1. Write a function called year2016 that returns a row-vector of struct-s whose elements correspond to the days of a month in 2016 as specified by the input argument. If the input is not an integer between 1 and 12, the function returns the empty array. Each struct should contain three fields with these (exact) field names: "month", "date", and "day" (all lower case).
• The month field must contain a string with the name of the month (first letter capitalized).
• The date field must contain a scalar specifying the day of the month.
• The day field must contain the three-letter abbreviation of the day chosen from this list: 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun'.
For example, here is a call of the function followed by a command that shows the seventh element of the struct array that is returned by the function:
2. A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Write a function that is called this way:
>> n = palin_product (dig, lim);
The function returns the largest palindrome smaller than lim that is the product of two dig digit numbers. If no such number exists, the function returns 0. (Inspired by Project Euler.)
3. Each number on telephone keypads, except 0 and 1, corresponds to a set of uppercase letters as shown in this list:
2 ABC, 3 DEF, 4 GHI, 5 JKL, 6 MNO, 7 PQRS, 8 TUV, 9 WXYZ
Hence, a phone-number specification can include uppercase letters and digits. Write a function called dial that takes as its input argument a string of length 16 or less that includes only these characters and returns as its output argument the telephone number as a uint64. Here is the input and output for one example of a call of the function:
Input: '1FUNDOG4YOU'
Output: 13863644968
You can assume that a phone number never starts with 0. If the input contains any illegal characters, the function returns 0. You are not allowed to use the built-in function strrep.
4. An n-by-n square logical matrix can be represented by a cell vector of n elements where the kth element corresponds to the kth row of the matrix. Each element of the cell vector is a row vector of positive integers in increasing order representing the column indexes of the logical true values in the given row of the matrix. All other elements in the given row of the logical matrix are false. Write a function called logiunpack that takes such a cell vector as its only input and returns the corresponding square logical matrix. For example, such a cell vector representation of a 100-by-100 logical matrix with the only true elements at indexes (10, 20) and (10, 75) would have only one non-empty element of the cell vector at index 10. That element is the vector [20 75].
5. Solve the inverse of the previous problem. That is, write a function called logipack that takes a square logical matrix as its only input argument and returns its cell vector representation as specified in the previous assignment. Note that empty array elements of the cell vector corresponding to rows with all false values must have a size of 0x0.
6. Write a function called digit_counter that takes the name of a text file as input and returns the number of digits (i.e., any of the characters, 0-to-9) that the file contains. If there is a problem opening the file, the function returns -1. WARNING: if you use the ‘w' flag with fopen, as opposed to ‘r', you will overwrite the file. The grader uses your own m files to check your function, so be careful!
7. Write a function called day_counter that returns the number of Mondays that fell on the first day of the month in a given year between 1776 and 2016 inclusive where the requested year is the only input to your function and it is a positive integer scalar. Note that a leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400. In a leap year, February has 29 days. You are not allowed to use the datenum built-in function. (Inspired by Project Euler.)
8. Write function called huge_add that adds together two positive integers of any length specified as strings using decimal notation. The single output argument is the result and it is a string as well. The inputs and output must contain digits only; no commas, spaces or any other characters are allowed. If any of these assumptions are violated by the input, the function returns the number -1.
9. 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. Write a function called smallest_multiple that returns a uint64, the smallest positive number that is evenly divisible by all of the numbers from 1 to n where n is a positive integer scalar and is the only input argument of the function. If the result would be greater than what can be represented as a uint64, the function returns 0. (Inspired by Project Euler.)