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- 13. Implement function triangleArea(a,b,c) that takes as input the lengths of the 3 sides of a triangle and returns the area of the triangle. By Heron's formula, the area of atriangle with side lengths a, b, and c is √ s ( s−a )( s−b)( s−c ) , where s=(a+b+ c )/ 2 .>>> triangleArea(2,2,2)1.732050807568877212. Consider the recursive function int gcd( int a, int b) int gcd( int a, int b){ if (b > a) return gcd(b,a); if ( b == 0 ) return a; return gcd( b, a% b); } How many invocation (calls) of the gcd() function will be made by the call gcd(72, 30)?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
- 1) Write a recursive void function that has one parameter that is a positive integer and that writes out that number of asterisks (*) to the screen, all on one line. How do I do this in python?The goal is to rewrite the function, below, such that passes in a different list of parameters, particularly eliminating the need to pass low and high for each recursive call to binary_search. defbinary_search(nums,low,high,item): mid=(low+high)//2iflow>high:returnFalse #The item doesn't exist in the list!elifnums[mid]==item:returnTrue# The item exists in the list!elifitem<nums[mid]:returnbinary_search(nums,low,mid-1,item)else:returnbinary_search(nums,mid+1,high,item) The new function should be prototyped below. The number of changes between the given version, and the one requested is not significant. defbinary_search(nums,item):pass# Remove this and fill in with your code Tip: If you consider that high and low are used to create a smaller version of our problem to be processed recursively, the version requested will do the same thing, just through a different, more Pythonic technique.Implement the sieve of Eratosthenes: a function for computing prime numbers, known to the ancient Greeks. Choose an integer n. This function will compute all prime numbers up to, and including, n. First insert all numbers from 1 to n into a set. Then erase all multiples of 2 (except 2); that is, 4, 6, 8, 10, 12, ... . Erase all multiples of 3, that is, 6, 9, 12, 15, ... . Go up to ?⎯⎯√n. The remaining numbers are all primes. Make sure that you use functions in your solution, including a main function. Define def sieveOfEratosthenes(n) that receives the maximum value and returns a list of all prime numbers less than or equal to this value in main() print the list of prime numbers.
- 7. Write a program that will create a dynamically created 1D array of length n (given by the user) and store first n odd numbers in it. Try printing the size of the array using size of() function. Are you satisfied with the result of size of() function? If no, explain why? need the solve in c++PYTHON!!!! Complete the below function which takes the coefficients of a polynomial P(x) as a tuple, and a list of values, and returns a list of computed values of P(x). Note that P() can be of any order. For example, P((2,-1,1), [1,2,3]) shall compute P(x) for x=1,2,3 P(x)=2x^2 -x +1 where x^2 denotes the square of x. Hence, the function must return [2,7,16], because P(1) is 2, P(2) is 7, and P(3) is 16. """ def P(coefs, vals):Q#2 Write a recursive function zeroCount ( int a[ ], int s, int e) that receives an array of integers a [], a start index s, and an end index e. The function should return the number of zeros in that array between s and e. int zeroCount ( int a[ ], int s, int e); Trace your function given the following array and function call. Draw your steps. int a[ ] = {1, 0, 0, 5}; int zeros = zeroCount(a, 0, 3); language c++
- Q6 In Python implement a recursive function named test() that accepts an integer parameter. If the parameter value is even then the test function should divide the parameter value by 2 and return this value. If the parameter value is odd, then the function should return 3 times the parameter value + 1. Then request a user to enter an integer number and recursively call converge() on that number until the function returns the value 1.This is for Java Write a recursive function that takes as a parameter a nonnegative integerand generates the following pattern of stars. If the nonnegative integer is 4,then the pattern generated is:**********Also, write a program that prompts the user to enter the number of lines inthe pattern and uses the recursive function to generate the pattern. Forexample, specifying 4 as the number of lines generates the above pattern. Java pleaseIn python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…