C/the.ansi.c.programming.language/c.programming.notes/homework/PS3.html

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   9 <title>Assignment #3</title>
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  12 <H1>Assignment #3</H1>
  13
  14
  15
  16
  17
  18 <B>Introductory C Programming
  19 <br>
  20 <br>
  21 UW Experimental College
  22 </B><br>
  23 <br>
  24 <B>Assignment #3
  25 </B><p><B>Handouts:
  26 </B></p><p><a href="PS3.html">Assignment #3</a>
  27 <br><a href="PS2a.html">Answers to Assignment #2</a>
  28 <br><a href="http://www.eskimo.com/~scs/cclass/notes/sx4.html">Class Notes, Chapter 4</a>
  29 <br><a href="http://www.eskimo.com/~scs/cclass/notes/sx5.html">Class Notes, Chapter 5</a>
  30 <p><B>Reading Assignment:
  31 </B></p><p><a href="http://www.eskimo.com/~scs/cclass/notes/sx3c.html">Class Notes, Chapter 3, Secs. 3.3-3.5</a>
  32 <br><a href="http://www.eskimo.com/~scs/cclass/notes/sx4.html">Class Notes, Chapter 4, Secs. 4.1-4.1.1, 4.3</a>
  33 <br><a href="http://www.eskimo.com/~scs/cclass/notes/sx5.html">Class Notes, Chapter 5, Secs. 5.1-5.3</a>
  34 <br>(optional)
  35 Class Notes,
  36 Secs. <a href="http://www.eskimo.com/~scs/cclass/notes/sx3f.html">3.6</a>,
  37 <a href="http://www.eskimo.com/~scs/cclass/notes/sx4ba.html">4.1.2-4.2</a>,
  38 <a href="http://www.eskimo.com/~scs/cclass/notes/sx4d.html">4.4</a>,
  39 <a href="http://www.eskimo.com/~scs/cclass/notes/sx5d.html">5.4</a>
  40 <p><B>Review Questions:
  41 </B></p><OL><li>How many elements does the array
  42 <pre>
  43         int a[5];
  44 </pre>
  45 contain?
  46 Which is the first element?
  47 The last?
  48 <li>What's wrong with this scrap of code?
  49 <pre>
  50         int a[5];
  51         for(i = 1; i &lt;= 5; i = i + 1)
  52                 a[i] = 0;
  53 </pre>
  54 <li>How might you rewrite the dice-rolling program (from the notes,
  55 chapter 4, p. 2) without arrays?
  56 <li>What is the difference between a <dfn>defining instance</dfn>
  57 and an <dfn>external declaration</dfn>?
  58 <li>What are the four important parts of a function?
  59 Which three does a caller need to know?
  60 </OL><br>
  61 <br>
  62 <p><B>Tutorial Section
  63 </B><OL><li>Here is another nested-loop example,
  64 similar to exercise 4 of assignment 1,
  65
  66 and to tutorial 3 of assignment 2.
  67 This one prints an addition table for sums from 1+1 to 10+10.
  68 <pre>
  69 /* print an addition table for 1+1 up to 10+10 */
  70
  71 #include &lt;stdio.h&gt;
  72
  73 int main()
  74 {
  75         int i, j;
  76         /* print header line: */
  77         printf("  ");
  78         for(j = 1; j &lt;= 10; j = j + 1)
  79                 printf(" %3d", j);
  80         printf("\n");
  81         /* print table: */
  82         for(i = 1; i &lt;= 10; i = i + 1)
  83                 {
  84                 printf("%2d", i);
  85                 for(j = 1; j &lt;= 10; j = j + 1)
  86                         printf(" %3d", i + j);
  87                 printf("\n");
  88                 }
  89         return 0;
  90 }
  91 </pre>
  92 The first <TT>j</TT> loop prints the top, header row of the table.
  93 (The initial <TT>printf("  ");</TT>
  94 is to make it line up with the rows beneath,
  95 which will all begin with a value of <TT>i</TT>.)
