As my title stated, I really need help with understanding D (https://mirror.codeforces.com/contest/2002). (Sorry, I'm really dumb :<<<). So the statement is like this (D1): Given a permutation with some persistent swap queries and a dfs algorithm, check if the permutation after each swap can form a dfs order of some perfect binary tree. I really think that as long as the permutation starts with 1, we can always recreate a perfect binary tree from the permutation. Because like if we assign a pointer p = 0, when we traverse on a binary tree, when we enter a node u, we can just assign p = p + 1, and then assign a[u] = P[p] (P is the original permutation), hence it always exists (Did I misread the statement??). Help me guys I'm really dumb :<<<

Don't apologize for being "dumb" — it's completely normal to have questions and misunderstandings! Let's break down the problem statement and your concerns:

Problem Statement:Given a permutation with some persistent swap queries, check if the permutation after each swap can form a DFS order of some perfect binary tree.Your Concern:You think that as long as the permutation starts with 1, you can always recreate a perfect binary tree from the permutation. You're suggesting that by assigning a pointer`p = 0`

and traversing the binary tree, you can assign values to the nodes according to the permutation`P`

.Misunderstanding:The problem is not asking you to recreate a perfect binary tree from the permutation. Instead, it's asking you to verify whether the permutation after each swap can form aDFS orderof some perfect binary tree. In other words, you need to check if the resulting permutation can be used as a DFS order of aperfect binary tree.Key Point:The key point is that theDFS orderof a perfect binary tree is not just about assigning values in the correct order. It's also about the structure of the tree. Aperfect binary treehas a specific structure, where each node has at most two children (left and right). The DFS order should reflect this structure.Correct Approach:To solve this problem, you need to check if the permutation after each swap can be used as a DFS order of a perfect binary tree. You can do this by iterating through the permutation and checking if each node has at most two children (left and right). You can also use a graph data structure to represent the binary tree and verify that it satisfies the properties of a perfect binary tree.Hint:To simplify the problem, you can start by assuming that the permutation is initially a valid DFS order of a perfect binary tree. Then, you can apply the swap queries and check if the resulting permutation is still a valid DFS order of a perfect binary tree.I hope this helps clarify things! If you have more questions or need further guidance, feel free to ask.

First of all thank you for answering my question.

But I still don't really grasp it. In this example (https://mirror.codeforces.com/contest/2002/problem/D1)

they say 1 3 5 4 2 6 7 can't be a dfs order of some perfect binary tree. But what about this tree

Anyway thanks for your time!!

They're specifically talking about a perfect binary tree in which the parent of $$$i$$$ is $$$\left\lfloor\frac{i}{2}\right\rfloor$$$ for each $$$i$$$. This isn't true for your tree.

if you ever feel useless, remember that there are someone copy pasting people's questions into chatgpt and pasting the answer without changing a single word

I'm really desperate at solving this problem. Perhaps you can help me :>

The AI guy wasted our 4 calorie and 3 brain cells.

i wrote that myself