CS100M Spring 2001           Solutions to Prelim T3                    April 17

===============================================================================
Q1. [30 pts]  graded out of 34 pts: "extra" pts above 30 become bonus pts
===============================================================================

Output: bye

Q1                                                  
=================================================== 
||            main                   isEven      ||
||   +---+    +---------/---------+  +-----/---+ || 
|| n | 3 |    |      +-/-+        |  |   +/--+ | ||
||   +---+    | args |/*-+------+ |  | n / 4 | | || 
||            |      /---+      | |  |  /+---+ | || 
||   +---+    |     /           | |  +-/-------+ || 
|| g | *-+-+  |   +/--+         | |              ||
||   +---+ |  | w / *-+--+      | |              || 
||         |  |  /+---+  |      | |              || 
|| isEven  |  +-/--------+------+-+              || 
|| main    |             |      |                ||
===========+=============+======+================== 
           |             |      |                   
Object     |             |      |      String       
===========+=============+======+====  ===============
||         |             |      |  ||  ||           ||
||         |             V      |  ||  ||           ||
||         |     +-----/--+     |  ||  ||           ||
||         |+----+-* n/ll | 0   |  ||  ||           ||
||         ||    +---/-/--+     |  ||  ||           ||
||         ||+---+-* n/ll | 1   |  ||  ||           ||
||         |||   +---/----+     V  ||  ||           ||
||         VVV              2   ?  ||  ||           ||
||        +---+                    ||  ||           ||
||        | *-+--------------------++--++-->"bye"   ||
||      0 | *-+----------/---------++--++-->"Hi"    ||
||        +---+                    ||  ||           ||
||        | *-+----------/---------++--++-->"lo"    ||
||      1 | *-+--------------------++--++-->"adieu" ||
||        +---+                    ||  ||           ||
||      2                          ||  ||           ||
=====================================  ===============

===============================================================================
Q2. [30 pts]  Bonus: 4 pts to correctly preserve case; 1 pt for concise code
===============================================================================
+ each blank is worth about 2 points;
  2nd $char[]$ is worth 1 about pt, 2nd $.toCharArray()$ is worth about 1 pt
+ first box is worth about 4 pts
+ second box is worth about 10 points

public class Q2 {
  // new string with each letter replaced by the one 13 letters later
  public static String rot13( String s ) {
      // convert $s$ to array $c$ of characters and array $U$ of characters;
      // convert all letters in $U$ to upper case
          char[] c = s.toCharArray();
          char[] U = s.toUpperCase().toCharArray();
      // loop over each character, converting letters;  
      // inv: already processed positions $[0..i-1]$
      int i = 0 ;
      while ( i != U.length ) {
          if ( 'A' <= U[i] && U[i] <= 'Z' ) { // character is a letter?
              // convert letter to an integer $0..25$
                  int letter = U[i] - 'A';
              // compute new letter and store back into array   |<--BONUS-->|
                  c[i] = (char) (((letter + 13) % 26) + 'A'   +  c[i] - U[i] );
          }
          i += 1;
      }
      return new String(c);
  }

  // an example of a call to $rot13$
  public static void main(String[] args) {
      System.out.println( "CS100M --> " + rot13("CS100M") );
} } // end of main method, class Q2


===============================================================================
Q3. [2 free pts + 18 blanks * 1 pt / blank = 20 pts]
===============================================================================

int stop = 100 ; // stopping value
TokenReader in = new TokenReader(System.in);
System.out.println( "Please enter integer sequence terminated by " + stop );
int num = in.readInt(); // current input value
// these variables are based on the input read so far, excluding $num$
    int mode     = num;    // last mode
    int freq     = 0;      // frequency of $mode$
    String mode2 = "none"; // 2nd-to-last mode as a string
    int prev     = num;    // previous input value
    int prevFreq = 0;      // frequency of $prev$
// read $stop$-terminated input sequence while maintaining definitions above
while ( num != stop ) {
    // update previous input value and its frequency
        if ( num == prev ) { prevFreq = 1 + prevFreq; }
        else               { prevFreq = 1; }
        prev = num;
    // update last mode and its frequency and 2nd to last mode
        if ( prevFreq >= freq ) { // new last mode?
            if ( prevFreq > freq ) { // new frequency?
                mode2 = "none";
            } else {
                mode2 = "" + mode;
            }
            mode = prev;
            freq = prevFreq;
        }
    num = in.readInt(); // read next input
}
System.out.println( mode2 ) ; // display 2nd-to-last mode

===============================================================================
Q4. [5+5=10 pts]
===============================================================================

(a) circle defeats; cross out others    (b) SSD winners as letters: A, E, F
   1   2   3    4   5   6    7   8   9       2                5    topmost sets
1  -  -4- [9]   -   -   -   [5]  -   -     /^ \             /^ \      {1, 2, 3}
2 [7]  -  -7-   -   -   -    -   -   -    9    7           7    7     {4, 5, 6}
3 -8- [9]  -    -   -   -    -   -   -   /      V         /      V   
4  -   -   -    -  [7] -2-  [5]  -   -  3 <--9-- 1       4 <--9-- 6 123 winner
5  -   -   -   -5-  -  [7]   -   -   -            \     /             drop 7s:
6  -   -   -   [9] -6-  -    -   -   -             5   5                2/1 (7)
7 -1-  -   -   -2-  -   -    -  [5] -4-             V V               1 wins
8  -   -   -    -   -   -   -3-  -  [7]              7              456 winners
9  -   -   -    -   -   -   [7] -5-  -             /^ \               drop 7s:
                                                  7    5                4/5 (7)
                                                 /      V               5/6 (7)
                                                9 <--7-- 8            5 & 6 win