1 Program descriptions

You will write six programs for this project. Except where explicitly noted, your programs may assume that their inputs are properly formatted. However, your programs should be robust. Your program should not assume that it has received the proper number of arguments, for example, but should check and report an error where appropriate. Except when specified, you may report errors in any manner you prefer.

Programs should always terminate with exit code 0 (that is, return EXIT_SUCCESS or 0 frommain).

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1.1 llist: Linked list

Write a program llist that maintains and manipulates a sorted linked list of integers according to instructions received from standard input. The linked list is maintained in order, meaning that each integer will be larger than the one preceeding it.

llist maintains a linked list containing zero or more integers, ordered from least to greatest.llist will need to allocate space for new nodes as they are created using malloc; any allocated space should be deallocated using free before llist terminates.

It supports two operations: insert n Adds an integer n to the list. If n is already present in the list, it does nothing. The

instruction format is an i followed by a space and an integer n. delete n Removes an integer n from the list. If n is not present in the list, it does nothing. The

instruction format is a d followed by a space and an integer n.

After each command, llist will print the length of the list followed by the contents of the list, in order from first (least) to last (greatest).

Your program will halt once it reaches the end of standard input.

Input format Each line of the input contains an instruction. Each line begins with a letter (either i or d), followed by a space, and then an integer. A line beginning with i indicates that the integer should be inserted into the list. A line beginning with d indicates that the integer should be deleted from the list.

Your program will not be tested with invalid input. You may choose to have llist terminate in response to invalid input.

Output format After performing each instruction, llist will print a single line of text containing the length of the list, a colon, and the elements of the list in order, all separated by spaces.

Usage Because llist reads from standard input, you may test it by entering inputs line by line from the terminal. You may use any invalid input, such as #, to terminate your session.

$ ./llist i5 1:5 d3

1:5 i3 2:35 i 500

3 : 3 5 500 d5 2 : 3 500 #

Alternatively, you may use the shell to provide a file to llist using input redirection, e.g.,

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$ ./llist < tests/test.01.txt 1 : 10 2 : 10 11 3 : 9 10 11 

2 : 9 10

1.2 mexp: Matrix exponentiation

Write a program mexp that multiplies a square matrix by itself a specified number of times. mexptakes a single argument, which is the path to a file containing a square (k k) matrix M and a non-negative exponent n. It computes Mn and prints the result.

Note that the size of the matrix is not known statically. You must use malloc to allocate space for the matrix once you obtain its size from the input file.

To compute Mn, it is sufficient to multiply M by itself n1 times. That is, M3 = M M M. Naturally, a different strategy is needed for M0.

Input format The first line of the input file contains an integer k. This indicates the size of the matrix M, which has k rows and k columns.

The next k lines in the input file contain k integers. These indicate the content of M. Each line corresponds to a row, beginning with the first (top) row.

The final line contains an integer n. This indicates the number of times M will be multiplied by itself. n is guaranteed to be non-negative, but it may be 0.

For example, an input file file.txt containing

3 123 456 789 2

indicates that mexp must compute

1 2 32456.

789

Output format The output of mexp is the computed matrix Mn. Each row of Mn is printed on a separate line, beginning with the first (top) row. The items within a row are separated by spaces.

Using file.txt from above,

$ ./mexp file1.txt 30 36 42 66 81 96 102 126 150 

1.3 stddev: Standard deviation

Write a program stddev which computes the mean and standard deviation of a sequence of numbers. The program will take no arguments, and will read the sequence of numbers from standard input.

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Background Let X be a set of numbers. The mean of X is defined asxX x

X= |X| , (1)

where |X| is the number of elements in X. That is, X is the sum of the elements in X divided by the number of elements.

The standard deviation of X is the square root of the mean squared difference between each element of X and X. That is,

xX(xX)2 s= |X| (2)

Note that the mean and standard deviation are not defined if X = . Your program must detect this condition, and avoid dividing by zero.

Input The input to stddev is a sequence of zero or more decimal numbers, separated by whitespace (e.g., newlines). The input is terminated when the input ends.

Your program will not be tested with invalud input. You may have stddev terminate after reading invalid input.

For example,

 82.5 1000.6699 10 11.11 

-45 #

Output Your program will output two lines after it has completed its computation, giving the mean and standard deviation of its input. To minimize discrepencies caused by rounding error, the output will be rounded to an integer using the %.0f formatting code.

