来自：查字典高考网 2009-11-12
Complete Search
The Idea
Solving a problem using complete search is based on the ``Keep It Simple, Stupid'' principle. The goal of solving contest problems is to write programs that work in the time allowed, whether or not there is a faster algorithm.
Complete search exploits the brute force, straight-forward, try-them-all method of finding the answer. This method should almost always be the first algorithm/solution you consider. If this works within time and space constraints, then do it: it's easy to code and usually easy to debug. This means you'll have more time to work on all the hard problems, where brute force doesn't work quickly enough.
In the case of a problem with only fewer than a couple million possibilities, iterate through each one of them, and see if the answer works.
Careful, Careful
Sometimes, it's not obvious that you use this methodology.
Problem: Party Lamps [IOI 98]
You are given N lamps and four switches. The first switch toggles all lamps, the second the even lamps, the third the odd lamps, and last switch toggles lamps 1, 4, 7, 10, ... .
Given the number of lamps, N, the number of button presses made (up to 10,000), and the state of some of the lamps (e.g., lamp 7 is off), output all the possible states the lamps could be in.
Naively, for each button press, you have to try 4 possibilities, for a total of 410000 (about 106020 ), which means there's no way you could do complete search (this particular algorithm would exploit recursion).
Noticing that the order of the button presses does not matter gets this number down to about 100004 (about 1016 ), still too big to completely search (but certainly closer by a factor of over 106000 ).
However, pressing a button twice is the same as pressing the button no times, so all you really have to check is pressing each button either 0 or 1 times. That's only 24 = 16 possibilities, surely a number of iterations solvable within the time limit.
Problem 3: The Clocks [IOI 94]
A group of nine clocks inhabits a 3 x 3 grid; each is set to 12:00, 3:00, 6:00, or 9:00. Your goal is to manipulate them all to read 12:00. Unfortunately, the only way you can manipulate the clocks is by one of nine different types of move, each one of which rotates a certain subset of the clocks 90 degrees clockwise.
Find the shortest sequence of moves which returns all the clocks to 12:00.
The ``obvious'' thing to do is a recursive solution, which checks to see if there is a solution of 1 move, 2 moves, etc. until it finds a solution. This would take 9k time, where k is the number of moves. Since k might be fairly large, this is not going to run with reasonable time constraints.
Note that the order of the moves does not matter. This reduces the time down to k9 , which isn't enough of an improvement.
However, since doing each move 4 times is the same as doing it no times, you know that no move will be done more than 3 times. Thus, there are only 49 possibilities, which is only 262,072, which, given the rule of thumb for run-time of more than 10,000,000 operations in a second, should work in time. The brute-force solution, given this insight, is perfectly adequate.
Sample Problems
Milking Cows [USACO 1996 Competition Round]
Given a cow milking schedule (Farmer A milks from time 300 to time 1000, Farmer B from 700 to 1200, etc.), calculate
The longest time interval in which at least one cow was being milked
The longest time interval in which no cow is being milked
Perfect Cows Perfect Cow Cousins [USACO 1995 Final Round]
A perfect number is one in which the sum of the proper divisors add up to the number. For example, 28 = 1 + 2 + 4 + 7 + 14. A perfect pair is a pair of numbers such that the sum of the proper divisor of each one adds up to the other. There are, of course, longer perfect sets, such that the sum of the divisors of the first add up to the second, the second's divisors to the third, etc., until the sum of the last's proper divisors add up to the first number.
Each cow in Farmer John's ranch is assigned a serial number. from 1 to 32000. A perfect cow is one which has a perfect number as its serial. A group of cows is a set of perfect cow cousins if their serial numbers form a perfect set. Find all perfect cows and perfect cow cousins.
retrieved from http://ace.delos.com/usacogate
【信息学联赛知识：Complete Search】相关文章：
[标签：竞赛联赛,数学联赛]
他高考作文仅得6分，总分428分，被985高校录取，却被导师拒绝！
北京新闻 2019 5.9万余北京考生今日高考 语文试题鼓励创造性阅读与表达
视频|2019全国高考今日开考: 语文特级教师评析上海卷高考作文
美术联考用纸上海考试模拟试卷纸高考统考纸 4k水粉纸素描纸 速写纸卡纸美术模拟测试试卷纸 美术考试专用纸
张雪峰高考志愿填报指南 第28集 高考志愿分析，材料科学与工程专业，就业很一般，建议慎重选择
学渣儿子高考，英语选择题全选B！老师通报成绩的那一刻父亲懵了
1000张学生用草稿纸考研专用免邮空白便宜薄演草演算纸白纸本书写纸批发打草a4大张实惠装18k高考数学草稿本
张雪峰高考志愿填报指南 第47集 高考志愿，令人头疼的数学系，才是专业万金油，毕业后机会多
高考阅卷名师给考生的高考作文密训课 第5集 高考作文审题实操方法精讲（三）
