Hello, I have a question for all the REDS/yellows on codeforces, How do you learn algorithm fast?

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Hello, I am looking for a solution for the problem Hermes. Here is a link to the problem: https://ioinformatics.org/files/ioi2004problem2.pdf ; I have solved this problem for 90% using DP with 3 states, but my solution has a very big memory complexity [20000*2000*2]. My solution is taken from this video: https: https://www.youtube.com/watch?v=bLDy1woBliA ; I have read the official IOI solution, but I don't understand it. BTW for those who want to solve it for the subtask for 50% you can use dp and store your position {N}, your x-axis and y-axis in a 3 dimensional DP. The mem. comp. for this solution is 80*2000*2000; Thanks in advance, hope you have a great day!