Leetcode 688 - analysis of knight probability in chessboard

Leetcode 688 analysis of dynamic programming

Leetcode 688 - Knight probability chessboard

I do not really understand the algorithm until I read the blog:
http://zxi.mytechroad.com/blog/dynamic-programming/688-knight-probability-in-chessboard/

Here is the analysis to help me understand the algorithm:

How to think about the algorithm using dynamic programming? We first have to define variables, kSteps, row, col, 
dp[kSteps][row][col] := number of ways to move to (col, row) after k steps. 

dp[kSteps][row][col] = sum(dp[kSteps - 1][y][x]), for all (x,y) can move to (col, row). 

answer = dum(dp[kSteps][row][col] / (8^kSteps)

Time complexity:  O(k*N^2)
Space complexity: O(k*N^2) -> O(N^2)

Let us go over an example using N = 3, K = 2, r = 0, c = 0
*  *  *       *  *  *        2  *  1
*  *  *   =>  *  *  1    =>  *  *  0 
*  *  *       *  1  *        1  0  *

So using the above steps, we can tell that the probability is (2+1+1)/ (8^2) = 0.0625