67 lines
2.5 KiB
Text
67 lines
2.5 KiB
Text
---
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id: proposing
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title: Proposing Problems for USACO Monthlies
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author: Benjamin Qi
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description: Includes how you should (preferably) format your submissions.
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---
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Anyone can propose problems for monthly contests. Email your proposal to Professor Dean. In the [past](http://www.usaco.org/index.php?page=viewproblem2&cpid=817), contestants have even written problems for their own divisions (though this is not common).
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- All problems should have 10 test cases at minimum (I believe that the maximum was 21 for [valleys](http://www.usaco.org/index.php?page=viewproblem2&cpid=950)). You do not need to include these in your proposal.
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- All statements must eventually be converted to the following format. It's not required, but please save us time by following it as best you can.
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<Spoiler title="2020 Open Gold - Favorite Colors">
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```
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http://www.usaco.org/index.php?page=viewproblem2&cpid=1042
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bolded text should be surrounded by [b][/b], italics by [i][/i]
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use [ol][/ol] for numbered list
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---
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Each of Farmer John's $N$ cows ($1\le N\le 2\cdot 10^5$) has a favorite color.
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The cows are conveniently labeled $1\ldots N$ (as always), and each color can be
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represented by an integer in the range $1\ldots N$.
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There exist $M$ pairs of cows $(a,b)$ such that cow $b$ admires cow $a$
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($1\le M\le 2\cdot 10^5$). It is possible that $a=b$, in which case a cow
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admires herself. For any color $c$, if cows $x$ and $y$ both admire a cow with
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favorite color $c$, then $x$ and $y$ share the same favorite color.
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Given this information, determine an assignment of cows to favorite colors such
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that the number of distinct favorite colors among all cows is maximized. As
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there are multiple assignments that satisfy this property, output the
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lexicographically smallest one (meaning that you should take the assignment that
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minimizes the colors assigned to cows $1\ldots N$ in that order).
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[input]
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The first line contains $N$ and $M$.
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The next $M$ lines each contain two space-separated integers $a$ and $b$
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($1\le a,b\le N$), denoting that cow $b$ admires cow $a$. The same pair may
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appear more than once in the input.
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[/input]
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[output]
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For each $i$ in $1\ldots N$, output the color of cow $i$ in the desired
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assignment on a new line.
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[/output]
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[example]
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In the attached image, the circles with bolded borders represent the cows with
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favorite color 1.
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[section|SCORING:]
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[ul]
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[li]Test cases 2-3 satisfy $N,M\le 10^3$. [/li]
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[li]Test cases 4-10 satisfy no additional constraints. [/li]
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[/ul]
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[/section]
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```
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</Spoiler> |