Math 211 Assignments

Assignments

Assignment 1:

Initialize a string, print it, then print a newline, then print the string backwards, then print another newline. Use "for" loops.
Due Thursday, January 22, 1998 at midnight.
The assignment is to consist of one file named assignment1.c and it should be left in your math211hw directory.

Assignment 2:

Expand on your program from Assignment1.

Set aside space for a 200 character string.
Read standard input until you encounter the EOF or a newline character or you get to 200 characters, saving the characters as you receive them in your string. Hence your string should either be exactly 200 characters long or else should end with the last character you received before you got the newline or the EOF.
Print the string you just received backwards.
Finally, print out one newline character.
Due Tuesday, January 27, 1998 at midnight.
The assignment is to consist of one file named assignment2.c and it should be left in your math211hw directory.

Assignment 3:

Write a function to add matrices.

The declaration should be
- void AddMatrices(short, short, short *, short *, short *);
where the first short is the number of rows and the second is the number of columns; the first short pointer points to the start of the first matrix of the sum, the second pointer points to the second matrix and the third pointer points to the answer.
The file should be called AddMatrices.c
In the code examples for Friday, Feb. 6 is a program TestAddMatrices.c which you can use to test your program. Copy it to your math211hw directory and compile with
- cc TestAddMatrices.c AddMatrices.c
Due Thursday, February 12, 1998 at midnight.
To check if your file can be picked up by the grading program, logon to one of the SUN's, type aok and then hit return or enter.

Assignment 4:

Write a function SwitchRows(matrix*,short, short) which takes a matrix and two row numbers and switches the two rows. Write a similar function SwitchCols(matrix*,short, short) which switches two columns.

Assignment 5:

Copy NumToString.c and NumToString.h from the Web-page to your math211hw directory.

Write a file StringToNum.c This file is to contain one function with declaration
short StringToNum(char*string, long *value, char base);
This function should take a 0-terminated string and convert it into a long, assuming that the string is the base "base" representative for the number. If errors are incountered, the function should return -1. otherwise, return 1. The only reason the routine should fail is if the string contains a character which is not a + or a - or a digit as the first character or a digit as latter characters, where digit varies depending on the base. A character of '0'-'9' is a valid character as long as it is less than the value of the base; if the base is 16 (HEX) additional valid characters are 'A'-'F'. If a bad character is encountered, display an error message stating
Bad character. ASCI= xx, char= x\n
where the first xx is the ASCI value of the character on which your routine choked and the x is the character. Please be careful to display the warning precisely as indicated.
2. Write a file Main.c which does the following: It starts
```
#include 
#include "NumToString.h"

short StringToNum(char*string, long *value, char base);

....
```
The file should contain only one function main. main expects two arguments: the first is a -xxxxxx and the second is a string. The -xxxxxx argument does the following. Each x is a digit 0-9. The first x denote the base of the string in the second argument, 2-9 or else 0=base 10 or 1=base 16 (HEX). Subsequent x's are bases for answers. First check that you have two inputs and if you do not, or if the first one does not start with a '-', put up the following error message and exit.
Useage: -xxxx yyyyy\n
Next, your routine should collect the two inputs, figure out the first base, and convert the second string to a long. If this succeeds, run through the subsequent x's, convert each to a base and then convert the entered number to that base and print it out on a separate line. Make sure your program finishes with the prompt on the line immediately below your last output.
A working version of this program can be had by just typing hw. For example hw -10 AA should take the HEX number AA and return the decimal number 170. You can also explore directly how errors are to be handled.
Due Friday, March 16, 1998 at midnight.

