Description

Introduction to Programming with MATLAB
• Unless otherwise indicated, your function should not print anything to the Command Window, but your function will not be counted incorrect if it does.
• Note that you are not required to use the suggested names of input variables and output variables, but you must use the specified function names.
• Finally, read the instructions on the web page on how to test your functions with the auto-grader program provided, and what to submit to Coursera to get credit.
• Note that starred problems, marked by ***, are harder than usual, so do not get discouraged if you have difficulty solving them.

1. Write a function called sparse_array_out that takes two input arguments and returns one output argument. Its first argument is a two-dimensional array of doubles, which it writes into a binary file. The name of that file is the second argument to the function. The file must have the following format. It starts with three uint32 scalars specifying the number of rows of the array followed by the number of columns followed by the number of non-zero elements in the array. Then each non-zero element of the array is represented by two uint32 scalars and a double scalar in the file in this order: its row index (uint32), its column index (uint32), and its value (double). Note that this file format is an efficient way to store a so-called “sparse array”, which is by definition an array for which the overwhelming majority of its elements equal 0. The function’s output argument is of type logical and equals false if there was a problem opening the file and true otherwise.
2. Write a function called sparse_array_in that reads a two-dimensional array of doubles from a binary file whose name is provided by the single input argument of the function. The format of the file is specified in the previous problem. The function returns the two-dimensional array that it reads from the file as an output argument. Note that if you call sparse_array_out with an array called A and then call sparse_array_in using the same filename and save the output of the function in variable B, then A and B must be identical. If there is a problem opening the file, the function returns an empty array.

function [row,col,numrows,numcols,summa] = maxsubsum(A)
where row and col specify the indexes of the top left corner of the submatrix with the maximum sum, numrows and numcols are its dimensions, and summa is the sum of its elements.
7. *** Write a function called queen_check that takes an 8-by-8 logical array called board as input. The variable board represents a chessboard where a true element means that there is a queen at the given position (unlike in chess, there can be up to 64 queens!), and false means that there is no piece at the given position. The function returns true if no two queens threaten each other and false otherwise. One queen threatens the other if they are on the same row, on the same column, or on the same diagonal.
8. *** Write a function called bell that returns the first n rows of the Bell triangle, where n is an input argument. For a precise definition, see http://en.wikipedia.org/wiki/Bell_triangle. The function must return an n-by-n array where the top left triangle contains the Bell triangle with each row of the Bell triangle positioned diagonally—bottom-left-to-upper-right—and the bottom right triangle contains only zeros. If n is not a positive integer, the function returns an empty array. As an illustration, the call bell(7) should return this array:
1 2 5 15 52 203 877
1 3 10 37 151 674 0
2 7 27 114 523 0 0
5 20 87 409 0 0 0
15 67 322 0 0 0 0
52 255 0 0 0 0 0
203 0 0 0 0 0 0
9. *** Write a function called roman2 that takes a string input representing an integer between 1 and 399 inclusive using Roman numerals and returns the Arabic equivalent as a uint16. If the input is illegal, or its value is larger than 399, roman2 returns 0 instead. The rules for Roman numerals can be found here: http://en.wikipedia.org/wiki/Roman_numerals. Use the definition at the beginning of the page under the “Reading Roman Numerals” heading. In order to have unambiguous one-to-one mapping from Roman to Arabic numbers, consider only the shortest possible roman representation as legal. Therefore, only three consecutive symbols can be the same (IIII or VIIII are illegal, but IV and IX are fine). Also, a subtractive notation cannot be followed by an additive one using the same symbols making strange combinations, such as IXI for 10 or IXX for 19, illegal also.

10. *** We start this problem with a tutorial on North America’s most popular bowling game. In it contestants attempt to knock down as many as possible of ten pins that are standing at one end of an alley by rolling balls at them from the other end. A bowling game consists of ten “frames” for each player, and each player’s frame except for the tenth consists of either one or two attempts to knock down the pins. After each player’s frame is complete, all ten pins are set up again. The pins knocked down by one player have no effect on the other player. They could in fact compete on separate alleys.
Frames are of different types. A frame in which all ten pins are knocked down by the first ball is a “strike”, and after a strike the second ball of the frame is omitted. A frame in which all ten pins are knocked down with two balls (the first ball having left some standing) is a “spare”. A frame with fewer than ten pins down is an “open”. A spare in the tenth frame earns the bowler one “bonus” ball for that frame, which is simply an extra ball; a strike in the tenth earns two bonus balls, and if the first of these two extra balls knocks everything down, all ten pins are set up again for the second ball.
Frame 1 2 3 4 5 6 7 8 9 10
Pins 9 1 0 10 10 10 6 2 7 3 8 2 10 9 0 9 1 10
Type spare spare str ike str ike open spare spare str ike open spare +
bonus
Score 10 30 5 6 7 4 82 100 120 1 39 148 168
As another example, a “perfect” game, which is 12 strikes in a row, has the maximum possible score— 300.
Write a function called bowl that takes a vector of integers specifying the sequence of pins down after each ball and returns the final score. For example, for the frames in our example above, the input would be [9 1 0 10 10 10 6 2 7 3 8 2 10 9 0 9 1 10] and the output would be
168. If the input is not a valid sequence for a full game, the function returns -1.

Note that some of these problems were adapted from Dr. John Dalbey’s computer science class at Cal Poly.