  96 Then, the <TT>i</TT> loop prints the rest of the table,
  97 one row per value of <TT>i</TT>.
  98 For each value of <TT>i</TT>, we print that value
  99 (on the left edge of the table),
 100 and then print the sums
 101 resulting from adding that value of <TT>i</TT>
 102 to ten different values of <TT>j</TT>
 103 (using a second, inner loop on <TT>j</TT>).
 104 <br>
 105 <br>
 106 Make a simple modification to the program to print a multiplication table,
 107 or a subtraction table.
 108 <li>Here is yet another nested-loop example.
 109 It is very similar to the one above,
 110 except that rather than printing the sum <TT>i+j</TT>,
 111 it determines whether the sum is even or odd,
 112 using the expression
 113 <TT>(i+j) % 2
 114 </TT>.
 115 The <TT>%</TT> operator, remember, gives the remainder when dividing,
 116 and
 117 an
 118 even number gives a remainder of 0 when dividing by 2.
 119 Depending on whether the sum is even or odd,
 120 the program prints an asterisk or a space.
 121 Type in and run the program, and look at the pattern that results.
 122 <pre>
 123 #include &lt;stdio.h&gt;
 124
 125 int main()
 126 {
 127         int i, j;
 128         for(i = 1; i &lt;= 10; i = i + 1)
 129                 {
 130                 for(j = 1; j &lt;= 10; j = j + 1)
 131                         {
 132                         if((i + j) % 2 == 0)
 133                                 printf("* ");
 134                         else    printf("  ");
 135                         }
 136                 printf("\n");
 137                 }
 138         return 0;
 139 }
 140 </pre>
 141 (Why are there parentheses around
 142 <TT>i + j</TT>
 143 in the expression
 144 <TT>(i + j) % 2
 145 </TT>?
 146 What if they were left out?)
 147 <br>
 148 <br>
 149 Modify the program to print a pattern of <TT>.</TT> and <TT>#</TT> characters,
 150 or X's and O's.
 151 If you wish, experiment by taking the remainder
 152 when dividing by 3 or 4, instead.
 153 Since the remainder when dividing by 3 can be 0, 1, or 2,
 154 you could use a cascaded <TT>if</TT>/<TT>else</TT> statement
 155 to print one of three characters for each sum
 156 (or one of four if taking the remainder when dividing by 4).
 157 <li>Later in this assignment
 158 (exercise 3),
 159 you're asked to create a simple function to compute the squares of numbers.
 160 Sometimes,
 161 rather than writing a function
 162 which will compute a value each time it's called,
 163 it's useful to build an array
 164 containing all the values we might need.
 165 Here is a program which declares an array,
 166 then fills it with the squares of the numbers from 1 to 10:
 167 <pre>
 168 #include &lt;stdio.h&gt;
 169
 170 int main()
 171 {
 172         int i;
 173         int squares[11];        /* [0..10]; [0] ignored */
 174         /* fill array: */
 175         for(i = 1; i &lt;= 10; i = i + 1)
 176                 squares[i] = i * i;
 177         /* print table: */
 178         printf("n\tsquare\n");
 179         for(i = 1; i &lt;= 10; i = i + 1)
 180                 printf("%d\t%d\n", i, squares[i]);
 181         return 0;
 182 }
 183 </pre>
 184 There's one slight trick in the declaration of the <TT>squares</TT> array.
 185 Remember that arrays in C are based at 0.
 186 So if we wanted an array to hold the squares of 10 numbers,
 187 and if we declared it as
 188 <TT>int squares[10];
 189 </TT>the array's 10 elements would range from
 190 <TT>squares[0]</TT> to <TT>squares[9]</TT>.
 191 This program wants to use elements
 192 from <TT>squares[1]</TT> to <TT>squares[10]</TT>,
 193 so it simply declares the array as having size 11,
 194 and wastes the 0th element.
 195 <br>
 196 <br>
 197 The program also uses the tab character, <TT>\t</TT>,
 198 in its printouts,
 199 to make the columns line up.
