Differentiator

Problem

Calculate the absolute difference between two input values. If the difference is greater than 5, print true, otherwise print false.

13. Differentiator, Comet 64

Solution 1

If a and b are given numbers, we want to calculate the number

c := abs(a - b)

where abs(x) is the absolute value function. Print true if c > 5; print false otherwise.

int = input;           // Read the first input.
int = input - int;     // Difference between two input values.
check int < 0;         // Is the difference negative?
jump if false: print;  // If non-negative, go to "print".
int = int * -1;        // Otherwise, convert to positive.
print:                 // The "print" branch.
    check int > 5;     // Is difference > 5?
    output = bool;     // Print the boolean result.

Solution 2

If a and b are given numbers, we have the difference

d := a - b

The difference is greater than 5 provided that either of the following conditions is true:

• d > 5; or
• d < -5

This solution is optimal, according to the game.

int = input - input;  // Difference between 2 input values.
check int > 5;        // Is difference > 5?
jump if true: print;  // If so, go to "print".
check int < -5;       // Is difference < -5?
print:                // The "print" branch.
    output = bool;    // Print the boolean result.

Solution 3

If a and b are given numbers, we want to calculate the difference

d := a - b

We have three cases:

1. If the difference is d := 5 or d := -5, then the square is d^2 := 25.
2. If 0 <= d < 5 or -5 < d <= 0, then 0 <= d^2 < 25.
3. If d > 5 or d < -5, then d^2 > 25.

We only need to test whether d^2 > 25. If true, then the difference is more than 5 units. Otherwise, the difference is at most 5 units. This solution is optimal, according to the game.

int = input - input;  // d := a - b
int = int * int;      // d^2
check int > 25;       // Is d^2 > 25?
output = bool;        // Print the boolean result.