n natural numbers, e.g.:1,2,3,... def totalN(n): totalN = 0 for i in range(1,n+1): totalN = totalN + i return totalN # 2. calculate sum of the cube of the first m natural numbers, e.g.:1,8,27,... ### After you define/write/complete the function totalMCube(m), remove the # sign as below to ENABLE next line of code ###def totalMCube(m):### YOUR TURN TO DEFINE/WRITE/COMPLETE function totalMCube(m) as below, based on totalN(n) # 3. call two functions defined previously within main() function def main(): print("This program computes the total and total of cubes of the first") print("N/M natural numbers.\n") n,m = input("Please enter a value for N and M: ").split(",") print("The total of the first", n, "natural numbers is", totalN(int(n)))### After you define/write/complete the function totalMCube(m),...

Rooks on a rampage def safe_squares_rooks(n, rooks): A generalized n-by-n chessboard has been invaded by a parliament of rooks, each rook represented as a two-tuple (row, column) of the row and the column of the square that the rook is in. Since we are again computer programmers instead of chess players and other normal folks, our rows and columns are numbered from 0 to n - 1. A chess rook covers all squares that are in the same row or in the same column. Given the board size n and the list of rooks on that board, count the number of empty squares that are safe, that is, are not covered by any rook. To achieve this in reasonable time and memory, you should count separately how many rows and columns on the board are safe from any rook. Because permuting the rows and columns does not change the answer to this question, you can imagine all these safe rows and columns to have been permuted to form an empty rectangle at the top left corner of the board. The area of that safe rectangle is...

JAVA The loop continuation condition is the inverse of the loop termination condition. True False

Sevens rule, zeros drool def seven_zero(n): Seven is considered a lucky number in Western cultures, whereas zero is what nobody wants to be. Let us briefly bring these two opposites together by looking at positive integers that consist of some solid sequence of sevens, followed by some (possibly empty) solid sequence of zeros. Examples integers of this form are 7, 77777, 7700000, 77777700, and 70000000000000. A surprising theorem proves that for any positive integer n, there exist infinitely many integers of such seven- zero form that are divisible by n. This function should return the smallest such seven-zero integer. Even though discrete math and number theory help, this exercise is not about coming up with a clever symbolic formula and the proof of its correctness. This is rather about iterating through the numbers of this constrained form of sevens and zeros efficiently and correctly in strictly ascending order, so that the function can mechanistically find the smallest working...

Course: Computer Engineering CE102

Caesars Cypher in C programming language How do you program an encryption and decryption for a Caesars Cypher that covers all the possible ASCII characters? In this there should be a shift over K = 5 but the example below is K = 3. This should result in actual character and not the control ASCII represenations. For example: >>> $ encrypt(I have a key)N%mf{j%f%pj~>>> $ encrypt(see me at 3)xjj%rj%fy%8>>> $ decrpyt(|jfw%ns%gqzj)wear in blue Assume that the text parsing method has been succesful and it's the encryption/decryption of the char array that needs to be factored. Formula Encryption -> C = E(k, P) = (P + k) (mod 26) Decryption -> P = D(k, C) = (C - k) (mod 26) Where k = 5

For any binary string x, let #0(x) and #1(x) denote the number of 0’sand the number of 1’s in x, respectively. Design a DFA to accept the following language:L = {x | x ∈ {0, 1}∗, the summation 3 · #0(x) + 2 · #1(x) is divisible by 5}

please code in python You place a pawn at the top left corner of an n-by-n chess board, labeled (0,0). For each move, you have a choice: move the pawn down a single space, or move the pawn down one space and right one space. That is, if the pawn is at position (i,j), you can move the pawn to (i+1,j) or (i+1, j+1). Ask the user for the size of a chessboard, n (integer). Find the number of different paths starting from (0,0) that the pawn could take to reach each position on the chess board. For example, there are two different paths the pawn can take to reach (2,1). Look at the diagrams below to convince yourself of this. You can see the four paths that you can take by move 2. Start -> Move 1 -> Move 2 (0,0) -> (1,0) -> (2,1) (0,0) -> (1,0) -> (2,0) (0,0) -> (1,1) -> (2,1) (0,0) -> (1,1) -> (2,2) Print the board with the number of ways to reach each square labeled as shown below. For example: Enter a board size: 4 1 0 0 0 1 1 0 0 1 2 1 0 1 3 3 1

# NumberFun.py # using multiple functions. # copy/paste this program to run it first, you are supposed to use Google Chrome as Internet Browser for this course. # 1. calculate sum of the first n natural numbers, e.g.:1,2,3,... def sumN(n): sumN = 0 for i in range(1,n+1): sumN = sumN + i return sumN # 2. calculate sum of the square of the first m natural numbers, e.g.:1,4,9,... ### After you define/write/complete the function sumMSquare(m), remove the # sign as below to ENABLE next line of code ####def sumMSquare(m):### YOUR TURN TO DEFINE/WRITE/COMPLETE function sumMSquare(m) as below, based on sumN(n) # 3. call two functions defined previously within main() function def main(): print("This program computes the total and total of squares of the first") print("N/M natural numbers.\n") n,m = input("Please enter a value for N and M: ").split(",") print("The total of the first", n, "natural numbers is", sumN(int(n)))### After you define/write/complete the function sumMSquare(m), remove...

Duplicate digit bonus def duplicate_digit_bonus(n): Some people ascribe deep significance to numerical coincidences, so that consecutive repeated digits or other low description length patterns, such as a digital clock blinking 11:11, seem special and personal to them. Such people then find numbers with repeated digits to be more valuable and important than all the ordinary and pedestrian numbers without any obvious pattern. For example, getting inside a taxicab flashing an exciting number such as 1234 or 6969 would be far more instagrammable than a more pedestrian taxicab adorned with some dull number such as 1729.Assume that some such person assign a meaningfulness score to every positive integer so that every maximal block of k consecutive digits with k>1 scores 10**(k-2) points for that block. A block of two digits scores one point, three digits score ten points, four digits score a hundred points, and so on. However, just to make this more interesting, there is also a special...