Let me start with “note that”.
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Codeforces (c) Copyright 2010-2026 Михаил Мирзаянов
Соревнования по программированию 2.0
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Auto comment: topic has been updated by Bovmelo (previous revision, new revision, compare).
"consider"
that is best proof
"It can be shown that"
It is obvious that
Trust me bro
I literally wrote this on a blog after the most crucial claim and no one questioned it
Thanks cf
Let's assume
I hate it when they use "it is easy to see that"
Me too.. and whenever this is written its always hard to see that
We can notice that
“bitset”
well known trick in china!
Hence Proved !
We can achieve this by. ..
" We don't have the strict proof, but we have faith and stress."
The proof is left as an exercise to the reader.
It would be thoroughly appreciated if lazy editorials put this rather than a low-effort explanation that clears up nothing.
Without loss of generality
obviously
This is a well-known fact that
I "Claim"
"Observation:"
from "someoldname" 's theorem it's obvious that...
"There are other approaches..."
We can prove by induction that ...
"from the following observations"
If you actually want to prove something: "Assume that"
Once you realize that you don't know how to prove something: "It's obvious that"
The proof is left as homework.
Source : https://mirror.codeforces.com/blog/entry/9070 (word "homework" written in tutorial of 351C + 351D)
And sometimes "homework" is harder than the actual problem, so we just "prove it by AC"
"Time complexity: O( )"
It can be proven that
We can use (smth) to optimize $$$\mathcal{O}(n^2)$$$ to $$$\mathcal{O}(n \log n)$$$ due to monge property
amonge us
"First of all"
Let's start with a naive solution
"We are programmers not mathematicians"
It was revealed to me in a dream