The output will have this form,

 mean: 105 stddev: 13 

Your program must use lower-case letters, with a single space after the colon. In the case where the input contains no numbers, your program will instead write no data.

Usage Because stddev reads from standard input, you may provide input numbers by typing into the terminal after invoking it.

$ ./stddev 45 8 3.2 

16

4

# mean: 18 stddev: 16 $ ./stddev # no data 

Alternately, you may instruct the shell to send a file to stddev using input redirection, e.g.,

$ ./stddev < some_file.txt mean: 10 stddev: 8 

Notes To compute the square root, you may use the sqrt function provided by math.h. Usingmath.h requires linking against the math library, so your makefile must include -lm as an option forgcc.

Your program will not know in advance how large its input will be, and will not be able to read its input more than once. You will need some way of storing a sequence of numbers whose size is not known in advance.

1.4 bst: Binary search trees

Write a program bst that manipulates binary search trees. It will receive commands from standard input, and print resposes to those commands to standard output.

A binary search tree is a binary tree that stores integer values in its interior nodes. The value for a particular node is greater than every value stored its left sub-tree and less than every value stored in its right sub-tree. The tree will not contain any value more than once. bst will need to allocate space for new nodes as they are created using malloc; any allocated space should be deallocated using free before bst terminates.

This portion of the assignment has two parts. Part 1 In this part, you will implement bst with three commands:

insert n Adds a value to the tree, if not already present. The new node will always be added as the child of an existing node, or as the root. No existing node will change or move as as result of inserting an item. If n is already present in the tree, bst will print duplicate. Otherwise, it will print inserted. The instruction format is an i followed by a decimal integer n.

search n Searches the tree for a value n. If n is present, bst will print present. Otherwise, it will print absent. The instruction format is an s followed by a space and an integer n.

print Prints the current tree structure, using the format in section 1.4.1. Part 2 In this part, you will implement bst with an additional fourth command:

delete n Removes a value from the tree. See section 1.4.2 for further discussion of deleting nodes. If n is not present, print absent. Otherwise, print deleted. The instruction format is a dfollowed by a space and an integer n.

5

2

15

36

4

Figure 1: A binary search tree containing six nodes

Input format The input will be a series of lines, each beginning with a command character (i, s,p, or d), possibly followed by a decimal integer. When the input ends, the program should terminate. Your program will not be tested with invalid input. A line that cannot be interpreted may be

treated as the end of the input.

Output format The output will be a series of lines, each in response to an input command. Most commands will respond with a word, aside from p. The format for printing is described in section 1.4.1.

Usage

$ ./bst i1 inserted i2 inserted i1 duplicate s3 absent

p (1(2)) #

1.4.1 Printing nodes

An empty tree (that is, NULL) is printed as an empty string. A node is printed as a (, followed by the left sub-tree, the item for that node, the right subtree, and ), without spaces.

For example, the output corresponding to fig. 1 is ((1)2((3(4))5(6))).

6

2

15

36

2

15

(a) Deleted 4

46

(b) Deleted 3

2

14

36

(c) Deleted 5

Figure 2: The result of deleting different values from the tree in fig. 1

1.4.2 Deleting nodes

There are several strategies for deleting nodes in a binary tree. If a node has no children, it can simply be removed. That is, the pointer to it can be changed to a NULL pointer. Figure 2a shows the result of deleting 4 from the tree in fig. 1.

If a node has one child, it can be replaced by that child. Figure 2b shows the result of deleting 3 from the tree in fig. 1. Note that node 4 is now the child of node 5.

If a node has two children, its value will be changed to the maximum element in its left subtree. The node which previously contained that value will then be deleted. Figure 2c shows the result of deleting 5 from the tree in fig. 1. Note that the node that previously held 5 has been relabeled 4, and that the previous node 4 has been deleted.

Note that the value being deleted may be on the root node.

1.5 life: Conways Game of Life

Write a program life that plays a specified number of steps in the Game of Life, given an intial configuration. life takes two arguments: an integer N indicating how many steps it should perform, and the name of a file containing the initial configuration.

If N is not a positive integer, or if the file does not exist or cannot be opened, life should report an error and terminate.

