The factorial of 0 is defined to be 1. The factorial of a positive integer is defined to be the product of that integer times the factorial of the next smaller nonnegative integer. We use the notation n! to express the factorial of the integer n. Thus the factorial of 3 (written 3!) is 3 × (2!) = 3 × (2 × (1!)) = 3 × (2 × (1 × (0!))) = 3 × (2 × (1 × (1))) = 6. Design a recursive
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- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Sasha likes exploring diverse mathematical articles, for instance, wizardry squares. However, Sasha comprehends that enchanted squares have as of now been examined by many individuals, so he sees no feeling of concentrating on them further. All things considered, he designed his own kind of square — a superb square. A square of size n×n is called prime if the accompanying three conditions are held all the while: all numbers on the square are non-negative integers not surpassing 105; there are no indivisible numbers in the square; amounts of integers in each line and every segment are indivisible numbers. Sasha has an integer n. He requests you to view as any great square from size n×n. Sasha is certain beyond a shadow of a doubt such squares exist, so help him! Input The principal line contains a solitary integer t (1≤t≤10) — the number of experiments. Every one…arrow_forwardWe usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits" {0, 1,...,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0, 1, ...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. a. How many 4-digit hexadecimals are there in which the first digit is E or F? 8192 b. How many 5-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? c. How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)?arrow_forwardA magic square is an n by n matrix in which each of the integers 1, 2, 3...n appears exactly once and all column sums, row sums, and diagonal sums are equal. For example, the following is a 5 by 5 magic square in which all rows, columns and diagonals sum to 65. 17 24 1 8. 15 23 7 14 16 4 6. 13 20 22 10 12 19 21 3 11 18 25 9 The following is a procedure for constructing an n by n magic square for any ODD integer n. Place 1 in the middle of the top row. Then.m after integer k has been placed, move up one row and one column to the right to place the next integer k+1 unless one of the following occurs: If a move takes you above the top row in the jth column, move to the bottom of the jth column and place k+1 there. If the move takes you outside to the right of the square in the ith row place k+1 in the ith row in the left side. If the move takes you to an already filled square or if you move out of the square at the upper right hand corner place k+1 immediately below k. Write a C++ program…arrow_forward
- The Fibonacci sequence is defined as follows: ϕ0=0, ϕ1=1, ϕn=ϕn−1+ϕn−2. ϕ0=0, ϕ1=1, ϕn=ϕn−1+ϕn−2. Given an integer a, determine its index among the Fibonacci numbers, that is, print the number n such that ϕn=a. If a is not a Fibonacci number, print -1 . WRITE THE CODE IN PYTHON PLEASEarrow_forwardPython quesarrow_forwardNOTE: The algorithm should be written in pseudo code, (explanation of the algorithm rather than code)arrow_forward
- code in java pls Summary: Given integer values for red, green, and blue, subtract the gray from each value. Computers represent color by combining the sub-colors red, green, and blue (rgb). Each sub-color's value can range from 0 to 255. Thus (255, 0, 0) is bright red, (130, 0, 130) is a medium purple, (0, 0, 0) is black, (255, 255, 255) is white, and (40, 40, 40) is a dark gray. (130, 50, 130) is a faded purple, due to the (50, 50, 50) gray part. (In other words, equal amounts of red, green, blue yield gray). Given values for red, green, and blue, remove the gray part. Ex: If the input is: 130 50 130 the output is: 80 0 80 Find the smallest value, and then subtract it from all three values, thus removing the gray.arrow_forward(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?arrow_forwardUsing a Java program solve the following problem using arrays: Past A: Coupon collector is a classic statistic problem with many practical applications. The problem is to pick objects from a set of objects repeatedly and determine how many picks are needed for all the objects to be picked at least once. A variation of the problem is to pick cards from a shuffled deck of 52 cards repeatedly and find out how many picks are needed before you see one of each suit. Assume a picked card is placed back in the deck before picking another. Write a program to simulate the number of picks needed to get total of four cards from each different suit and display the four cards picked (it is possible that a card may be picked twice). Here is a sample run of the program: Queen of Spades 5 of Clubs Queen of Hearts 4 of Diamonds Number of picks: 12 Sample run explanation: As you see in the above run, 12 picks are made to get the four cards from different suits. The other 8 picks (12-4-8) were from the…arrow_forward
- n and n+1 are integers with the same number of positive divisions. Find the integers n from 1<n<107. For example, the positive divisors of 14 are 1, 2, 7, 14, and 15 are 1, 3, 5, 15. (P.s.: You have to done it by C++.)arrow_forwardNeed help in python. Problem: 2D random walk. A two dimensional random walk simulates the behavior of a particle moving in a grid of points. At each step, the random walker moves north, south, east, or west with probability 1/4, independently of previous moves. Compose a program that takes a command-line argument n and estimates how long it will take a random walker to hit the boundary of a 2n+1-by-2n+1 square centered at the starting point. //Given codeImport stdioImport randomImport sysn = int(sys.argv[1])//write code herestdio.write('The walker took ')stdio.write(c)stdio.writeln(' steps')arrow_forwardStart with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr