EW7 Assignment: (FCN) Functions

Transcription

1 EW7 Assignment: (FCN) Functions The purpose of this assignment is to introduce the concepts and syntax of writing functions in MATLAB. Note: Use the template provided (FCN Template.m) in the assignment download to complete this assignment. For this assignment the autograder does not rely on the format of this file, but it will help you to organize and test your functions. This completed assignment, named FCN Firstname Lastname.m, should be uploaded to Canvas along with the.mat file that is generated by the autograder. You may run the autograder as many times as you like to check your work as you complete the assignment; the.mat file will be regenerated each time, and your score will only be recorded based on the.mat file that you upload. You will also publish your m-files and upload a PDF version of the result to Canvas. Remember to upload the following to the Canvas website: FCN Firstname Lastname.m FCN Firstname Lastname.pdf FCN Score.mat All function files that you are asked to create Directions to upload files can be found at how-do-i-upload-a-file-to-my-assignment-submission Function Basics 1. Write a function called MyTimeConversion with the following function declaration line. 1 function [Hours, Minutes, Message] = MyTimeConversion (TotalMinutes) The input argument TotalMinutes should be a nonnegative scalar integer representing the total number of minutes in a specified time interval. The output arguments Hours and Minutes should be nonnegative scalars such that Hours*60 + Minutes = TotalMinutes and the value of Minutes must be less than 60. The output argument Message must be a char array. A few examples below illustrate what it s properties should be. Notice that time units should be singular (i.e. minute, hour) if the value is 1, and plural (i.e. minutes, hours) if the value is not equal to 1 (including 0). Also, if TotalMinutes equals 1, the verb should be is instead of are. For TotalMinutes = 151, Message should equal the char array 1 of 7

2 151 minutes are equal to 2 hours and 31 minutes. For TotalMinutes = 84, Message should equal the char array 84 minutes are equal to 1 hour and 24 minutes. For TotalMinutes = 60, Message should equal the char array 60 minutes are equal to 1 hour and 0 minutes. For TotalMinutes = 181, Message should equal the char array 181 minutes are equal to 3 hours and 1 minute. For TotalMinutes = 1, Message should equal the char array 1 minute is 0 hours and 1 minute. 2. To protect information security, secret messages are usually encrypted using an encryption key, turning them into a sequence of apparently meaningless characters called the ciphertext. The goal of encryption is that adversaries who intercept the ciphertext are not be able to determine anything about the original message. An authorized party, however, is able to decrypt the ciphertext if they know the key. Write a function Convert with function declaration line 1 function strout = Convert(strIn,key,mode) to encrypt or decrypt a message using some simple rules below. The input arguments are: strin: 1-by-N char array. It may be the original message, or it may be the ciphertext (see mode below) key: 1-by-K char array. It, along with a rule given below, defines exactly how strin is to be encrypted/decrypted; mode: char array that determines whether Convert is encrypting or decrypting. This input variable has two possible values, encrypt or decrypt. The output argument is: strout: 1-by-N char array. It is the encryption or decryption of strin The encryption/decryption method is described as follows: (a) Horizontally concatenate key with itself, creating a long string keyl, so that numel(keyl)>=numel(strin) is true. Then, remove (as needed) the last few characters in keyl so that numel(keyl)==numel(strin) is true. You can carry this process out exactly as described, or do this is a different manner, as long as the final value of keyl is correct. For example, if strin equals E7 is a course introducing Matlab. 2 of 7

3 and Key equals MonWed then keyl should equal MonWedMonWedMonWedMonWedMonWedMonW so that strin and keyl both have 34 characters. (b) Create double arrays that respectively contain the ASCII codes of the characters in instr and keyl. If mode is equal to encrypt, add these two double arrays, and then for each element in the array, add mod(i,10) to the i th element. In other words, add 1 to the first element, add 2 to the second element,... 9 to the ninth element, 0 to the tenth element, 1 to the eleventh element, and so on. If mode is equal to decrypt, perform the inverse procedure. (c) Finally, convert the resulting double array of ASCII codes into characters to produce the output argument strout. Note: If the user calls Convert with only two input arguments, then Convert should execute the decryption operation. If the user calls Convert with zero or one input arguments, then an appropriate error message should be executed. Test your function with the following code: 1 message = UC Berkeley is everything I hoped for. ; 2 secretkey = abc ; 3 ctext = Convert(message,secretKey, encrypt ); 4 Convert(ctext, secretkey, decrypt ) 3. In previous assignment (LOOPS) you wrote several code-sections that each performed some tasks on a row-vector containing only ones and zeros. In this problem, you will use those code-sections to make corresponding functions that also have some added functionality. Your functions will be tested on several arbitrary sequences of ones and zeros, of varying length, so be sure your code (which you may take from your submission although that is not required) is sufficiently general. In FCN Template, a place is provided for you to define your own vector of ones and zeros to test with. For example, you might use 1 V = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]; If a function requires the use of nargin, you should use it at the beginning of your function to set the default parameters before they are used. (a) Write a function called flipnth, that will flip every Nth entry of the input vector (make the entry 0 if it is 1 and make it 1 if it is 0) and return the modified vector. The function declaration line should be 1 function outvec = flipnth(invec,n) 3 of 7

4 The first input invec is a numeric vector of ones and zeros, like V above. The second input is a scalar integer greater than or equal to 1. The output outvec should be a numeric vector of ones and zeros of the same size as invec. If the function flipnth is called with only one input argument, then treat the value of N as equal to 1. This is called the default value. Hence the default behavior is to flip every element of the input vector. (b) Write a function called flipnthval with function declaration line 1 function outvec = flipnthval(invec,n,value) that will flip every Nth instance of a specified value (0 or 1) in an input vector and return the modified vector. The input invec is a numeric vector of ones and zeros. The input N performs the same role as in the previous function flipnth. The input value is which value (0 or 1) to flip. For example, if the function is called with N = 4 and value = 1, the function should flip every 4th occurrence of the value 1. If, on the other hand, the function is called with N = 2 and val = 0, the function should flip every 2nd occurrence of the value 0. The output outvec should be a numeric vector of ones and zeros of the same size as invec. If flipnthval is called with one argument, the default values of N and value are both 1. IfflipNthVal is called with two arguments (invec and N), set value to 1. (c) Write a function called findwithoverlap with function declaration line 1 function [numappear, idx] = findwithoverlap(invec,pattern) The input invec is a numeric vector of ones and zeros. The input pattern should be a row vector containing only ones and zeros and whose number of elements is less than or equal to that of invec. Your function should count how many instances of pattern occur in invec and return this number to numappear. Additionally, idx should be a 1-by-numAppear array that contains the starting index for each instance of the pattern. Overlap is allowed. 4. (a) Write a function padrv which takes a row vector v, an integer n and inserts zeros at the beginning of v to create a new vector which has length n. The new vector is returned as the output. If n is smaller than numel(v), then padrv should return the original vector v. The function declaration line should be 1 function vpad = padrv(v,n) The function padrv can be written rather simply, with only one line of code after the function declaration line. (Hint: remember the stacking properties of empty arrays). Test your implementation as shown below: 1 v = [ ]; 2 result9a1 = padrv(v,2); 3 result9a2 = padrv(v,9); 4 of 7