Assignment 6:

Go to your math211hw directory and type A6 and then hit enter. You should get a new directory called A6 in your space. If you already have a directory called A6 here, please rename it. Once you have this A6 directory, please do not move it. Inside A6 will be five files. You will need to add code to the files main.c and Qsort.c to get a working program. To compile your program use
cc main.c Qsort.c LibMatrix.c
To test your program, use a.out < t_file

The file t_file is a file of matrices so ReadMatrix can be used to read the file. Read the file into memory and sort the matrices according to the rule below. Then print out a list of numbers separated by spaces. At the end of the list, print a newline so the prompt appears immediately below your list of numbers. The first number is the number in the file of the "smallest" matrix, the next number is the number of the next smallest, etc. The first matrix in the file is number 1.

Given two matrices, matrix1 is less than matrix2 provided

The total number of entries in matrix1 is less than the total number of entries in matrix2 (total number of entries is number of rows times number of columns).
If both matrices have the same number of entries, then matrix1 has fewer rows than matrix2.
If both matrices have the same number of rows and columns, then the first entry of the first row of matrix1 is less than the corresponding entry of matrix2.
If both matrices have the same number of rows and columns and the same first entries, then the second entry of the first row of matrix1 is less than the corresponding entry of matrix2.
Continue working your way across the first row until you get to the end. Then compare the first entries in the second row and work your way across row 2. Continue across each row until you find entries which are not equal. If you never find such entries, then the two matrices are equal. In this case, leave them as you found them.

This assignment is due at midnight on Thursday, April 9.

Assignment 7:

Change the word count program to handle upper and lower case together. Get each word and check if it is already on the list. If it is, increment the upper case count if the word is upper case. If the word is lower case, increment the lower case count. Use the file "tree.c" from last Wednesday. This file can be copied from the web site. You will need to modify the structure and the routines that add a node and print the tree. You will also need to fix the string-copy function to store the word as lower case and you will need to write a new function to replace strcmp. As for printing, print your data as follows. Each line should begin with a word in lower case. Follow the word by a space and then an integer giving the number of times the word appeared in lower case, another space and finally the number of times the word appeared in upper case. Print _ if one of the cases is 0 rather than printing 0.
Name the file "tree.c".
This assignment is due at midnight on Tuesday, April 21.

Assignment 8:

Your last assignment is to write a function which balances trees. You are to write a function
struct tnode *balance(struct tnode*);
which takes a pointer to the root of a tree and returns a pointer to a possibly new root for the same tree with the pointers changed so that the tree is balanced. Call the file
balance.c
and leave it in your math211hw directory. Declare the structure "struct tnode" in a header file,
balance.h
and leave it in your math211hw directory as well. You may setup any node structure you like but you must have pointers left and right to the two branches. As a practical matter, you probably want to use the structure we've been using lately in class so you can test your function with a minimum of additional work, but suit yourself.

To explain "balanced" requires two notions. The first point is that a binary tree orders the data: everything down the left node comes before the current node; then comes the current node; and finally comes everything down the right node. The function treeprint is an example: it prints the nodes in this order.

There is also the notion of the height of a tree and the level of a node. Level is defined inductively: the root has level 0 and if a node has level n then both the right and left nodes have level n+1 (unless they are NULL). The height of a tree is the maximum level of any node. Notice by definition, if there are x nodes of level n, then there are at most 2x nodes of level n+1.

Two trees are equivalent if they induce the same order on the nodes. A "balanced" tree is a tree with the minimal height for the total number of nodes. It will have 1 node of level 0, 2 nodes of level 1, etc. down to 2^{n-1} nodes of level n-1 and finally it will have however many nodes of level n it needs to get the total right.

It is a theorem that any tree is equivalent to a balanced tree and the point of the exercise is to write a function that finds a balanced tree for a given tree.

Your function should work as follows. It should begin with a pointer to the root of the given tree and should return a pointer to the root of your balanced tree. It should also CHANGE the left&right pointers in the given tree so that the end result is balanced. Your function should make no assumptions about what kind of data is being organized, merely assume that if p points to a node, p->left and p->right point to the left and right nodes below p.

This assignment constitutes the take-home part of the final. It is due at the start of the final, Friday May 8 at 8am. I will do a pick-up on Monday, May 4 at 8am and if you have successfully completed the assignment I will let you know.
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