"Turn" [thematic learning] [computational geometry]

Original address: http://www.cnblogs.com/ch3656468/archive/2011/03/02/1969303.html

The basic cross product, dot product and convex hull and other things will not say anything, a search on the internet a lot, cut some of the basic familiar with the topic is almost.

Some basic topics can be searched on their own, such as this blog:http://blog.sina.com.cn/s/blog_49c5866c0100f3om.html

Next, the study of the semi-planar intersection, the thinking method to see 07 Zhu Zehian's national team paper, template code reference self-New elder brother:

Http://www.owent.net/2010/10/acm-%E8%AE%A1%E7%AE%97%E5%87%A0%E4%BD%95-%E4%B8%AA%E4%BA%BA%E6%A8%A1%E6%9D%BF.html

Some semi-planar topics:

POJ 3335 Rotating Scoreboard
http://acm.pku.edu.cn/JudgeOnline/problem?id=3335

POJ 3130 How I mathematician Wonder what do 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: The kernel of semi-planar intersection and the existence judgment of polygon

POJ 1279 Art Gallery
http://acm.pku.edu.cn/JudgeOnline/problem?id=1279
The nucleus of the half plane intersection to seek the area of the nucleus

POJ 3525 Most distant point from the Sea (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3525
Give a polygon, the inside of a point, its distance from the boundary of the polygon farthest, that is, the maximum radius circle in the polygon.
Solution: Semi-planar intersection + dichotomy method can be used. The distance between the two points, the edge inward approximation, until the accuracy is achieved.

POJ 3384 Feng Shui (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3384
Semi-planar intersection practical application, with two circles covering a polygon, asked to cover the area of the polygon.
Solution: Use half-plane intersection to move each edge of the polygon to "inside" to promote R, to get a new polygon, and then to find the furthest two points of the polygon.

POJ 1755 Triathlon (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1755
The semi-planar intersection judgment inequality has the solution. Pay attention to the choice of the positive and negative numbers in the transformation, which directly affects the direction of the semi-planar intersection.

POJ 2540 Hotter Colder
http://acm.pku.edu.cn/JudgeOnline/problem?id=2540
The area of the feasible area of linear programming is obtained by half plane intersection.

POJ 2451 Uyuw ' s Concert
http://acm.pku.edu.cn/JudgeOnline/problem?id=2451
Zzy for his NLOGN algorithm to solve the problem of semi-planar paper.

(The above topics from other people's blog, the back of a few questions I found myself)

POJ 1271 Nice Milkhttp://poj.org/problem?id=1271Black Book ExerciseUVA 11722 joining with FriendHttp://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=117&page=show_ problem&problem=2769Probability problem, this scale is a bit wasteful with half a plane, but it's a practice.Usaco March GOLD Starcowrafthttp://61.187.179.132:8080/JudgeOnline/showproblem?problem_id=1829 　　

Next a little bit of the coordinate rotation problem, in particular, can refer to Wuhan Daniel's blog http://dumbear.com/blog/?p=143

There's not much of a coordinate rotation problem.

HDU 1700 Points on Cyclehttp://acm.hdu.edu.cn/showproblem.php?pid=1700A question of comparative basisPOJ 3845 Fractalhttp://poj.org/problem?id=3845Pay attention to the value of EPSPOJ 1133 Starshttp://poj.org/problem?id=1133Harbin Online Contest 2010Http://acm.hrbeu.edu.cn/index.php?act=problem&id=1006&cid=16Three-dimensional coordinate rotation. This must have an account to be submitted, there is the second sample in sample Input "275" changed to "270"HDU 3623 covering Points (2010 Tianjin Network game c)http://acm.hdu.edu.cn/showproblem.php?pid=3623 (avionics does not have this problem)Http://acm.tju.edu.cn/toj/showp3740.htmlFzu 2002 Shade of Hallelujah Mountain (2010 Fuzhou Regional)http://acm.fzu.edu.cn/problem.php?pid=2002
HDU 4087 Aletter to Programmers (2011 Beijing live Match)http://acm.hdu.edu.cn/showproblem.php?pid=4087three-dimensional rotation matrix + matrix acceleration

Then there is a rotation jam , a good learning site http://cgm.cs.mcgill.ca/~orm/rotcal.html (but English), and later found a Daniel's blog there are some translations/HTTP// Blog.csdn.net/acmaker, combined to see a bit, the benefits of a lot ah.

