Please explain your approach.

You should no use recursive approach. This question can be solved in O(m1+m2+m3+....) where mi is the number of ingredients in the ith dish, you can see my code https://www.codechef.com/viewsolution/15833805 I used the logic that only maximum or minimum number in the previous dish will cause the highest quality hence check which one should be used it's kind of greedy approach.