2/1/2000
Thomas Yan
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suppose int variables a, b, c have been assigned values.
here are various attempts to print the maximum value,
with some questions for you to think about.

we recommend that you hand-trace and then actually run each
program segment on the following examples:

        a       b       c
        2       3       9
        3       9       9
        9       9       9       

we also recommend that you consider how hard it would be to
extend each valid approach to dealing with 5 variables (a, b, c, d, e).


"exponential tree" approach -- do you see how this approach
grows cumbersome very quickly as the number of variables
increases?

if (a >= b)
    if (a >= c)
        System.out.println("the max is " + a);
    else
        System.out.println("the max is " + c);
else
    if (b >= c)
        System.out.println("the max is " + b);
    else
        System.out.println("the max is " + c);


"exponential tree" with auxiliary variable -- do you see how the
print style is centralized and hence easy to modify?

int max;
if (a >= b)
    if (a >= c)
        max = a;
    else
        max = c;
else
    if (b >= c)
        max = b;
    else
        max = c;
System.out.println("the max is " + max);


"quadratic" attempt -- do you see why this "needs" $>=$ and $else$?

if (a > b && a > c)
    System.out.println("the max is " + a);
if (b > a && b > c)
    System.out.println("the max is " + b);
if (c > a && c > b)
    System.out.println("the max is " + c);


"quadratic" approach -- why does $b>=c$ instead of $b>=a && b>=c$ suffice?

if (a >= b && a >= c)
    System.out.println("the max is " + a);
else if (b >= c)
    System.out.println("the max is " + b);
else
    System.out.println("the max is " + c);


"linear, loop-like" approach -- do you agree this is the easiest
approach to extend to 5 variables?

int max; // max so far
max = a;
if (b > max)
    max = b;
if (c > max)
    max = c;
System.out.println("the max is " + max);


"linear" attempt -- why doesn't this work?

int max;
max = a;
if (b > max)
    max = b;
else if (c > max)
    max = c;
System.out.println("the max is " + max);