Write a recursive implementation of Euclid’s algorithm for finding the greatest common divisor (GCD) of two integers. Descriptions of this algorithm are available in algebra books and on the Web. Write a test program that calls your GCD procedure five times, using the following pairs of integers: (5,20), (24,18), (11,7), (432,226), (26,13). After each procedure call, display the GCD.
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- (a) Give a recursive definition of F(n) where F(n) =1+2+3+....+n. (b) Find the value of a4 if a1 = 1, a2 = 2, and an =an−1 + an−2 +· · ·+a1Write a program in elixir programming language and in which you have to find the factorial of 10 using recursionWrite a recursive method using java to return the sum of all numbers less or equal n divisible by 2 and 3
- write a recursive function(in python) that computes the determinant of a (random)square matrix, represented as a list of lists of numeric values. use main(3517) to produce the same number a the value above.The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names (until -1), and use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia -1 then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia partial code below, only lines 9-11, and 18 can be added onto, the rest must stay the same. #include <vector>#include <string>#include <iostream> using namespace std; // TODO: Write method to create and output all permutations of the list of names.void AllPermutations(const vector<string> &permList, const vector<string> &nameList) { } int main(int argc, char* argv[]) { vector<string> nameList; vector<string> permList; string name; // TODO: Read in a list of names; stop…
- Write a recursive Fibonacci function that computes the Fibonacci number for input n and prints each value computed in the series at each recursive step in the sequence from 0 to n, all in one line on the console. (In python)implement two recursive versions of the linear search that gets an array of songs and a title and searches for a song with the given title in the array. In this version, the function returns the first index of the array containing the number. If the number is not in the array, the function returns -1. int linear_search_rec_first(int* ar, int length, int number);For function log, write the missing base case condition and the recursive call. This function computes the log of n to the base b. As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 and log(10, 100) -> 2 public int log(int b, int n ) { if <<Missing base case condition>> { return 0; } else { return <<Missing a Recursive case action>> }}
- Write a program that will contain the following methods: printSub1, printSub2, printSub3, printSub4 – print all substrings of S using recursion. For example, if S = "abcd": printSub1 will print "a", "ab", "abc", "abcd", "b", "bc", "bcd", "c", "cd", "d" printSub2 will print "d", "cd", "bcd", "abcd", "c", "bc", "abc", "b", "ab", "a" printSub3 will print "a", "b", "c", "d", "ab", "bc", "cd", "abc", "bcd", "abcd" printSub4 will print "abcd", "bcd", "abc", "cd", "bc", "ab", "d", "c", "b", "a" Note that the actual output will not have quotation marks around the substrings. The substrings must print in the order shown for each method. You may only use these String methods in your work: length(), substring() Your main method in this program should provide an appropriate menu which allows the user the enter the string of their choice and pick any of the print substring options they want. write the methods recursively and in javaWrite a program that will contain the following methods: printSub1, printSub2, printSub3, printSub4 – print all substrings of S using recursion. For example, if S = "abcd": printSub1 will print "a", "ab", "abc", "abcd", "b", "bc", "bcd", "c", "cd", "d" printSub2 will print "d", "cd", "bcd", "abcd", "c", "bc", "abc", "b", "ab", "a" printSub3 will print "a", "b", "c", "d", "ab", "bc", "cd", "abc", "bcd", "abcd" printSub4 will print "abcd", "bcd", "abc", "cd", "bc", "ab", "d", "c", "b", "a" Note that the actual output will not have quotation marks around the substrings. The substrings must print in the order shown for each method. You may only use these String methods in your work: length(), substring() Your main method in this program should provide an appropriate menu which allows the user the enter the string of their choice and pick any of the print substring options they want. IN JAVAWrite a recursive implementation of Euclid's Algorith for finding the greatest common divisor(GCD) of two intergers. Descriptions of this algorithm are available in algebra books and on theweb. (Note: A nonrecursive version of the GCD problem was given in the programming exercisesfor Chapter 7.) Write a test program that calls your GCD procedure five times, using thefollowing pairs of integers: (5,20),(24,18),(11,7),(432,226),(26,13). After each procedure call,display the GCD.