 200 <br>
 201 <br>
 202 Modify the program so that it also declares and fills in
 203 a <TT>cubes</TT> array containing the cubes
 204 (third powers)
 205 of the numbers 1-10,
 206 and prints them out in a third column.
 207 <li>We're going to write a simple
 208 (<em>very</em> simple!)
 209 graphics program.
 210 We'll write a function <TT>printsquare</TT>
 211 which prints a square
 212 (made out of asterisks)
 213 of a certain size.
 214 Then we'll use our favorite for-<TT>i</TT>-equals-1-to-10 loop
 215 to call the function 10 times,
 216 printing squares of size 1 to 10.
 217 <pre>
 218 #include &lt;stdio.h&gt;
 219
 220 int printsquare(int);
 221
 222 int main()
 223 {
 224         int i;
 225         for(i = 1; i &lt;= 10; i = i + 1)
 226                 {
 227                 printsquare(i);
 228                 printf("\n");
 229                 }
 230         return 0;
 231 }
 232
 233 int printsquare(int n)
 234 {
 235         int i, j;
 236         for(i = 0; i &lt; n; i = i + 1)
 237                 {
 238                 for(j = 0; j &lt; n; j = j + 1)
 239                         printf("*");
 240                 printf("\n");
 241                 }
 242         return 0;
 243 }
 244 </pre>
 245 Type the program in and run it.
 246 Then
 247 see
 248 if you can modify
 249 it
 250 to print ``open'' squares,
 251 like this:
 252 <pre>
 253 ****
 254 *  *
 255 *  *
 256 ****
 257 </pre>
 258 instead of filled squares.
 259 You'll have to print the box in three parts:
 260 first the top row,
 261 then a number of ``<TT>*  *</TT>'' rows,
 262 and finally the bottom row.
 263 There's obviously no way to print ``open'' boxes of size 1 or 2,
 264 so don't worry about those cases.
 265 (That is,
 266 you can
 267 change the loop in the top-level <TT>main</TT> function to
 268 <TT>for(i = 3; i &lt;= 10; i = i + 1)
 269 </TT>.)
 270 </OL><br>
 271 <br>
 272 </p><p><B>Exercises
 273 </B>(pick three or four):
 274 </p><OL><li>Write code to sum the elements of an array of <TT>int</TT>.
 275 (Write it as a function, if you like.)
 276 Use it to sum the array
 277 <pre>
 278         int a[] = {1, 2, 3, 4, 5, 6};
 279 </pre>
 280 (The answer, of course, should be 21).
 281 <li>Write a loop to call the <TT>multbytwo()</TT> function (chapter
 282 5, section 5.1, p. 1) on the numbers 1-10.
 283 For extra credit,
 284 compile your <TT>main</TT> function and
 285 the <TT>multbytwo()</TT> function
 286 as two source files, one function per file.
 287 <li>Write a <TT>square()</TT> function and use it to print the squares
 288 of the numbers 1-10:
 289 <pre>
 290 1  1
 291 2  4
 292 3  9
 293 4  16
 294 ...
 295 9  81
 296 10 100
 297 </pre>
 298 <li>Write the function
 299 <pre>
 300         void printnchars(int ch, int n)
 301 </pre>
 302 which is supposed to print the character <TT>ch</TT>, <TT>n</TT> times.
 303 (Remember
 304 that <TT>%c</TT> is the <TT>printf</TT> format to use for printing characters.)
 305 For example, the call <TT>printnchars('x', 5)</TT> would print 5 <TT>x</TT>'s.  Use
 306 this function to rewrite the triangle-printing program of assignment
 307 1 (exercise 4).
 308 <li>Write a function to compute the factorial of a number, and use
 309 it to print the factorials of the numbers 1-7.
 310 (Extra credit:
 311 print the factorials of the numbers 1-10.)
 312 <li>(Kernighan and Ritchie)
 313 Write a function <TT>celsius()</TT> to convert
 314 degrees Fahrenheit to degrees Celsius.
