Path Finding using Dynamic Programming
How to compare the the Algorithms:

Either determine the complexity of your algorithm and the complexity of the solution in the tutorial.  

If you want to avoid to determine the complexity based on the source code you can simply implement the tutorial solution and compare the runtime of your algorithm and the runtime of the of the tutorial-algorithm.
To get a good idea of the complexity behavior of both algorithms you need inputs of different lengths to approximate the runtime related to the size of the input.

How to improve yours
If your approach is very different you might not be able to improve your algorithm by looking on the tutorial-algorithm because they are too different.
If the Tutorial-algorithm is better at all, you can try to understand the steps it does and try to memorize the general idea of this steps for your next algorithms that address similar problems.