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 Ninto 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

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 Ninto 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

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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Use following series to do the given task; 135 79 11 13 15 1719 21 23 25 27 29 31 ... Given the number N of odd numbers in a certain line, your task is to determine the sum of the last three numbers of that line. For example N = 5 means, the third line, the last three numbers are 13, 15 and 17. The summation of these three numbers is 45. InputThe first line tells the number of test cases. From the next line, the input is a sequence of lines, one odd number N (1 < N <1000000000) per line. OutputFor each input line write the sum of the last three odd numbers written in that line of series with N numbers.
On the planet Tatooine, droids do computations in base-6. What is the greatest base-6 number with three different digits? (Your base-6 number must have a separate digit for each digit.) Make a decimal out of your answer (base-10).
Can someone help me to answer this activity? Factorial of a number is defined as: n! = n(n-1)(n-2)(n-3)...(2)(1) For example, 4! = 4*3*2*1 The n! can be written in terms of (n-1)! as: n! = n* (n-1)! (n-1)! = (n-1)*(n-2)! and so forth. Thus, in order to compute n!, we need (n-1)!, to have (n-1)!, we need (n-2)! and so forth. As you may immediately notice, the base case for factorial is 1 because 1! = 1. Write a program that uses a recursive function called factorial that takes an integer n as its argument and returns n! to the main.
Show that the following statements are equivalent, where n is an integergreater than or equal to 2. “n is even” and “n – 1 is odd”2. “n is even” and “n2 is even”3. “n – 1 is odd” and “n2 is even”
To represent an integer value of n in decimal, we need to use ⌈log10(n + 1)⌉ digits . Verify this using n = 35, 1290. Note that for any real number x, ⌈x⌉ is the smallest integer that is greater than x, this means we always round up. For example, ⌈10.3⌉ = 11, ⌈−5.2⌉ = −5. To represent an intege value of n in binary, we need to use ⌈log2(n + 1)⌉ binary digits . Verify this using n = 35, 1290. Use the definition of logarithmic function to show that log2n / log10n = log210
The following is an addition problem in binary notation. Each letter represents a unique binary digit. Which letter represents 1 and which represents 0? Design an algorithm for solving problems like this. YXX+ XYX=XYYY
python this is connected to the last problem - the second part of the question is added. my attempt on this problem shows that the part b) (approaches N*NH) is not really wokring.. a) (answered) with a function “harmonic(n)” that computes the n-th harmonic number, write a function “harmonic_all(n)” that returns the number of values generated until all values are obtained as a function of the range of possible values n, then write a function “harmonic_sim(n)” that repeats “harmonic_all(n)” a total of n_sim = 100 times. (Attaching the code from the answer for a) d) Show that as n increases (e.g., with a doubling experiment), from n = 2 to n_max = 1,000, the value of “coupon_sim(n)” approaches “n * Hn”.
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply dynamic programming. Do not use recursion/memoization. Make sure ALL test cases return expected outputs. Sample Input 04 412340123 Sample Output 013715 Explanation 0You are given the sequence 1,2,3,4.F0 = A0 = 1F1 = A1 + F0 = 2 + 1 = 3F2 = A2 + F1 + F0 = 3 + 3 + 1 = 7F3 = A3 + F2 + F1 + F0 = 4 + 7 + 3 + 1 = 15 The actual code def solve(k,a): MOD = 1000000007 # compute and return answer here q, n = list(map(int,input().rstrip().split(" ")))a = [int(input().rstrip()) for i in range(n)]outs = []for i in range(q): k = int(input().rstrip()) outs.append(solve(k,a))print("{}".format("\n".join(list(map(str,outs)))))
HALP m + n = 2k + 2k = 4k therefore adding even numbers always gives an even number. The above is wrong because.... it doesn't consider the case when adding to odd numbers m and n are different so you cannot use 2k for both it doesn't consider what m and n are for particular values in the integers it doesn't consider the case when m is even and n is odd
Use Sage to program Exercise 5.In 1202 AD, Leonardo Pisano asked the following famous problem:A certain man had a pair of rabbits together in a certain enclosedplace, and one wishes to know how many are created from the pair inone year when it is the nature for of them in a single month to bearanother pair, and in the second month those born bear also. Becausethe abovewritten pair in the first month bore, you will double it. therewill be two pairs in one month. One of these, namely the first, bears inthe second month, and thus there are in the second month three pairs;of these in one month two are pregnant, and in the third month 2pairs of rabbits are born, and thus there are 5 pairs in the month;...Explain how the rabbits reproduce. Create a list F where F[x] is the number ofrabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].
I wrote the following program for this problem and it works, but is too slow on big numbers. How could i make it faster? Problem: We want to represent positive integer n as a sum of addends, where each addends is an integer number containing only 1s. For example, we can represent 121 as 121=111+11+–1. Help us to find the least number of digits 1 in such sum. Input: The first line of the input contains integer n (1 ≤ n < 1015). Output: Print expected minimal number of digits 1. (ex. input:121, output:6) My solution: import java.util.Scanner; public class Main { staticlong[] en=newlong[]{1,11,111,1111,11111,111111,1111111,11111111,111111111,1111111111, 11111111111L,111111111111L,1111111111111L,11111111111111L,111111111111111L,1111111111111111L}; public static void main(String[] args){ Scanner scanner =new Scanner(System.in); System.out.println(rekisto(scanner.nextLong())); } static long rekisto(long s){ if(s==0){ return 0; } int dolzina…
c++ Implement a function that recursively calculates the nth number in the Fibonacci sequence of numbers. The Fibonacci sequence starts at 0 and 1. Each number thereafter is the sum of the two preceding numbers. This gives us the following first ten numbers: 0,1,1,3,5,8,13,21,34, .... Input Expected output0 01 17 139 34