CP TOOLKIT V2 NEW UPDATE!!!

This new update comes PACKED with a ton of new features, which I'll list below.

Newly Added Core Features

Graph Editor An intuitive editor where nodes move smoothly. Build and edit graphs with drag-and-drop interaction.

Graph Generator Generate Trees, Cactus Graphs, Complete Graphs, Connected Graphs, Planar Graphs, Forests, and more. Perfect for creating custom test cases.

Big Integer Calculator Handles large integer operations with full precision. Great for number theory problems.

Array Visualizer Cleanly displays 1D and 2D arrays. Automatically adjusts font size and cell spacing for large arrays.

NTT-Friendly Prime Generator Select primes of specific length and base. Browse from a list of 320,000 preprocessed primes.

Primitive Root / Discrete Log / Discrete Root Calculators No need to implement these manually anymore. Let the site compute them for you instantly.

Original post starts here...

Hello everyone! I just released an AWESOME new tool and I'm here to spread the word.

Introducing...

PS/CP Toolkit --> biximo.net <--

So, what is this thing?

If you’ve ever done competitive programming (CP) or problem solving (PS), you probably know how annoying it can be to do certain things manually. And while you'd think there’d be a convenient website with all the tools in one place... turns out, nope. No one made one.

So I did.

PS Toolkit V1 is packed with useful number theory tools — and more features are on the way! Please check it out and share if you find it helpful!

Features

PrimeBrowser

Explore all prime numbers up to $$$2^{63} - 1$$$

GetKthPrime

Quickly find the $$$k$$$-th prime number (up to $$$2^{31} - 1$$$)

CountPrimes

Count how many primes are less than or equal to a given number

PrimeFactorize

Perform prime factorization on integers up to $$$2^{63} - 1$$$

countCoprime (Euler's phi function)

Compute Euler's totient function $$$\varphi(n)$$$ efficiently (up to $$$2^{63} - 1$$$)

CountDivisors

Count the exact number of divisors of a number

GetHighlyCompositeNumber

Get the $$$n$$$-th highly composite number

GetPrimeGap

Find the largest gap between consecutive primes

IsPrime

Fast and accurate primality testing (up to $$$2^{63} - 1$$$)

I recently came across a claim about binary trees that I was unable to prove. Given a binary tree, $$$\sum{|child_l|\times |child_r| } = O(N^2)$$$

Could someone provide proof and/or a way to intuitively explain this?

I recently came across a very interesting Data Structure, that to me, was completely revolutionary in how I view data structures. That is, Implicit Treaps. But on to my question: Now that I'm pretty familiar with the implementation of Treaps and its applications, should I learn Splay Trees (I will learn it regardless eventually, but I have a competition coming up and time is limited)? To narrow down the question, are there problems that can be solved with Splay Trees but not with Treaps?

Through a brief research session, I found the following blog from CF that partially answers my question. https://mirror.codeforces.com/blog/entry/60499 Apparently, Link Cut Trees can be maintained with Splay Trees in N log N time while Treaps have an additional log factor. Are there other instances of this?