CSC195, Class 34: More on Exam 2 and readLine

Overview:
* readLine
  + Testing, continued
  + An incorrect solution
  + Developing a correct solution
* Efficient exponentiation
* strncpy

Notes:
* Happy April Fool's day!
* Rearranging schedule so that there's not a gap in this 
  discussion.
* Read Gries 10 for tomorrow.

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What kinds of tests should we put in the file we're reading:
* Ones in which the string we're reading is
  less than max characters
    empty line
    other things in between
    max-1
  equal to max characters
  more than max characters
  at least twice as many

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int 
readLine(FILE *file, char string[], int max) {
  char c;
  int i;
  for(i = 0; ((c=getc(file))!=EOF) && (c != '\n') && (i < max-1); i++)
    string[i] = c;
  string[i++] = '\0';
  if (i >= max) 
    return 0;
  else if (c == EOF)
    return 1;
  else if (c == '\n')
    return 1;
  else
    return 0;
} /* readLine(FILE *, char[], int) */


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Iterative efficient exponentiation

   x^2k = (x^k)^2
   x^(k+1) = x * x^k
   x^0 = 1

double 
expt1(double base, int power) {
  int tmp;
  if (power == 0) 
    return 1;
  else if (power % 2 == 0) {
    tmp = expt1(base, power/2);
    return tmp*tmp;
  }
  else
    return base * expt1(base, power-1);
}

O(log_2(n))

How do we make this iterative (using loops)?

Two key ideas:
   x^2k = (x^2)^k
   x^(k+1) = x * x^k
   We can accumulate those extra base*'s in another variable

double
expt2(double base, int power)
{
  double extra = 1;
  /* original_base^original_power = extra*base^power */
  while (power > 1) {
    if (power % 2 == 0) {
      base = base*base;
      power = power/2;
    }
    /* original_base^original_power = extra*base^power */
    else {
      extra = base * extra;
      power = power-1;
    }
    /* original_base^original_power = extra*base^power */
  } 
  /* original_base^original_power = extra*base^power */
  return extra*base;
} /* expt2(double, int) */

How would we write a test program for this?

(1) Print some values you know
2^3
2^10
2^100 (NOT)
Use a variety of exponents and compare to the result from
the function in math.h