Just Around
Problem
Round each integer to the nearest tens.
Solution 1
To round a floating point number to the nearest tens, we divide the number by 10 and treat the problem as if we are rounding the number to the nearest integer. Then multiply the result by 10 to obtain the desired number. The algorithm for rounding to the nearest integer is
round(x) := floor(x + 0.5)
where the floor(x) function of x is the same as the integer part of a
floating point number x. This solution is optimal, according to the game.
reg = input / 10; // Divide the input by 10.
int = reg + 0.5; // floor(x + 0.5)
int = int * 10; // Multiply by 10 to undo division.
output = int; // Print the result.
Solution 2
This solution exploits how floating point numbers are represented and handled in the Comet 64 computer. The computer allows for up to two decimal digits following the decimal point. If a floating point number cannot fit in the representation used by the computer, then the third decimal digit is rounded. The rounding rule is rounding half up. For example, the number 1.123 is rounded to 1.12 and 1.125 is rounded to 1.13. To round an input number to the nearest tens, we divide the input by 1000 so the computer would round the result to two decimal places. Then multiply the rounded number by 1000 to obtain the integer rounded to the nearest tens. This solution is optimal, according to the game.
reg = input / 1000; // Round to 2 decimal places.
int = reg * 1000; // Integer rounded to nearest tens.
output = int; // Print rounded number.