5 The result should be that result9a1 equals [ ], and result9a2 equals [ ]. (b) Write a function unpad, which takes a row vector w, removes all zeros at the beginning of the vector and returns the remaining elements of the vector, i.e it drops the zeros at the beginning of the vector. The function declaration line should be 1 function b = unpad(v) The function unpad can be written rather simply, with only one line of code after the function declaration line. (Hint: the function find may be useful). Test your implementation in your main script file as shown below: 1 w = [ ]; 2 result9b = unpad(w); Your result should be that result9b equals the array [ ]. (c) Write a function polyadd which takes row vectors p1 and p2, interpreted as coefficients of two polynomials and returns the row vector that contains the coefficients of the sum of the two polynomials. The function declaration line of polyadd is 1 function psum = polyadd(p1,p2) You will need to use the functions padrv and unpad, which you created in parts (a) and (b). However, we require you to implement these as subfunctions (named LOCALpadrv and LOCALunpad) in the function file polyadd.m. Input arguments p1 and p2 are row vectors that respectively contain the coefficients (in decreasing degree) of the two polynomials that are to be added. For example, if the two polynomials that you want to add are P 1 (x) = x and P 2 (x) = x 2 + 2x + 1, the row vectors of their coefficients are respectively p1 = [1 0 3] and p2 = [-1 2 1]. The output argument psum is a row vector that contains the coefficients of the resulting polynomial addition. The result of adding the two polynomials is 2x+4, which is represented by the row vector of its coefficients psum = [2 4]. The output psum must be in the unpadded format. For instance, polyadd([-2,3,1],[2,2,2]) should output [5 3], not [0 5 3]. As an example, test your function with the following code. 1 p1 = [1 0 3]; 2 p2 = [-1 2 1]; 5 of 7

6 3 result9c1 = polyadd(p1,p2); 4 5 p3 = [ ]; 6 p4 = [-1 2 1]; 7 result9c2 = polyadd(p3,p4); 8 Hint: It may be helpful to use the max and numel functions. 5. Medieval MATLAB: The basic premises of the game is to have two players take turns attacking each other. Each player has four options to pick from during their turns: attack with a sword, attack with a bow and arrow, use their shield, or rest. After each selection, the opposing player s health along with the attacking player s endurance are affected as described by the chart below. Players with no endurance cannot use items that require endurance. The player that loses all of their health first loses. In this problem, we ll write the first function towards completing a full game implementation. In later assignments, we ll continue the development. Write a function called oneround, with function declaration line 1 function [dh1, de1, dh2, de2] = oneround(u1,u2,a,b,c,d,a,b,d) The function has nine input arguments. The first two, u1 and u2, represent the action (Sword, Bow&Arrow, Shield, Rest) of player 1 and player 2, respectively. For simplicity, use integer values to represent the action, namely 1 represents Sword, 2 represents Bow&Arrow, 3 represents Shield, and 4 represents Rest The last 7 input arguments model the effects of the various combinations of battles. By changing the values of these input arguments, the caller can change the outcome of battles between the two players. The function has 4 output arguments, which are the resultant change in the health (dh) and endurance (de) of each player. The function oneround should implement the table shown below. Player 2 Sword Bow&Arrow Shield Rest Player 1 Sword dh1=-a dh2=-a dh1=-b dh2=-a dh1=0 dh2=0 dh1=0 dh2=d-a de1=-a de2=-a de1=-a de2=-b de1=-a de2=-c de1=-a de2=d Player 1 Bow&Arrow dh1=-a dh2=-b dh1=-b dh2=-b dh1=0 dh2=0 dh1=0 dh2=d-b de1=-b de2=-a de1=-b de2=-b de1=-b de2=-c de1=-b de2=d Player 1 Shield dh1=0 dh2=0 dh1=0 dh2=0 dh1=0 dh2=0 dh1=0 dh2=d de1=-c de2=-a de1=-c de2=-b de1=-c de2=-c de1=-c de2=d Player 1 Rest dh1=d-a dh2=0 dh1=d-b dh2=0 dh1=d dh2=0 dh1=d dh2=d de1=d de2=-a de1=d de2=-b de1=d de2=-c de1=d de2=d 6 of 7

7 However, in order to introduce a small amount of nonrepeatability, each computed nonzero value (change in health and endurance) is to be randomly perturbed by ±15% in each call to oneround. Recall that RAND creates a random number between 0 and 1. Hence *(2*(rand-0.5)) creates a random number between 0.85 and For the combinations that return 0 in the table above, perturb those by a random number between -0.1 and 0.1. Test oneround with parameter values that satisfy A > B > D > 0, d > a > b > c > 0 7 of 7