Knights Tour -- Something I am doing wrong

I have an assignment to write a knights tour backtracking program in Java where the professor says to:

Eliminate backtracking time by:

Find the knights with the least possible moves
Sort those moves from knight with least moves to greatest moves
Backtrack if that path fails

I have done that with and attempted some other optimizations but my algorithm is still pretty slow for most squares. I went online and found my algorithm was pretty similar to others. I even took the algorithm from here and found it ran slow on the same spaces as mine (ahem pretty much never finishes) I was ready to call it until I took my processor's version from his website and it ran instantaneously on the squares every other version I had seen had run slowly on, he even showed me his code in his office last week and I recall it looking very similar. I have also seen questions on this site asking about their slow backtracking programs for knights tour. How is this possible!? Virtually every other source I have seen can confirm that this algorithm is slow except for my professor. My code:

```
/*!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!//
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!//
//Grid.java THIS IS WHERE THE MEAT AND POATATOS IS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!//
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!//
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!//
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*/
public class Grid
{
//Constants to keep things consistant and avoid errors.//
public final static char OBSTICLE_TILE_SYMBOLE = '0';
public final static char OPEN_TILE_SYMBOLE = '1';
private Tile[][] tileGrid;
/*****
'Makes for a nice api to do things this way,
no construtor discourages the user from *
** makin

Broken sort

When inserting elements into your list in sorted order, you don't insert the element at the correct index:

for( int i = 0; i  0 )
                {
                    tilesToTry.add( ( i - 1 ), currentHopTile );
                    tilesToTryLengths.add( ( i - 1 ), Integer.valueOf( CURRENT_LENGTH ) );
                    foundAPlace = true;
                    break;
                }
            }
        }

Suppose you had 10 elements already sorted and your new element were larger than index 4 but smaller than index 5. Your new element should be inserted at index 5 and shift all the other elements down. In your code, however, you are inserting at index 4, which is incorrect. You also have a check for i > 0 which is wrong. Your code should be changed to this:

for (int i = 0; i < AMOUNT_OF_TILES_TO_TRY; ++i)
           {
                if (CURRENT_LENGTH < tilesToTryLengths.get(i).intValue())
                {
                    tilesToTry.add(i, currentHopTile);
                    tilesToTryLengths.add(i, Integer.valueOf(CURRENT_LENGTH));
                    foundAPlace = true;
                    break;
                }
           }

StackExchange Code Review Q#107923, answer score: 4