Meaningless Operations
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive […]
Month: May 2020
Magic Stones
Grigory has $n$ magic stones, conveniently numbered from $1$ to $n$. The charge of the $i$-th stone is equal to $c_i$. Sometimes Grigory gets bored and selects […]
Tree-Tac-Toe
The tic-tac-toe game is starting on a tree of $n$ vertices. Some vertices are already colored in white while the remaining are uncolored. There are […]
Nearest Leaf
Let’s define the Eulerian traversal of a tree (a connected undirected graph without cycles) as follows: consider a depth-first search algorithm which traverses vertices of […]
Ilya and a Colorful Walk
Ilya lives in a beautiful city of Chordalsk. There are $n$ houses on the street Ilya lives, they are numerated from $1$ to $n$ from […]
Alyona and a Narrow Fridge
Alyona has recently bought a miniature fridge that can be represented as a matrix with $h$ rows and $2$ columns. Initially there is only one […]
Ramesses and Corner Inversion
Ramesses came to university to algorithms practice, and his professor, who is a fairly known programmer, gave him the following task. You are given two […]
Frets On Fire
Miyako came to the flea kingdom with a ukulele. She became good friends with local flea residents and played beautiful music for them every day. […]
Pavel and Triangles
Pavel has several sticks with lengths equal to powers of two. He has $a_0$ sticks of length $2^0 = 1$, $a_1$ sticks of length $2^1 […]
Niyaz and Small Degrees
Niyaz has a tree with $n$ vertices numerated from $1$ to $n$. A tree is a connected graph without cycles. Each edge in this tree […]
Tree Diameter
There is a weighted tree with $n$ nodes and $n-1$ edges. The nodes are conveniently labeled from $1$ to $n$. The weights are positive integers […]
Frog Jumping
A frog is initially at position $0$ on the number line. The frog has two positive integers $a$ and $b$. From a position $k$, it […]
Hot is Cold
You are given an array of $n$ integers $a_1, a_2, \ldots, a_n$. You will perform $q$ operations. In the $i$-th operation, you have a symbol […]
Zoning Restrictions
You are planning to build housing on a street. There are $n$ spots available on the street on which you can build a house. The […]
Leaf Partition
You are given a rooted tree with $n$ nodes, labeled from $1$ to $n$. The tree is rooted at node $1$. The parent of the […]
Satanic Panic
You are given a set of $n$ points in a 2D plane. No three points are collinear. A pentagram is a set of $5$ points […]
Three Integers Again
We have three positive integers $a$, $b$ and $c$. You don’t know their values, but you know some information about them. Consider all three pairwise sums, i.e. […]
