Write a recursive method that returns the value of N! (N factorial) using the definition given in this chapter. Explain why you would not normally use recursion to solve this problem.

Using the recursion three method find the upper and lower bounds for the following recur- rence (if they are the same, find the tight bound). T(n) = T(n/2) + 2T(n/3) + n.

java language

Tracing the Recursion. Observe the recursive solution provided below and answer the followingquestions:1. Which line(s) of this program define(s) the base case of the binary() method?2. Which line(s) of this program include recursive call(s)?3. Trace the recursion below. You must show the tracing step by step (write themdown); otherwise – little to no credit!4. At what step of your recursion tracing did you hit the base case?5. What is the final output of this code?

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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){ }

Write a recursive method that gets three parameters as input: an array of integers called nums, an integer called index,and an integer called The purpose of this method is to return true if value is stored in the array starting at nums[index]. That is, you have to check if value is equal to nums[index] or nums[index +1] or nums[index +2 ] .... nums[nums.length -1]. Do not use loops.(java code)

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Write and test a Java/Python recursive method for finding the minimum element in an array, A, of n elements. What the running time? Hint: an array of size 1 would be the stop condition. The implementation is similar to linearSum method in lecture 5 examples. You can use the Math.min method for finding the minimum of two numbers.

Implement the logarithmBase22 method which, given a long integer number, returns the result of Logz2(number), rounded down to the nearest floor integer. Design and implement this as a recursive method. Read the test cases in the JUnit tester file for more detailed specification.

write a code in java (using recursion)

Write a recursive method called add(int n). This method adds the integers from 0 to some value n. For example, the call to add(4) would return 10 (4+3+2+1=10).