Problem solving issue

Everytime i solve any DSA problem or problem in any contest I experience it to be a new one in which I usually not able to relate it with a common algorithm or previously done question, so by hit and trial or sometimes I come with the solution ,but mostly I seemed to give up and move to solution since preparing for internships I have a time limit of question upto 30 min otherwise I gonna waste a lot of time on single question overthinking and following hit and trial by submitting . For example I was doing this question https://www.geeksforgeeks.org/find-minimum-number-of-merge-operations-to-make-an-array-palindrome/

here I think a lot but not able to think even brute force so this gives me a lot pressure in my mind and sometimes demotivating too. Can someone suggest how to fix this problem and move ahead in coding journey. I usually relate it with the fact when we were in school we used to do mathematics which has question related to a particular concept which we were able to judge like differentiation , i want that same intution in coding but not able to get that and feel usually bad ,can someone explain me and guide me in this journey to excel.