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Background The Game of Life is a cellular automaton created by John Conway. It is an example of a zero-player game, where each step is completely determined by the current state of the board. Life is played on an infinite, two-dimensional grid of square cells. Each cell has eight neighbors,

which are the cells that share a side or a corner with it. At any time, each cell is either populated or unpopulated. If a cell is populated at time t but has fewer than two populated neighbors or more than three populated neighbors, it will be unpopulated at time t + 1. If a cell is unpopulated at time t but has exactly three populated neighbors, it will be populated at time t + 1.

The idea is that populations require a certain size in order to thrive, and can expand if they are large enough, but cannot become so dense that they overtax their local resources.

An infinite grid is impractical to simulate, so we will use a grid that wraps around, so that the top row and bottom row are neighbors, as are the left and right sides.1

Your program will read an initial board from a file and output the configuration that board would reach after N steps.

Input format The input file has two parts. The first line contains two integers, h and w, indicating the height and width of the board, respectively.

The following h lines describe the board. Each row is given by a line containing w characters, indicating the status of a cell. A populated cell is indicated by an asterisk (*) and an unpopulated cell by a period (.).

For example, an input file board.txt might contain

55 ..... ..*.. ..*.. ..*.. .....

Your program will not be tested with invalid input.

Output format The output of life is another board configuration, in the same format as the input.

Usage

$ ./life 1 board.txt ..... ..... .***. 

..... ..... $ ./life 2 board.txt ..... ..*.. ..*.. 

1That is, the grid has the topology of a torus.

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..*.. .....

1.6 queens: (N + 1)-queens

Write a program queens that implements part of the search process for solving the N-queens problem. queens has one required argument and two optional arguments. The required argument will always occur last: it is the name of a file containing a chessboard.

The two optional arguments may occur individually or together in any order. They are +2, which indicates that queens should report whether two queens may be placed on the board (Part 2), and

-w, which allows for the presence of warrior queens (Part 3). This portion of the assignment has three parts, two of which are required. The third part will be

counted as extra credit.

Background A chessboard is an 8 8 grid of squares, each of which may contain up to one chess piece.

The queen is the most powerful piece in chess, capable of moving any number of squares vertically, horizontally, or diagonally, provided that it does not change direction during the move.

The N-queens problem asks how many ways N queens can be arranged on a board such that no queen can take another. That is, no queen can be moved to a square occupied by another queen in a single move.

Part 1 Your program will be given a chessboard with some number of queens already placed. Your program must first determine whether any queen can take any other queen. If so, it will printInvalid. If not, it will determine, for each empty square, whether a queen placed there could be taken by any other queen. It will print a new chessboard with these available squares marked with q.

Part 2 When +2 is given, your program will further determine if there is any way to place twoadditional queens on the board such that no queen can take any other queen. If this is possible,queens will print Two or more. If only one queen may be placed, queens will print One. If no queens may be placed, queens will print Zero.

Part 3 (Extra credit) A warrior queen is a queen that fights on horseback, and thus may move like a queen or like a knight. The knight moves in an L-shape: two squares horizontally and one square vertically, or two squares vertically and one square horizontally. Thus, a warrior queen may reach up to eight squares that a regular queen in the same position could not.

When -w is given, queens will consider boards that may contain warrior queens and distinguish between squares where a warrior queen may be placed (marked w) and squares where only a regular queen may be placed (marked q). Additionally, queens will accept chessboards containing warrior queens.

Input format The input will contain a chessboard, specified as eight lines containing eight characters. A . indicates an empty space, and a Q indicates a queen.

A W indicates a warrior queen. Behavior is unspecified if the chessboard contains a warrior queen, but the -w option has not been given.

Your program will not be tested with incorrectly formatted chessboards. 9

Output format If any queens on the board may take another, queens will print Invalid and terminate. Otherwise, queens will print a chessboard similar to the input, but with additional symbols q and w to indicate squares where a queen or warrior queen may be placed. The mark wwill only be used if the -w option is given.

Next, if the +2 option is given, queens will print Zero, One, or Two or more, depending on how many additional queens may be safely placed on the board.

Usage Assume the file board.txt contains the following chessboard:

........ ........ ....Q... ......Q. ........ ..Q..... ........ ........ 

Then,

$ ./queens board.txt qq...q.. qq.....q ....Q... 

......Q. q....... ..Q..... .....q.q .q.q.q.q $ ./queens +2 -w board.txt ww...q.. 

ww.....q ....Q... ......Q. q....... ..Q..... .....w.w .q.q.w.w Two or more