2.2 KiB
2.2 KiB
| id | title | author |
|---|---|---|
| proposing | Proposing Problems for USACO Monthlies | Benjamin Qi |
Anyone can propose problems for monthly contests (email your proposal to Professor Dean).
In the past, contestants have even written problems for their own divisions!
All statements must eventually be converted to the following format; please save us time by following it as best you can.
2020 Open Gold - Favorite Colors
http://www.usaco.org/index.php?page=viewproblem2&cpid=1042
bolded text should be surrounded by [b][/b], italics by [i][/i]
use [ol][/ol] for numbered list
---
Each of Farmer John's $N$ cows ($1\le N\le 2\cdot 10^5$) has a favorite color.
The cows are conveniently labeled $1\ldots N$ (as always), and each color can be
represented by an integer in the range $1\ldots N$.
There exist $M$ pairs of cows $(a,b)$ such that cow $b$ admires cow $a$
($1\le M\le 2\cdot 10^5$). It is possible that $a=b$, in which case a cow
admires herself. For any color $c$, if cows $x$ and $y$ both admire a cow with
favorite color $c$, then $x$ and $y$ share the same favorite color.
Given this information, determine an assignment of cows to favorite colors such
that the number of distinct favorite colors among all cows is maximized. As
there are multiple assignments that satisfy this property, output the
lexicographically smallest one (meaning that you should take the assignment that
minimizes the colors assigned to cows $1\ldots N$ in that order).
[input]
The first line contains $N$ and $M$.
The next $M$ lines each contain two space-separated integers $a$ and $b$
($1\le a,b\le N$), denoting that cow $b$ admires cow $a$. The same pair may
appear more than once in the input.
[/input]
[output]
For each $i$ in $1\ldots N$, output the color of cow $i$ in the desired
assignment on a new line.
[/output]
[example]
In the attached image, the circles with bolded borders represent the cows with
favorite color 1.
[section|SCORING:]
[ul]
[li]Test cases 2-3 satisfy $N,M\le 10^3$. [/li]
[li]Test cases 4-10 satisfy no additional constraints. [/li]
[/ul]
[/section]