No Cheating(Google Code Jam 2008 Round 3C)二分图最大独立集

最新推荐文章于 2019-09-10 19:11:00 发布

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最新推荐文章于 2019-09-10 19:11:00 发布 · 727 阅读

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#No Cheating #Google Code Jam 2008 #挑战程序设计竞赛 #最大独立集问题

本地一所高中的期末考试将在一个大教室中举行，但有些学生总是试图在考试中偷看别人的答案！教室被视为一个M行N列的矩形网格，每个单元格代表一个座位。为了防止作弊，必须确保每个人不能看到其他人的答案。题目要求确定最多可以安排多少名学生坐下，使得没有人能看到其他人的答案。输入包含教室的尺寸和座位状态，输出能容纳的最大学生数。案例限制和数据规模也给出。

来自《挑战程序设计竞赛》

1.题目原文

https://code.google.com/codejam/contest/32002/dashboard#s=p2

Problem

A local high school is going to hold a final exam in a big classroom. However, some students in this school are always trying to see each other's answer sheet during exams!

The classroom can be regarded as a rectangle of M rows by N columns of unit squares, where each unit square represents a seat.

The school principal decided to set the following rule to prevent cheating:
Assume a student is able to see his left, right, upper-left, and upper-right neighbors' answer sheets. The assignment of seats must guarantee that nobody's answer sheet can be seen by any other student.

As in this picture, it will not be a good idea to seat anyone in A, C, D, or E because the boy in the back row would be able to see their answer sheets. However, if there is a girl sitting in B, he will not be able to see her answer sheet.