## Editorial for Max's Anger Contest Series 1 P5 - Slacking Subsequences

Remember to use this editorial

**only**when stuck, and**not to copy-paste code from it**. Please be respectful to the problem author and editorialist.**Submitting an official solution before solving the problem yourself is a bannable offence.**Author:

##### Subtask 1

Realize a DP state:

- : the minimum sum of absolute differences for the integer in the array with a subsequence of length .

Then, for each given state, consider choosing any integer in the array before the one:

Thus, , where and represents the absolute difference between and .

**Time Complexity:**

##### Subtask 2

Realize that the transition can be optimized with Fenwick trees or segment trees:

- Maintain for all integers that come before but have with at the index.
- Maintain for all integers that come before but have with at the index.

Then, for each given state, , where returns the minimum for all indices less than or equal to and returns the minimum for all indices greater than .

**Time Complexity:**

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