The following statements are True or False. Write the correct answer as True or False on your sheet. You must write the full word: if you write T or F, you will not receive any credit. No explanation required. All log are log,. i. The asymptotic runtime of Mergesort does not change if, instead of generating 2 subproblems each of size n/2, we generate and solve recursively 3 subproblems each of size n/3. ii. nº1 = 2((log n)1º)
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- Which is the base case of the following recursion function: def mult3(n): if n == 1: return 3 else: return mult3(n-1) + 3 else n == 1 mult3(n) return mult3(n-1) + 3Which of the following statement(s) is/are correct about recursion? Group of answer choices A.indication of good use of recursion: difficulty to trace down the sequence of recursive calls B.gives cleaner code but has high cost C.never be used as substitute for a simple ‘for’ loop D.bad idea to use it to evaluate simple mathematical functions. E.All of the aboveGiven a positive integer 'n', find and return the minimum number of steps that 'n' has to take to get reduced to 1. You can perform any one of the following 3 steps:1.) Subtract 1 from it. (n = n - 1) ,2.) If its divisible by 2, divide by 2.( if n % 2 == 0, then n = n / 2 ) ,3.) If its divisible by 3, divide by 3. (if n % 3 == 0, then n = n / 3 ). Write brute-force recursive solution for this.Input format :The first and the only line of input contains an integer value, 'n'.Output format :Print the minimum number of steps.Constraints :1 <= n <= 200 Time Limit: 1 secSample Input 1 :4Sample Output 1 :2 Explanation of Sample Output 1 :For n = 4Step 1 : n = 4 / 2 = 2Step 2 : n = 2 / 2 = 1 Sample Input 2 :7Sample Output 2 :3Explanation of Sample Output 2 :For n = 7Step 1 : n = 7 - 1 = 6Step 2 : n = 6 / 3 = 2 Step 3 : n = 2 / 2 = 1 SolutionDp///.
- case #5 int i , p =1; for(i=1;i<=n;i++) p = p*i case #6 int rec(int r) { if(r==0) return 1; else return r*(rec(r-1); } Compare the two methods (#5 and #6 above) and answer the following: What is the “stopping” case for each (what causes the methods to “end”)? How do you guarantee that the methods will “stop” (infinite loop, infinite recursion)? Which method one is “better”? Why?The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…Given is the code to print numbers from 1 to n in increasing order recursively. But it contains few bugs that you need to rectify such that all the test cases pass.Input Format :Integer nOutput Format :Numbers from 1 to n (separated by space)Constraints :1 <= n <= 10000Sample Input 1 : 6Sample Output 1 :1 2 3 4 5 6Sample Input 2 : 4Sample Output 2 :1 2 3 4.
- Remove the left recursion from the productions: S ->A a |b A ->A c |S d | €The sorted values array contains the sixteen integers 1, 2, 3, 13, 13, 20, 24, 25, 30, 32, 40, 45, 50, 52, 57, 60. How many recursive calls are made by our binarySearch method given an initial invocation of binarySearch(45, 0, 15)? A. 3. B. 1. C. 4 D. 2. E. 0 A recursive definition is a definition (choose the best answer): A. that is recursive. B. in which something is defined in smaller terms of itself. C. which uses a mathematical equation. D. where a base case is defined. E. that repeats itself. Recursion is implemented by the system: A. using run time storage allocation. B. using static storage allocation. C. using a single static "stack frame". D. using compile time storage allocation.Choose the correct one for the following recursive method when n is 3 int recursiveSum(int n) { if (n==0) return 0; return n+recursiveSum(n-1); } a. First and Last recursive call share the same copy of parameter n in memory. b. Every recursive call shares the same copy of parameter n in memory. c. There will be a separate copy of parameter n in memory for each recursive call. d. none of these e. Only First and Last recursive call have separate copies of parameter n in memory.
- Please solve the following recursion question in Java.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.The Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match!