Below are a series of problems you need to solve using recursive functions. You will write a program that will read commands from an input file, with each command referring to one of the recursive problems to be executed. Each command will be followed (on the same line of input) by the respective parameters required for that problem. Implementation Each recursive function MUST have a wrapper function enclosing it where you will do input/output file processing as well as calling the actual recursive function. From Wikipedia, A wrapper function is a function in a computer program whose main purpose is to call a second function. As an example, here is one of the wrapper functions you will use: void KnightsFlip(FILE *fin, FILE *fout); This would be the wrapper function for one of the recursive problems, called KnightsFlip (described, in detail, below). These wrapper functions will simply do three things: 1. deal with the processing of the input file 2. most importantly, the wrapper function will make the initial call to your recursive function that will actually solve the problem. 3. Finally, the wrapper functions will print to the output file. Note: printing to the output file may also occur in the actual recursive functions. Of course, at your own discretion (meaning, your own choice), you can make auxiliary functions for your recursive functions to use, such as functions to swap values in an array, take the sum of an array of values, printing functions, etc. Five Problems to Solve Using Recursion: (1) KnightsMultiply Write a recursive function that multiplies all values from k up to n and returns the result (as a double). For example: if k = 5, and n = 10, then multiply 5 * 6 * 7 * 8 * 9 * 10 to return 151200. (2) KnightsFlip You have an index card with the letter K written on one side, and F on the other. You want to see ALL of the possible ways the card will land if you drop it n times. Write a recursive function that prints each session of dropping the cards with K's and F's. For example of you drop it 4 times in a given session, all possible ways to drop it are as follows: KKKK KKKF KKFK KKFF KFKK KFKF KFFK KFFF FKKK FKKF FKFK FKFF FFKK FFKF FFFK FFFF *Note: The possible ways would have to print in this specific order. (3) KnightsShape Simply write a recursive function that prints a large X composed of smaller X's with a given width, n, which is guaranteed to be odd. Example for an X of width n = 7: X X X X X X X X X X X X X *Note: to be clear, the width is the length (number) of Xs along one line of the large X. (4) KnightsScotch No, this has nothing to do with drinking Scotch! Suppose you are playing a special game of hopscotch on a line of integer numbers drawn on the ground like so: 4 4 1 5 2 6 3 4 2 0 (Although playing this game, while drinking Scotch, would certainly be entertaining!) The number, with a square around it, indicates where you are currently standing. You can move left or right down the line by jumping the number of spaces indicated by the number you are standing on. So if you are standing on a 4, you can jump either left 4 spaces or right 4 spaces. You cannot jump past either end of the line. For example, the first number (4) only allows you to jump right, since there are no numbers to the left that you can jump to. The goal: you want to get to the 0 at the far end (right side) of the line. You are also guaranteed that there will be only one zero, which, again, will be at the far right side. (5) KnightsDepot You are working on an engineering project with other students and are in need of 2x4s (2 by 4s) of various lengths. Thankfully, UCF has its very own Depot store: KnightsDepotso you dont have to drive far. Unfortunately, KnightsDepot only carries 2x4s in fixed lengths. So your team will have to purchase the 2x4s and then cut them as needed. Because of your tight college student budget, you want to buy the least number of 2x4s in order to cover the lengths requested by your team. The recursive function you are designing will return the minimum number of 2x4s you need to purchase, in order to cover the lengths requested by your team. Example: Array of 2x4 lengths requested by your team: { 6, 4, 3, 4, 1, 3 } Fixed length of 2x4s at KnightsDepot: 6 (so each purchased 2x4 has a length of 6) A possible arrangement of of 2x4s: { 6 } { 3, 3 } { 4, 1 } { 4 } Minimum number of 2x4s needed to purchase: 4 Wrapper Functions As mentioned, you MUST use the following five wrapper functions EXACTLY as shown: void KnightsMultiply(FILE *fin, FILE *fout); void KnightsFlip(FILE *fin, FILE *fout); void KnightsShape(FILE *fin, FILE *fout); void KnightsScotch(FILE *fin, FILE *fout); void KnightsDepot(FILE *fin, FILE *fout); Input File Specifications You will read in input from a file, "KnightsRecurse.in". Have this AUTOMATED. Do not ask the user to enter KnightsRecurse.in. You should read in this automatically (this will expedite the grading process). The file will contain an arbitrary number of lines and on each line there will be a command. Each command will be followed by relevant data as described below (and this relevant data will be on the same line as the command). We will not tell you the number of commands in the file. So how do you know when youve read all the commands in the input file? You can use the function feof(FILE * file) to determine if you have reached the end of the file. The commands (for the five recursive functions), and their relevant data, are described below: KnightsMultiply - This command will be followed by the following information: k and then n, as described above. KnightsFlip - This command will be followed by a single integer, n, as described above. KnightsShape - This command will be followed by a single integer, n, as described above. KnightsScotch - This command will be followed by an integer, start, representing the initial position on the line you are playing on (0 means the far left, the first position); size, the number of integers drawn on the ground; size will be followed by size number of integers, the integers drawn on the ground. (see input file for examples) KnightsDepot - This command will be followed by an integer maxlen, which represents the maximum 2x4 length the store sells; size, the number of 2x4s your team needs; size will be followed by size number of integers, the length of each 2x4 your team needs. It is guaranteed that the requested lengths will all be less than or equal to the maxlen sold by the store. Output Format Your program must output to a file, called "KnightsRecurse.out". You must follow the program specifications exactly.

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