/**
* Recursively print the steps required to move all rings to the destination maintaining the invariant that no larger
* ring can ever be on top of a smaller ring. The thing to remember here is that the first step is to get all rings
* except the largest one to the last peg first, using the middle peg. The second step is to transfer the largest ring
* from the first peg to the middle peg. The final step is to transfer all of the rings, except the largest, to the
* middle peg, using the first peg. The recursion may seem daunting but focusing on those three steps makes this
* problem pretty straightforward. You don't have to understand how everything is being handled recursively. If you
* understand and handle the outer conditions properly, the rest will take care of itself.
* This works by first recursively moving all rings from peg 0 to peg 2 using peg 1 as an intermediary. Then it
* recursively moves all rings from peg 2 to peg 1 using peg 0 as an intermediary. It will be easier to see what is
* happening in the example.
*
* i.e.
* If the starting number of rings is 3, from peg is 0, to peg is 1 and use peg is 2.
*
* $numberOfRings = 3
* $pegs = [
* [
* 0 => 3,
* 1 => 2,
* 2 => 1
* ],
* [],
* [],
* ]
* $fromPeg = 0
* $toPeg = 1
* $usePeg = 2
*
* Is the $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 2
* $fromPeg = 0
* $toPeg = 2
* $usePeg = 1
*
* Is the $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 1
* $fromPeg = 0
* $toPeg = 1
* $usePeg = 2
*
* Is the $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 0
* $toPeg = 2
* $usePeg = 1
*
* Is the $numberOfRings > 0? No
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 0 to peg 1
* $pegs = [
* [
* 0 => 3,
* 1 => 2
* ],
* [
* 0 => 1
* ],
* []
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 2
* $toPeg = 1
* $usePeg = 0
*
* Is $numberOfRings > 0? No
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 0 to peg 2
* $pegs = [
* [
* 0 => 3
* ],
* [
* 0 => 1
* ],
* [
* 0 => 2
* ]
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 1
* $fromPeg = 1
* $toPeg = 2
* $usePeg = 0
*
* Is $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 1
* $toPeg = 0
* $usePeg = 2
*
* Is $numberOfRings > 0? No
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 1 to peg 2
* $pegs = [
* [
* 0 => 3
* ],
* [],
* [
* 0 => 2,
* 1 => 1
* ]
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 0
* $toPeg = 2
* $usePeg = 1
*
* Is $numberOfRings > 0? No
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 0 to peg 1
* $pegs = [
* [],
* [
* 0 => 3
* ],
* [
* 0 => 2,
* 1 => 1
* ]
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 2
* $fromPeg = 2
* $toPeg = 1
* $usePeg = 0
*
* Is $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 1
* $fromPeg = 2
* $toPeg = 0
* $usePeg = 1
*
* Is $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 2
* $toPeg = 1
* $usePeg = 0
*
* Is $numberOfRings > 0? No
* <<< FIRST RECURSIVE CALL RETURN
*
* Move ring from peg 2 to peg 0
* $pegs = [
* [
* 0 => 1
* ],
* [
* 0 => 3
* ],
* [
* 0 => 2
* ]
* ]
*
* <<< SECOND RECURSIVE CALL END >>>
* $numberOfRings = 0
* $fromPeg = 1
* $toPeg = 0
* $usePeg = 2
*
* Is $numberOfRings > 0? No
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 2 to peg 1
* $pegs = [
* [
* 0 => 1
* ],
* [
* 0 => 3,
* 1 => 2
* ],
* []
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 1
* $fromPeg = 0
* $toPeg = 1
* $usePeg = 2
*
* Is $numberOfRings > 0? Yes
* <<< FIRST RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 0
* $toPeg = 2
* $usePeg = 1
*
* Is $numberOfRings > 0? No
* <<< FIRST RECURSIVE CALL RETURN >>>
*
* Move ring from peg 0 to peg 1
* $pegs = [
* [],
* [
* 0 => 3,
* 1 => 2,
* 2 => 1
* ],
* []
* ]
*
* <<< SECOND RECURSIVE CALL BEGIN >>>
* $numberOfRings = 0
* $fromPeg = 2
* $toPeg = 1
* $usePeg = 0
*
* Is $numberOfRings > 0? No
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< SECOND RECURSIVE CALL RETURN >>>
* <<< SECOND RECURSIVE CALL RETURN >>>
*
* @param int $numberOfRings
* @param array[\SplStack] $pegs
* @param int $fromPeg
* @param int $toPeg
* @param int $usePeg
*/
function printTowerOfHanoiSteps($numberOfRings, $pegs, $fromPeg, $toPeg, $usePeg)
{
if ($numberOfRings > 0) {
printTowerOfHanoiSteps($numberOfRings - 1, $pegs, $fromPeg, $usePeg, $toPeg);
printf('Move %d from peg %d to peg %d', $pegs[$fromPeg]->top(), $fromPeg, $toPeg);
print PHP_EOL;
$pegs[$toPeg]->push($pegs[$fromPeg]->top());
$pegs[$fromPeg]->pop();
printTowerOfHanoiSteps($numberOfRings - 1, $pegs, $usePeg, $toPeg, $fromPeg);
}
}
$to = 0;
}
} elseif ($i % PEG_COUNT == 2) {
// Either move from peg 0 to peg $destination or peg $destination to peg 0
if ($pegs[$destination]->isEmpty() || !$pegs[0]->isEmpty() && $pegs[0]->top() < $pegs[$destination]->top()) {
$from = 0;
$to = $destination;
} else {
$from = $destination;
$to = 0;
}
} else {
// Either move from peg $destination to peg $auxiliary or peg $auxiliary to peg $destination
if ($pegs[$auxiliary]->isEmpty() || !$pegs[$destination]->isEmpty() && $pegs[$destination]->top() < $pegs[$auxiliary]->top()) {
$from = $destination;
$to = $auxiliary;
} else {
$from = $auxiliary;
$to = $destination;
}
}
$pegs[$to]->push($pegs[$from]->pop());
printf('Move #%d: from peg %d to peg %d', $i, $from, $to);
print PHP_EOL;
$i++;
}
}
$inputHelper = new InputHelper();
$numberOfRings = (int) $inputHelper->readInputFromStdIn('Enter the number of rings to move: ');
printTowerOfHanoiSteps($numberOfRings);
