You can read the input into the status table which has a number 'x' inside the cell "[i][j]" if the difference in height between two piles (red and black) after you remove 'i' cards from the first pile and 'j' from the second one is 'x'.
For the first statement example, the table is: {{0,-1,0,1,0},{-1,-2,-1,0,-1},{-2,-3,-2,-1,-2},{-1,-2,-1,0,-1},{0,-1,0,1,0}} (you can view it using "Wolfram|Alpha" service).

Thus, you are to "move" over the table cells from the top left-hand one to the bottom right-hand one, but you can't visit cells with the values different from -1,0,1. Use DP with the diagonal process to draw the right way.