Write a recursive function called collatz that takes in a single positive integer argument n and returns the list of numbers in the collatz sequence from n to 1, inclusive. For example, suppose your initial number was 5. Then the collatz sequence would be the following: The initial number is 5. 5 is odd, so the next number is 5*3 + 1 = 16 16 is even, so the next number is 16//2 = 8 8 is even, so the next number is 8//2 = 4 4 is even, so the next number is 4//2 = 2 2 is even, so the next number is 2//2 = 1 We have reached 1, so the sequence is complete, and the function would return the list [5,16,8,4,2,1]

Write a recursive function called collatz that takes in a single positive integer argument n and returns the list of numbers in the collatz sequence from n to 1, inclusive. For example, suppose your initial number was 5. Then the collatz sequence would be the following: The initial number is 5. 5 is odd, so the next number is 5*3 + 1 = 16 16 is even, so the next number is 16//2 = 8 8 is even, so the next number is 8//2 = 4 4 is even, so the next number is 4//2 = 2 2 is even, so the next number is 2//2 = 1 We have reached 1, so the sequence is complete, and the function would return the list [5,16,8,4,2,1]

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 21PE

See similar textbooks

Similar questions

Mathematics is a very crucial subject in our life. It gives a power to calculate the daily things. Rajesh is the one of the brightest student in this subject so he has an integer N. His task is to break N into some number of (integer) powers of 2. TO achieve this, he can perform the following operation several times (possibly, zero): Choose an integer X which he already has, and break X into 2 integer parts (Y and Z) such that X = Y + Z. Find the minimum number of operations required by Rajesh to accomplish his task using Python Language. Input 1 3 Output 1
bool isprime(long n) /* fixed from to https://www.geeksforgeeks.org/euclid-euler-theorem/?ref=lbp */{ // check whether a number is prime or not int i; for (i = 2; i * i <= n; i++) if (n % i == 0) return false; return true;}
The Computer Science club is sponsoring a jigsaw puzzle contest. Jigsaw puzzles are assembled by fitting 2 pieces together to form a small block, adding a single piece to a block to form a bigger block, or fitting 2 blocks together. Each of these moves is considered a step in the solution. Use the second principle of induction to prove that the number of steps required to assemble an n-piece jigsaw puzzle is n − 1.
le.com/forms/d/e/1FAlpQLSc6PlhZGOLJ4LOHo5cCGEf9HDChfQ-tT1bES-BKgkKu44eEnw/formResponse The following iterative sequence is defined for the set of positive integers: Sn/2 3n +1 ifn is odd if n is even Un = Using the rule above and starting with 13, we generate the following sequence: 13 u13 = 40 u40 =20 u20 = 10→ u10 =5 u5 = 16 u16 = 8 ug = 4 → Us =2 u2 =1. It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. The below function takes as input an integer n and returns the number of terms generated by the sequence starting at n. function i-Seq (n) u=n; i=%3; while u =1 if statement 1 u=u/2; else statement 2 end i=i+1; end statement 1 and statement 2 should be replaced by: None of the choices statement 1 is "mod(u,2)=D%3D0" and statement 2 is "u = 3*u+1;" statement 1 is "u%2" and statement 2 is "u = 3*u+1;" O statement 1 is "mod(n,2)=30" and statement 2 is "u = 3*n+1;"
Write an algorithm that asks the user to enter a positive integer n and prints the sum of the divisors of n.
cancellation error occurs when you aremanipulating a very large number with a very small number. The large numbermay cancel out the smaller number. For example, the result of 100000000.0 +0.000000001 is equal to 100000000.0. To avoid cancellation errors and obtainmore accurate results, carefully select the order of computation. For example, incomputing the following summation, you will obtain more accurate results bycomputing from right to left rather than from left to right: Write a program that compares the results of the summation of the preceding series,computing from left to right and from right to left with n = 50000.
= = 2×2 and 6 = (a) A composite number is a positive integer that has at least one divisor other than 1 and itself. For example, 2 1×2 is not a composite number but 4 2 × 3 are composite numbers. A logic circuit has four binary input variables, A, B, C and D. The output Z of the logic circuit is 1 if the unsigned integer represented by the binary number ABCD is a composite number. Using variables A and B for the select inputs S1 and S0 of a 4-to-1 multiplexer, implement the logic function Z(A, B, C, D) using this multiplexor and other logic gates.
python In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case…
Sudoku is a popular logic puzzle that uses a 9 by 9 array of squares that are organized into 3 by 3 subarrays. The puzzle solver must fill in the squares with the digits 1 to 9 such that no digit is repeated in any row, any column, or any of the nine 3 by 3 subgroups of squares. Initially, some squares are filled in already and cannot be changed. For example, the following might be a starting configuration for a Sudoku puzzle: Create a class SudokuPuzzle.java Download SudokuPuzzle.java that has the attributes • board—a 9 by 9 array of integers that represents the current state of the puzzle, where 0 indicates a blank square • start—a 9 by 9 array of boolean values that indicates which squares in board are given values that cannot be changed and the following methods: • SudokuPuzzle—a constructor that creates an empty puzzle • toString—returns a string representation of the puzzle that can be printed • addInitial(row, col, value)—sets the given square to the given value as an…
Part 2: Binary Arithmetic One of the most common operations we perform on binary numbers (and all numbers) is addition. It can be cumbersome to convert your binary numbers to decimal just to add them and convert them back, so instead we will be learning how to add binary numbers directly. Binary addition works the same way as decimal addition, with the added restriction that each digit can only go up to 1. Let's consider the possibilities for adding the values of any 2 single digits together: 0 + 0 0 + 1 1 + 0 1 + 1 0 1 1 10 (remember that 10 in binary represents the number 2) In that last case, the result is larger than a single digit. When adding larger binary numbers, that means we have to carry the 1 over to the next column. This presents us with another new case: what happens if we have 1 + 1 + carried 1? In that case, the result is 11, which means that column's result is 1, and we carry 1 to the next column. Below is an example of adding two binary numbers that shows all…
%3B for ( int i = 0; i < n; ++i ) { for ( int j= 0; j< n; ++j) { sum += f( j, 10 ); } } iii. int sum = 0; %3D Assume f(n, m) runs in O( n + m) time.
(b) The Fibonacci numbers for n 0, 1,...are defined as follows. fib (0)-0 fib (1) 1: fib (n) fib (n- 1) + fib (n - 2): Consider the following piece of code that calculates the Fibonacci numbers. int fib ( int n){ if (n is 0) return 0 else if (n is 1) return 1 else return fib (n- 1)+ fib (n- 2) What is the worst-case complexity of the above code?