Meet in the Middle lecture & problem-solving starts in an hour https://www.twitch.tv/errichto. See the problem list below. I will later update this blog with codes and written explanations.
UPD, video recording: https://youtu.be/18sJ3mK173s, some codes from the stream: https://ideone.com/1uScID
P1. Knapsack with $$$n \leq 40$$$ and values up to $$$10^9$$$ https://cses.fi/problemset/task/1628
P2. Given a sequence $$$a_1, a_2, \ldots, a_n$$$ ($$$n \leq 2000$$$), count increasing subsequences of length 3.
P3. 4-SUM, find four values that sum up to the target value https://cses.fi/problemset/task/1642
P4. Find a string with the standard polynomial hash equal to the target value $$$X$$$ modulo $$$10^9+7$$$. The hash is computed by converting characters a-z into 0-25 and multiplying every character by the next power of 26. Find a solution without just converting $$$X$$$ to base $$$26$$$.
P5. You're given a graph: $$$n \leq 300$$$, $$$m \leq n\cdot(n-1)/2$$$. Count paths made of 5 nodes. Nodes and edges can be repeated.
Bonus 1: Count simple paths only. No repetitions allowed.
Bonus 2: $$$n, m \leq 2000$$$
Similar problem: https://codeforces.com/blog/entry/94003
P6. You're given a sequence $$$n \leq 10^6, 0 \leq a_i < M = 10^9$$$. Find two subsequences with equal sums modulo $$$M$$$. https://quera.ir/problemset/olympiad/34090. The two subsequences can have common elements.
P7. Number Clicker https://codeforces.com/contest/995/problem/E. You start with the number $$$a$$$ and want to get $$$b$$$ in at most 200 moves. You can increment, decrement or change the current number into its modular inverse, all modulo prime $$$p$$$. Find any valid sequence of moves.