Big Brother

Problem

Read three numbers in a row and determine the maximum.

17. Big brother, Comet 64

Solution 1

Let x, y, z be three numbers read in a row. We have these cases:

1. x < y and y < z, so max = z
2. x < y and z <= y, so max = y
3. y <= x and x < z, so max = z
4. y <= x and z <= x, so max = x

int = input;             // Read in x.
reg = input;             // Read in y.
check int < reg;         // Is x < y?
jump if false: ylessx;   // If not, go to "ylessx".
int = input;             // Read in z.
check reg < int;         // Is y < z?
jump if true: zmax;      // If so, go to "zmax".
output = reg;            // Otherwise, y is maximum.
jump to: end;            // Go to "end".
ylessx:                  // y <= x
    reg = int;           // Set x := y.
    int = input;         // Read in z.
    check reg < int;     // Is x < z?
    jump if true: zmax;  // If so, go to "zmax".
    output = reg;        // Otherwise, print x.
    jump to: end;        // Go to "end".
zmax:                    // Maximum is z.
    output = int;        // Print z.
end:                     // End of program.

Solution 2

Let x, y, z be three numbers read in a row. Let the registers int and reg hold the values of x and y, respectively. Note the symmetry between x < y and y <= x. In the cases from Solution 1, consider the symmetry between cases (1) and (2), and cases (3) and (4). If x < y, use int to store the value of z. If y <= x, we set reg := int and use int to store the value of z. In both cases, reg := max(x, y). This solution is optimal, according to the game.

int = input;              // Read in x.
reg = input;              // Read in y.
check int < reg;          // Is x < y?
jump if true: less;       // If so, go to "less".
reg = int;                // Otherwise, set reg := int.
less:                     // The "less" branch.
    int = input;          // Read in z.
    check int < reg;      // Is z < max(x, y)?
    jump if true: print;  // If so, go to "print".
    reg = int;            // The max of all 3 numbers.
print:                    // The "print" branch.
    output = reg;         // Print the maximum.