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- The nth harmonic number is defined non-recursively as: H(n)=1+1/2+1/3+1/4+...+1/n Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named “harmonic” that accepts an int parameter n and recursively calculates and returns the nth harmonic number. Write a test program that displays the harmonic numbers, H(n)=1,2,3,4...10Write a recursive method called doubleDigits that accepts an integer n as a parameter and returns the integer obtained by replacing every digit of n with two of that digit. For example, doubleDigits(348) should return 334488. The call doubleDigits(0) should return 0. Calling doubleDigits on a negative number should return the negation of calling doubleDigits on the corresponding positive number; for example, doubleDigits(–789) should return –778899.solve it without using Arrays and the method should take int and return a String Write a recursive method in java that returns a string that contains the octal representation of a positive integer. Test your method. Hint: An octal number is the base-8 number system, and uses the digits 0 to 7. For example, the number 12 can be converted to octal number as follows: Divide by 8, the remainder represents the first digit so 12/8 = 1 and the remainder is 4 so the first digit is 4. The quotient is 1. Then we divide 1 over 8 we get zero and the remainder is 1. The second digit is 1 and we stop. The equivalent octal number for 12 is 14.
- Write a recursive method that gets three parameters as input: an array of integers called nums, an integer called index, and an integer called value. The purpose of this method is to count how many times value appears in the array starting at nums[index]. Do not use loops. (Java code)Write a recursive method that gets two parameters as input: an array of integers called nums and an integer called index. The purpose of this method is to return the following: nums[index] * nums[index+ 1] * nums[index+ 2] * .. nums[nums.length-1]. Do not use loops. (java code)Write a static recursive method that returns the number of digits in theinteger passed to it as an argument of type int. Allow for both positiveand negative arguments. For example, –120 has three digits. Do not countleading zeros. Embed the method in a program, and test it.
- Do not use static variables to implement recursive methods. USING JAVA: // P6 public static int countSubstrings(String s1, String s2) { } Write a recursive method countSubstrings that counts the number of non-overlapping occurrences of a string s2 in a string s1. Use the method indexOf() from String class. As an example, with s1=”abab” and s2=”ab”, countSubstrings returns 2. With s1=”aaabbaa” and s2=”aa”, countSubstrings returns 2. With s1=”aabbaa” and s2=”AA”, countSubStrings returns 0. Show the output on the following strings: s1 = “Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities. Java applications are typically compiled to bytecode (class file) that can run on any Java Virtual Machine (JVM) regardless of computer architecture.…The nth harmonic number is defined non-recursively as H(n) = 1+1/2+1/3+1/4+⋯+1/n Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named “harmonic” that accepts an int parameter n and recursively calculates and returns the nth harmonic number. Write a test program that displays the harmonic numbers, H(n), for n = 1,2,3,⋯,10.Given a list of integers, you want to know whether it is possible to divide the integers into two sets, so that the sums of the two sets are the same. Every integer must be in one set or the other. Write a recursive helper method that takes any number of arguments you like, and make the initial call to your recursive helper method from equalSum(). Do not use any loops or regular expressions. Test case 1: equalSum([2, 3, 5]) true Test case 2: equalSum([2, 2, 5]) false
- java Write a recursive method largestDigitthat accepts an integer parameter and returns the largest digit value that appears in that integer. Your method should work for both positive and negative numbers. If a number contains only a single digit, that digit's value is by definition the largest. The following table shows several example calls: Call Value Returned largestDigit(14263203) 6 largestDigit(845) 8 largestDigit(52649) 9 largestDigit(3) 3 largestDigit(0) 0 largestDigit(-573026) 7 largestDigit(-2) 2 Obey the following restrictions in your solution: You may not use a String, Scanner, array, or any data structure (list, stack, map, etc.). Your method must be recursive and not use any loops (for, while, etc.). Your solution should run in no worse than O(N) time, where N is the number of digits in the number.Write a recursive solution to the problem below. You MUST use only one method, and that method must have the provided method header. You are allowed to use loops, but you must also use recursion. Given a word of length n, print every possible word of length n that can be made with those characters. Note: The order of the output does not matter, only that all possibilities are listed. Example: Input: rot Output: rot, rto, otr, ort, tro, tor Input: frog Output: frog, frgo, fogr, forg, fgro, fgor, rogf, rofg, rgfo, rgof, rfog, rfgo, ogfr, ogrf, ofrg, ofgr, orgf, orfg, gfro, gfor, grof, grfo, gofr, gorf public void printAllPossibilities (String prefix, String suffix){ }Given a list of integers, you want to know whether it is possible to divide the integers into two sets, so that the sum of one set is odd, and the sum of the other set is a multiple of 10. Every integer must be in one set or the other. You can write a recursive helper method that takes any number of arguments and then call it inside the method, but you cannot use any loops. Test cases: oddAndTen([5, 5, 3]) true oddAndTen ([5, 5, 4]) oddAndTen ([5, 5, 4, 1]) false true