Everytime I get a 3-D DP problem, I'm able to figure out that the problem can be solved using 3-D DP, I'm also able to define the DP sometimes, but I'm never able to define the base cases and therefore can't solve the problem. Can you please recommend some Standard/Good 3-D DP problems that I can practice?

For Eg. There was this problem: An array of n integers is given. Each element of the array is an integer value > 0. You have to divide the array in 2 parts such that the difference between the sizes of the two parts cannot be greater than 1 and the difference between the summation of elements of the two parts is minimised.

How do I solve this problem?

How often have you seen questions requiring KMP algorithm or using the LPS array in some way, in any of the CF problems?