Is there any general way of approaching any problems like this...

Suppose, Given two arrays A and B, we have to select any subsequence of A, which satisfies the given properties (XYZ) having minimum or maximum value.

Suppose any selected subsequence of A is S = {A_i1, A_i2, A_i3, ..., A_ik} which satisfy the given properties (XYZ), then the value of Subsequence S is V = {B_i1 @ B_i2 @ B_i3 @ ... @ B_ik}, where @ is any function.

Our goal is to minimize or maximize or ..., the value V of subsequence S.

P.S.: Share any resources related to this, if any.

Problem 1 : 510D - Fox And Jumping

Share your own way to solve problems like this.

P.S.: Comments some more related problems, if you know.