FrogJump

A small frog wants to get to the other side of the road. The frog is currently located at position X and wants to get to a position greater than or equal to Y. The small frog always jumps a fixed distance, D.

Count the minimal number of jumps that the small frog must perform to reach its target.

Write a function:

function solution($X, $Y, $D);

that, given three integers X, Y and D, returns the minimal number of jumps from position X to a position equal to or greater than Y.

For example, given:

  X = 10
  Y = 85
  D = 30
the function should return 3, because the frog will be positioned as follows:

after the first jump, at position 10 + 30 = 40
after the second jump, at position 10 + 30 + 30 = 70
after the third jump, at position 10 + 30 + 30 + 30 = 100
Write an efficient algorithm for the following assumptions:

X, Y and D are integers within the range [1..1,000,000,000];
X ≤ Y.

**************************************** SOLUTION ************************************************   

 if ((!is_integer($X) || ($X < 1 || $X > 1000000000)) ||
        (!is_integer($Y) || ($Y < 1 || $Y > 1000000000)) ||
        (!is_integer($D) || ($D < 1 || $D > 1000000000)) ||
        $X > $Y
    ) {
        return 0;
    }

    $distance      = $Y - $X;
    $jumpsRequired = $distance / $D;

    if (intdiv($distance, $D) !== 0) {
        $jumpsRequired++;
    }

    return (int)$jumpsRequired;