Hi everyone,

A few months ago, I participated in a contest and encountered a geometry problem that has been stuck in my head ever since. I have tried searching for the official editorial or any existing solutions, but I couldn't find any.

Could you please provide some hints, a full solution, or even approaches for the subtasks? Since my English is not very good, I'm afraid that re-explaining the problem myself might lead to misunderstandings or incorrect terminology. Therefore, I have included the original problem link here for accuracy: problem here

Thank you very much for your help!

My friend gave me an interesting problem:

Given connected, weighted graph with N nodes and M edges. There are Q queries, each of two types:

• Type 1: 1 i Remove edge numbered $$$i$$$ $$$(1 \le i \le M)$$$
• Type 2: 2 u v Find a path from u to v with the minimum total XOR value (edges may be traversed multiple times). If no path exists, return $$$–1$$$.

Constraints:

$$$(1 ≤ N, M, Q ≤ 2×10^5)$$$

$$$(1 ≤ u,v ≤ N; 0 ≤ w ≤ 10^9)$$$

Guys, i need help with this problem from a offline contest i participated ;(

Given an integer $$$k$$$ ($$$k\le10^{100}$$$) from input

Construct a directed graph that sastified all the following conditions:

• at most 1 edge between any pair of nodes

• the graph must have at most 500,000 nodes and 1,000,000 edges

• graph must be acyclic (no cycle)

• must be exactly k ($$$k\le10^{100}$$$) distinct paths from node 1 to the node with largest index (node n)

Thank yall!