Original address: http://www.cnblogs.com/ch3656468/archive/2011/03/02/1969303.html
There is not much to say about the basic cross product, dot product and convex hull. I search a lot on the Internet, and I am basically familiar with some topics.
Some basic topics can be searched by yourself, such as this blog: http://blog.sina.com.cn/s/blog_49c5866c0100f3om.html
Next, I studied the half-plane intersection. For the thinking method, see Zhu Zeyuan's national team paper in 2007. For the template code, please refer to the self-school Daniel Tao:
Some questions about half-plane intersection:
POJ 3335 Rotating Scoreboard
http://acm.pku.edu.cn/JudgeOnline/problem?id=3335
POJ 3130 How I Mathematician Wonder What You Are!
http://acm.pku.edu.cn/JudgeOnline/problem?id=3130
POJ 1474 Video Surveillance
http://acm.pku.edu.cn/JudgeOnline/problem?id=1474
Knowledge point: Half-plane intersection to find the kernel of polygon, existence judgment
POJ 1279 Art Gallery
http://acm.pku.edu.cn/JudgeOnline/problem?id=1279
Intersection of half planes Find the kernel of a polygon and find the area of the kernel
POJ 3525 Most Distant Point from the Sea (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3525
Given a polygon, find a point inside which is the farthest from the boundary of the polygon, That is, the circle with the largest radius in the polygon.
Solution: You can use the half plane intersection + bisection method to solve. Divide this distance, and the edges approach inwards until accuracy is achieved.
POJ 3384 Feng Shui (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3384
The practical application of half plane intersection, covering a polygon with two circles, and asking the maximum area that can cover the polygon.
Solution: Use half-plane intersection to push each edge of the polygon "inside" R together to get a new polygon, and then find the two farthest points of the polygon.
POJ 1755 Triathlon (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1755
Half-plane intersection to judge whether the inequality has a solution. Pay attention to the choice of the sign of the inequality in the transformation, which directly affects the direction of the half-plane intersection.
POJ 2540 Hotter Colder
http://acm.pku.edu.cn/JudgeOnline/problem?id=2540
Half-plane intersection to find the area of feasible region of linear programming.
POJ 2451 Uyuw's Concert
http://acm.pku.edu.cn/JudgeOnline/problem?id=2451
Zzy's title for his paper on the nlogn algorithm to solve the half-plane intersection problem.
(The above topics are from other people's blogs, and there are a few more questions that I found myself)
POJ 1271 Nice Milk
http://poj.org/problem?id=1271
Black Book Exercises
UVA 11722 Joining with Friend
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=117&page=show_problem&problem=2769Probability
problem, this scale is a bit wasteful to use half plane intersection, but it should be practiced
USACO 2010 MARCH GOLD StarCowraft
http://61.187.179.132:8080/JudgeOnline/showproblem?problem_id=1829
Next, I made a little bit of the problem of coordinate rotation. For details, please refer to Wuhan Daniel's blog post http://dumbear.com/blog/?p=143
Coordinate rotation topics are not cut much
HDU 1700 Points on Cycle
http://acm.hdu.edu.cn/showproblem.php?pid=1700
A basic question
POJ 3845 Fractal
http://poj.org/problem?id=3845
Pay attention to the value of eps
POJ 1133 Stars
http://poj.org/problem?id=1133
Harbin Online Contest 2010
http://acm.hrbeu.edu.cn/index.php?act=problem&id=1006&cid=163D
coordinate rotation. This requires an account to submit, and the "275" of the second Sample in the Sample Input is changed to "270"
HDU 3623 Covering Points (2010 Tianjin Online Competition Question C)
http://acm.hdu.edu.cn/showproblem.php?pid=3623 (Avionics does not have this question)
http://acm.tju.edu.cn /toj/showp3740.html
FZU 2002 Shade of Hallelujah Mountain (2010福州regional)
http://acm.fzu.edu.cn/problem.php?pid=2002
HDU 4087 ALetter to Programmers (2011 Beijing Live)
http://acm.hdu.edu.cn/showproblem.php?pid=4087
3D Rotation Matrix + Matrix Acceleration
Then there is the rotation jam, a good learning website http://cgm.cs.mcgill.ca/~orm/rotcal.html (but it is in English), and later found a big cow's blog with some translations http:/ /blog.csdn.net/ACMaker , I took a look at it together, and it has a lot of benefits.
Some rotating stuck issues
POJ 2187 Beauty Contest
http://acm.pku.edu.cn/JudgeOnline/problem?id=2187
The convex hull finds the farthest point pair. You can enumerate violently, or you can use a rotating jam.
POJ 3608 Bridge Across Islands
http://acm.pku.edu.cn/JudgeOnline/problem?id=3608
The closest distance between two convex hulls.
