def sum_even(n): total = 0 for i in range(2, n+1, 2): total += i return total def min(t): m = 0 for i in t: if i < m: m = i return m Hint: You may find it necessary to add an extra parameter for the recursive version.
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- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.1. Write a recursive function that takes a string as an input and returns the reverse of the string. 2.Write a recursive function rec_string that produces the output shown below for the corresponding function calls. Write a main function to test the function. Method call rec_string(‘abcde’), will produce the following output: *ede cde bcde abcde Method call rec_string(‘abc’), will produce the following output: *cbc abc 3. Write a recursive function for Euclid's algorithm to find the greatest common divisor (gcd) of two positive integers. gcd is the largest integer that divides evenly into both of them. For example, the gcd(102, 68) = 34. You may recall learning about the greatest common divisor when you learned to reduce fractions. For example, we can simplify 68/102 to 2/3 by dividing both numerator and denominator by 34, their gcd. Finding the gcd of huge numbers is an important problem that arises in many commercial applications. We can efficiently compute the gcd using the…Given two integers x snf y, the following recurrsive definition determined the greatest common divisor of x and y, Write gcd(xy). Write a recursive function, gcd, that takes two integers as parameters and returns the greatest commmon divisorof numbers.Also write a program to test your function. Write a recursive function,reverseDigits, that takes an integer as a parameter snd returns the number with the digits reversed. Also write a program to test your application.
- 1. Implement a recursive function called firstTwo that returns the sum of the firsttwo digits in a positive number. If there is only one digit, that digit is returned.Note this function is returning an integer, not printing. There should be no use ofcout within your function.Title line: int firstTwo(int n)ex. firstTwo(8325) returns 11ex. cout << firstTwo(428); // prints 62. Implement a function called findMinGap that will return the smallest gap betweenadjacent entries of an integer array. A gap between two numbers is the absolutevalue of their difference. For example, if an array contains the elements {10, 14,-5, -3, 0, 5, 7}, the minimum gap is 2 (between -5 and -3).Title line: int findMinGap(int array[], int length)3. Implement a function called findLargestIndex which returns the index of the rowwith the largest sum.ex. int array[3][6] = {{3, 6, 8, 2, 4, 1}, // sum = 24{2, 4, 5, 1, 3, 4}, // sum = 19{1, 0, 9, 0, 1, 0}}; // sum = 11If the findLargestIndex function was called…1. Implement a recursive function called firstTwo that returns the sum of the firsttwo digits in a positive number. If there is only one digit, that digit is returned.Note this function is returning an integer, not printing. There should be no use ofcout within your function.Title line: int firstTwo(int n)ex. firstTwo(8325) returns 11ex. cout << firstTwo(428); // prints 62. Implement a function called findMinGap that will return the smallest gap betweenadjacent entries of an integer array. A gap between two numbers is the absolutevalue of their difference. For example, if an array contains the elements {10, 14,-5, -3, 0, 5, 7}, the minimum gap is 2 (between -5 and -3).Title line: int findMinGap(int array[], int length)3. Implement a function called findLargestIndex which returns the index of the rowwith the largest sum.ex. int array[3][6] = {{3, 6, 8, 2, 4, 1}, // sum = 24{2, 4, 5, 1, 3, 4}, // sum = 19{1, 0, 9, 0, 1, 0}}; // sum = 11If the findLargestIndex function was called…(Recursive Greatest Common Divisor) The greatest common divisor of integers x and y isthe largest integer that evenly divides both x and y. Write a recursive function gcd that returns thegreatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equalto 0, then gcd(x, y) is x; otherwise gcd(x, y) is gcd(y, x % y), where % is the remainder operator.
- 1. Write a recursive function that takes as a parameter a nonnegative integer and 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 in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern. 2. A palindrome is a string that reads the same both forward and backward. For example, the string "madam" is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameter.Write a recursive function called `productMatch` which takes an array of numbers and a target product and returns a boolean indicating whether any pair of distinct numbers matches the product when multiplied together. Your function should accept a default argument called whichholds the return value. Each recursive step should reduce the size of thenumbers array after checking to see if pairs of numbers multiply to match thetarget product.Write a recursive function that takes as a parameter a nonnegative integer and 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 in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern.
- Question: First write a function mulByDigit :: Int -> BigInt -> BigInt which takes an integer digit and a big integer, and returns the big integer list which is the result of multiplying the big integer with the digit. You should get the following behavior: ghci> mulByDigit 9 [9,9,9,9] [8,9,9,9,1] Your implementation should not be recursive. Now, using mulByDigit, fill in the implementation of bigMul :: BigInt -> BigInt -> BigInt Again, you have to fill in implementations for f , base , args only. Once you are done, you should get the following behavior at the prompt: ghci> bigMul [9,9,9,9] [9,9,9,9] [9,9,9,8,0,0,0,1] ghci> bigMul [9,9,9,9,9] [9,9,9,9,9] [9,9,9,9,8,0,0,0,0,1] ghci> bigMul [4,3,7,2] [1,6,3,2,9] [7,1,3,9,0,3,8,8] ghci> bigMul [9,9,9,9] [0] [] Your implementation should not be recursive. Code: import Prelude hiding (replicate, sum)import Data.List (foldl') foldLeft :: (a -> b -> a) -> a -> [b] -> afoldLeft =…Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.For function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}