 315 (The conversion formula
 316 is &#176;C = 5/9 <TT>*</TT> (&#176;F - 32).)
 317 Use it to print a Fahrenheit-to-Centigrade table
 318 for -40 to 220 degrees Fahrenheit, in increments of 10 degrees.
 319 (Remember that <TT>%f</TT> is the <TT>printf</TT> format to use for printing floating-point
 320 numbers.
 321 Also, remember
 322 that the integer expression <TT>5/9</TT> gives 0,
 323 so you <em>won't</em> want to use integer division.)
 324 <li>Modify the dice-rolling program
 325 (Sec. 4.1)
 326 so that it computes the average
 327 of all the rolls of the pair of dice.
 328 Remember that integer division
 329 truncates, so you'll have to declare some of your variables as
 330 <TT>float</TT> or <TT>double</TT>.
 331 <br>
 332 <br>
 333 For extra credit, also compute the standard deviation, which can
 334 be expressed as
 335 <blockquote>sqrt((sum(x*x) - sum(x)*sum(x)/n) / (n - 1))
 336 </blockquote>(where the notation sum(x) indicates summing all values of x,
 337 as usually expressed with the Greek letter sigma;
 338 there is <em>not</em> such a sum() function in C!)
 339 If you put the line
 340 <pre>
 341         #include &lt;math.h&gt;
 342 </pre>
 343 at the top of the file, you'll be able to call <TT>sqrt()</TT>.
 344 <br>
 345 <br>
 346 (See the note in Assignment #2, Exercise 5, about compiling with
 347 the math library under Unix.
 348 There are better ways of computing
 349 the standard deviation, but the above expression will suffice
 350 for our purposes.)
 351 <li>Write either the function
 352 <pre>
 353         randrange(int n)
 354 </pre>
 355 which returns random integers from 1 to <TT>n</TT>, or the function
 356 <pre>
 357         int randrange2(int m, int n)
 358 </pre>
 359 which returns random integers in the range <TT>m</TT> to <TT>n</TT>.  Use your function
 360 to streamline the dice-rolling program a bit.
 361 <br>
 362 <br>
 363 The header file <TT>&lt;stdlib.h&gt;</TT> defines a constant, <TT>RAND_MAX</TT>, which
 364 is the maximum number returned by the <TT>rand()</TT> function.
 365 A better
 366 way of reducing the range of the <TT>rand()</TT> function is like this:
 367 <pre>
 368         rand() / (RAND_MAX / N + 1)
 369 </pre>
 370 (where <TT>N</TT> is the range of numbers you want).
 371 <br>
 372 <br>
 373 Extra credit: investigate the behavior of <TT>randrange(2)</TT>, both using
 374 the ``obvious'' range-reduction technique (the modulus operator <TT>%</TT>,
 375 as shown in the notes) and this improved method.  If your library's
 376 implementation of <TT>rand()</TT> is a good one, you won't see a difference.
 377 But if you're not so lucky, you may see something very surprising.
 378 <li>Rewrite the dice-rolling program to also print a histogram.
 379 For example, if there are 21 rolls of 7, the output line ``<TT>7: 21</TT>''
 380 should also contain a horizontal row of 21 asterisks.
 381 (Use the <TT>printnchars</TT> function from exercise 4, if you wish.)
 382 The output might look like this:
 383 <pre>
 384 2: 2    **
 385 3: 5    *****
 386 4: 4    ****
 387 5: 10   **********
 388 6: 15   ***************
 389 7: 28   ****************************
 390 8: 12   ************
 391 9: 9    *********
 392 10: 7   *******
 393 11: 5   *****
 394 12: 3   ***
 395 </pre>
 396 </OL><hr>
 397 <hr>
 398 <p>
 399 This page by <a href="http://www.eskimo.com/~scs/">Steve Summit</a>
 400 // <a href="copyright.html">Copyright</a> 1995-9
 401 // <a href="mailto:scs@eskimo.com">mail feedback</a>
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