The above two questions can refer to the blog: http://www.cppblog.com/staryjy/archive/2009/11/19/101412.html (the above code is very good)
POJ 2079 Triangle
http://poj.org/problem?id=2079
This question thinks that O(N^2) complexity will time out, and the result is O(N^2) complexity
UVA 10173
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=13&problem=1114&mosmsg=Submission+received+with+ID+8029560
Given a point set S, find the minimum covering rectangle of S
Then looked at some scanlines or something.
Recommend a few good topics:
POJ 2932 Coneology
http://poj.org/problem?id=2932
HDU 3124 Moonmist
http://acm.hdu.edu.cn/showproblem.php?pid=3124
Nearest circle pair problem (bisection + scan line)
HDU 3867 Light and Shadow
http://acm.hdu.edu.cn/showproblem.php?pid=3867
(scan by polar angle) Note - PI and PI position segmentation
I saw some random algorithms below: (Gu Yan's paper in 2008 - "On the Application of Randomization Ideas in Geometric Problems")
(1) Random Increment Method: This algorithm is very sharp, reducing some computational geometry problems to an n complexity. (typically with minimal circle coverage)
I found a random incremental algorithm with minimum circle coverage on the Internet. The code inside is good, but the explanation is not very clear. It is recommended to read "Computational Geometry Algorithms and Applications (3rd Edition)" (translated by Deng Junhui, published by Tsinghua University Press) in the The content in the chapter "4.7 Minimum Enclosing Circle" on page 91 is more detailed and clear. For the code, I refer to this blog's http://blog.csdn.net/pvpishard/archive/2011/01/27/6167262.aspx
(2) Simulated annealing: refer to Gu Yan's paper
The topic of simulated annealing:
POJ 1379 Run Away
http://poj.org/problem?id=1379
POJ 2420 A Star not a Tree?
http://poj.org/problem?id=2420
URAL 1520 Empire Strikes Back (recommended)
http://acm.timus.ru/problem.aspx?space=1&num=1520
Gu Yan thesis example, good topic
POJ 2069 Super Star
http://poj.org/problem?id=2069
This question I WA and TLE many times
POJ 3301 Texas Trip
http://poj.org/problem?id=3301
This question can also be three-
pointed SPOJ 4409 Circle vs Triangle
https://www.spoj.pl/problems/AREA1/simulated
annealing + analytic geometry
POJ 3285 Point of view in Flatland
http://poj.org/problem?id=3285
The difficulty of this problem is to find a suitable evaluation function, of course, this problem can also be done by solving a system of equations
POJ 2600 Geometrical dreams
http://poj.org/problem?id=2600
This question is not a simulated annealing question, but it can be done with simulated annealing. Non-simulated annealing methods are also not difficult
Analytic geometry, plane closest point pair, . . . These are not very deep.
For origami problems, see Daniel dumbear's blog http://dumbear.com/blog/?p=249
two questions
POJ 1921 Paper Cut
http://poj.org/problem?id=1921
This question is relatively easy to do compared to the next question
POJ 3806 Origami Through-Hole
http://poj.org/problem?id=3806
This problem is a bit troublesome to deal with, I debugged it for a long time
The area of the circle is merged and intersected. For details, please refer to the blog of AekdyCoin Daniel
The area of the circle is combined: http://hi.baidu.com/aekdycoin/blog/item/c1b28e3711246b3f0b55a95e.html
The area of the circle: http://hi.baidu.com/aekdycoin/blog/item/12267a4e9476153bafc3abbd.html
topic:
SPOJ 8073 The area of the union of circles
https://www.spoj.pl/problems/CIRU/
SPOJ 3863 Area of circles
https://www.spoj.pl/problems/VCIRCLES/
SPOJ 8119 CIRU2
https://www.spoj.pl/problems/CIRUT/Extension
of circle area union
HDU 3467 Song of the Siren
http://acm.hdu.edu.cn/showproblem.php?pid=3467
HDU 3239 Jiajia's Robot (recommended)
http://acm.hdu.edu.cn/showproblem.php?pid=3239
A very ingenious question, I learned the method only after reading the message in AC Daniel's blog.
For the method, see a message in the AC Daniel blog: http://hi.baidu.com/aekdycoin/blog/item/12267a4e9476153bafc3abbd.html
The area of the convex polygon and
I first read the blog of AC Daniel and learned the O(N^3) method. Later, when I was working on Codeforces, I found that there was an O(N^2*logN) method, and it was not cumbersome.
AC Daniel's blog post: http://hi.baidu.com/aekdycoin/blog/item/fbe5a03232c71952ad4b5fcc.html
Codeforces Round #83 DIV1's E question can't pass the 49th set of data with the O(N^3) method, and then studied the codes of other Daniel's convex polygon intersections
http://codeforces.com/contest/107/status/E
First, I looked at dagon's code and found that there was actually a problem with his code, and the data of Codeforces was not found. Then read the code of syntax_error,
I found that he did it with a method similar to trapezoidal division, and the complexity was O(N^2*logN), so I learned it decisively.
Topic: http://codeforces.com/contest/107/problem/E
For details: http://www.cnblogs.com/ch3656468/archive/2011/10/17/2215551.html
There is a class of problems that give some points and tell you which points are connected by lines, and there are no other intersections between these line segments except the endpoints (sometimes these line segments have to be processed by themselves).
