NDP is what I said above, you can test a solution in polynomial time. You should get an algorithms textbook to read about time complexity of algorithms if the "Time Complexity" page on wikipedia doesn't make sense to you. I used Cormen's textbook in my algorithms class. This is important, you're going to have trouble if you don't really understand the asymptotic (as the data structure gets large) difference between, for example, searching a list and searching a tree.
From my limited understanding a list is a data structure that contains an ordered number of items. For example a linked list that has a pointer to the next item in the data structure that keeps the list in order. A tree data structure has sub-sets of linked nodes starting at a 'root' node, much like a tree.
The list and the tree don't themselves have time complexity; operations on them do. Finding an element in a list takes O(n) time; in the worst case, you have to check every element of the list. Finding an element in a balanced binary tree takes O(log n) time: at each step, you halve the number nodes you need to check.
The balanced binary tree search operation is an example of something whose cost grows very slowly even as the size of the tree grows rapidly.
There are algorithms that are hard the same way the O(log n) tree is easy: they grow exponentially with the size of input, so very small changes in the input size can drastically increase their cost.
What is this "O"? This is what I am talking about, the Wikipedia article and even this thread throw out variables without defining what they are. "O" and "n" what are they, how do I calculate them? How do they work? That is why none of this makes any sense that I can understand.
Seriously, what is "n" often used to signify in math? Stop thinking of reasons to complain and read for comprehension. Then you will be halfway through O(n).
Then if you write down what you think O signifies, you will be at least 3/4 to the answer instead of part way. Nobody can learn for you. Only you can put forth the effort required.
Most variables in math are unknown until you are given enough information to solve them.
Suppose I gave you J(log y) and then told you that you have to solve for it. What does it mean, how do you calculate it, how does it work, cowboy up and do it man!
What do you mean what are the values of J and y? It is math, just do it! Write down what you think J and y signifies. You will be 3/4th the way to the answer instead of part way. Nobody can learn it but you. Only you can put forth the effort.