Then the question asks you
1 Area of each small polygon
2 How many K polygons do not contain points and line segments inside
3 The outline of the figure enclosed by these line segments
The methods for such topics are similar, and similar methods can be found in many Daniel's blogs.
For example: gccfeli Daniel's blog: http://gccfeli.cn/2007/09/%E8%AE%A1%E7%AE%97%E5%87%A0%E4%BD%95-pku1092-%E5% A5%87%E7%89%B9%E7%9A%84%E6%8A%80%E5%B7%A7.html
watashi big cow blog: http://watashi.ws/blog/970/andrew-stankevich-3-solution/
Isun大牛的blog：http://hi.baidu.com/xh176233756/blog/item/29652646f0e870006a63e5cb.html
topic:
POJ 1092 Farmland
http://poj.org/problem?id=1092
ZOJ 2361 Areas / SGU 209
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=2361
A good question, there is a solution report in watashi's blog
POJ 3743 LL’s cake
http://poj.org/problem?id=3743
POJ 2164 Find the Border
http://poj.org/problem?id=2164
3D geometry
There is very little content about 3D geometry on the Internet, and the codes and topics can hardly be found, so I cut a few questions.
The two questions in the previous coordinate rotation:
Harbin Online Contest 2010
http://acm.hrbeu.edu.cn/index.php?act=problem&id=1006&cid=163D
coordinate rotation. This requires an account to submit, and the "275" of the second Sample in the Sample Input is changed to "270"
FZU 2002 Shade of Hallelujah Mountain (2010福州regional)
http://acm.fzu.edu.cn/problem.php?pid=2002
SGU 110 Dungeon
http://acm.sgu.ru/problem.php?contest=0&problem=110
3D light reflection
FZU 1981 Three kingdoms (2010 Fuzhou Online Competition)
http://acm.fzu.edu.cn/problem.php?pid=1981
Coordinate mapping, I used map to TLE at first, so I had to change the code without map
UVA 11275 3D Triangles
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=2250
HDU 4042 is an enhanced version of this question, I use the same code AC
for this question in the title Weird precision 0.000001 I didn't deal with it specially
HDU 4042 Fireworks (2011 Beijing Online Competition)
http://acm.hdu.edu.cn/showproblem.php?pid=4042
Very good problem (solution report: http://hi.baidu.com/%D0% A1%CE%E4rj/blog/item/0114bb2dcd4cdef78b13991d.html )
HDU 4087 ALetter to Programmers (2011 Beijing Live)
http://acm.hdu.edu.cn/showproblem.php?pid=4087
3D Rotation Matrix + Matrix Acceleration
Some other topics:
EOJ 283 Target Practice
http://202.120.106.94/onlinejudge/problemshow.php?pro_id=283
Search + Geometry
POJ 1688 Dolphin Pool
http://poj.org/problem?id=1688
There are several ways to do this
POJ 1981 Circle and Points
http://poj.org/problem?id=1981
is a very classic topic
POJ 3675 Telescope
http://poj.org/problem?id=3675
Common area of circles and polygons
POJ 1259 The Picnic
http://poj.org/problem?id=1259
Maximum convex hole, Computational Geometry + DP
POJ 1586 Three Sides Make a Triangle
http://poj.org/problem?id=1586
The content of the question is very simple and the method is obvious, but it is not easy to think about AC, the accuracy is disgusting, I just read the discussion The
HDU 3629 Convex (recommended)
http://acm.hdu.edu.cn/showproblem.php?pid=3629
is a good question. There are two ideas for this question:
1) http://apps.topcoder.com/ wiki/display/tc/TCO%2710+Online+Round+4
2) http://www.owent.net/2010/09/the-35th-acmicpc-asia-regional-tianjin-site-%E2%80% 94%E2%80%94-online-contest-1009-convex-%E8%A7%A3%E9%A2%98%E6%8A%A5%E5%91%8A.html
HDU 3644 A Chocolate Manufacturer's Problem (2010 Hangzhou Online Competition)
http://acm.hdu.edu.cn/showproblem.php?pid=3644
I originally wanted to use simulated annealing, but the result was hovering between WA and TLE, unable to AC
FZU 1973 How many stars (recommended) (2010 Fuzhou Online Competition)
http://acm.fzu.edu.cn/problem.php?pid=1973
A relatively classic topic
POI2007 Symmetry axis osi
http://www.zybbs.org/JudgeOnline/problem.php?id=1100
A very sharp question, the meaning of the question is to judge the number of symmetry axes of a polygon. (N^2) complexity,
this time O(N^2) will not work, and randomization will not pass, and finally this problem is solved under the guidance of the problem-solving report. For the first time, it was discovered that
the can be solved by the method of strings.
Problem solving report found on the Internet: http://hi.baidu.com/nplusnplusnplu/blog/item/d260baef2e9e9c5879f055cb.html