Some spin-jam topics

POJ 2187 Beauty Contest
http://acm.pku.edu.cn/JudgeOnline/problem?id=2187
Convex hull to find the farthest point pair. You can use the brute force enumeration or rotate the jam.

POJ 3608 Bridge Across Islands
http://acm.pku.edu.cn/JudgeOnline/problem?id=3608
The nearest distance of two convex bags.

The above two questions can refer to blog:http://www.cppblog.com/staryjy/archive/2009/11/19/101412.html (the above code is very good)

POJ 2079 Trianglehttp://poj.org/problem?id=2079The problem is that the complexity of O (n^2) will time out, and the result is O (n^2) complexityUVA 10173Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=13 &problem=1114&mosmsg=submission+received+with+id+8029560To set S for the minimum overlay rectangle of S 　　

And then I looked at a few scan lines and stuff like that.

Recommended some of the more good topics:

POJ 2932 Coneologyhttp://poj.org/problem?id=2932HDU 3124 Moonmisthttp://acm.hdu.edu.cn/showproblem.php?pid=3124Nearest round pair problem (binary + scan line)HDU 3867 Light and Shadowhttp://acm.hdu.edu.cn/showproblem.php?pid=3867(by extreme angle Scan) Note the position segmentation of-pi and PI

Here are some random algorithms:(08 Guo paper-"On the application of stochastic thinking in geometrical problems")

(1) random increment method : This algorithm is very sharp ah, some computational geometry of the problem reduced a n complexity. (typical with minimum round coverage)

On the net to find the minimum round coverage of the random increment algorithm, the code is good, is not very clear explanation, recommended to see the "Computational Geometry Algorithm and Application (3rd edition)" (Deng Junhui translation, Tsinghua University Press published) in the 91st page "4.7 min surrounded by the circle" in this chapter of the content, more detailed also very clear, Code I refer to this blog http://blog.csdn.net/pvpishard/archive/2011/01/27/6167262.aspx

(2) simulated annealing : reference Guo paper

The topic of simulated annealing:

POJ 1379 Run awayhttp://poj.org/problem?id=1379POJ 2420 A Star not a Tree?http://poj.org/problem?id=2420URAL 1520 Empire Strikes Back (recommended)http://acm.timus.ru/problem.aspx?space=1&num=1520Guo Paper example, good topicPOJ 2069 Super Starhttp://poj.org/problem?id=2069I wa and tle many times in this question.POJ 3301 Texas Triphttp://poj.org/problem?id=3301You can use three points for this question. 　　　　　　 Spoj 4409 Circle vs Trianglehttps://www.spoj.pl/problems/AREA1/Simulated annealing + analytic geometry POJ 3285 Point of view in Flatlandhttp://poj.org/problem?id=3285The difficulty of this problem is to find the appropriate evaluation function, of course, the problem can also be solved by solving the equation setPOJ 2600 Geometrical Dreamshttp://poj.org/problem?id=2600This is not a simulated annealing problem, but can be simulated annealing. The non-simulated annealing method is not difficult

analytic geometry , Planar nearest point pair , ... These are not very deep.

　　

Origami Questions see Daniel Dumbear's blog http://dumbear.com/blog/?p=249

Two topics

POJ 1921 Paper Cuthttp://poj.org/problem?id=1921This question is relatively good for the next question.POJ 3806 Origami Through-holehttp://poj.org/problem?id=3806It's a bit of a problem, I've been debugging for a long time. 　 　

　　round the area and turn , in detail you can see Aekdycoin Daniel's Blog

Area of the circle and: http://hi.baidu.com/aekdycoin/blog/item/c1b28e3711246b3f0b55a95e.html

Round area Sex: http://hi.baidu.com/aekdycoin/blog/item/12267a4e9476153bafc3abbd.html

Topic:

Spoj 8073 The area of the Union of Circleshttps://www.spoj.pl/problems/CIRU/Spoj 3863 area of circleshttps://www.spoj.pl/problems/VCIRCLES/Spoj 8119 CIRU2https://www.spoj.pl/problems/CIRUT/Expansion of the Circle area HDU 3467 Song of the Sirenhttp://acm.hdu.edu.cn/showproblem.php?pid=3467HDU 3239 Jiajia ' s Robot (recommended)http://acm.hdu.edu.cn/showproblem.php?pid=3239Very clever one problem, I read the AC Daniel Blog in the message to know the method.method See AC Daniel Blog in a message: http://hi.baidu.com/aekdycoin/blog/item/12267a4e9476153bafc3abbd.html 　　

The area of the convex polygon and

First read the AC Daniel's blog Learned O (n^3) method, and later in doing codeforces found O (N^2*logn) method, but also not cumbersome

AC Daniel's Blog: http://hi.baidu.com/aekdycoin/blog/item/fbe5a03232c71952ad4b5fcc.html

　　Codeforces Round #83 DIV1 's e-question using O (n^3) method to not lose the 49th set of data, and then study the other Daniel's convex polygon intersection code

Http://codeforces.com/contest/107/status/E

First read the Dagon code found in fact his code has a problem, codeforces data actually did not find out. And then looked at the Syntax_error code,

Found that he was using a similar method of trapezoidal dissection, complexity O (N^2*LOGN), decisive learning

Title: Http://codeforces.com/contest/107/problem/E

For details: http://www.cnblogs.com/ch3656468/archive/2011/10/17/2215551.html

　　

One of the topics is to give some points and tell you which points have connections between them, and there are no other intersections between the lines except the endpoints (sometimes these segments are processed by themselves).

And then the subject asks you to beg

1 area of each small polygon

2 How many K polygons have no points or segments inside

3 contour lines of the graphs that surround these segments

This kind of problem is similar to the method, in many Daniel's blog can be found in the same way.

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 Daniel's blog:http://watashi.ws/blog/970/andrew-stankevich-3-solution/

Isun Daniel's Blog:http://hi.baidu.com/xh176233756/blog/item/29652646f0e870006a63e5cb.html

Topic:

POJ 1092 Farmlandhttp://poj.org/problem?id=1092ZOJ 2361 AREAS/SGU 209http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=2361A good question, Watashi blog has a problem-solving reportPOJ 3743 LL ' s cakehttp://poj.org/problem?id=3743POJ 2164 Find the Borderhttp://poj.org/problem?id=2164

　　Three-dimensional geometry

On-line about the three-dimensional geometry of the content is very few, the code and the topic is not how to search, I also cut a few questions

Two to the question in the front coordinate rotation:

Harbin Online Contest 2010Http://acm.hrbeu.edu.cn/index.php?act=problem&id=1006&cid=16Three-dimensional coordinate rotation. This must have an account to be submitted, there is the second sample in sample Input "275" changed to "270"Fzu 2002 Shade of Hallelujah Mountain (2010 Fuzhou Regional)http://acm.fzu.edu.cn/problem.php?pid=2002
SGU Dungeonhttp://acm.sgu.ru/problem.php?contest=0&problem=110Three-dimensional light reflectionFzu 1981 Three Kingdoms (2010 Fuzhou online game)http://acm.fzu.edu.cn/problem.php?pid=1981Coordinate mapping, I started with the map has been tle, had to change to no map codeUVA 11275 3D TrianglesHttp://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem &problem=2250HDU 4042 is the enhanced version of this problem, I use the same code ACFor the bizarre accuracy of this question, 0.000001, I'm not dealing with it. HDU 4042 Fireworks (2011 Beijing Online game) 　　 http://acm.hdu.edu.cn/showproblem.php?pid=4042 It's a good question. (Problem solving report:Http://hi.baidu.com/%D0%A1%CE%E4rj/blog/item/0114bb2dcd4cdef78b13991d.html )HDU 4087 Aletter to Programmers (2011 Beijing live Match)http://acm.hdu.edu.cn/showproblem.php?pid=4087Three-dimensional rotation matrix + matrix acceleration

Some other topics:

Eoj 283 Target Practicehttp://202.120.106.94/onlinejudge/problemshow.php?pro_id=283Search + GeometryPOJ 1688 Dolphin Poolhttp://poj.org/problem?id=1688There are several ways to do this question.POJ 1981 Circle and Pointshttp://poj.org/problem?id=1981It's a classic topic.POJ 3675 Telescopehttp://poj.org/problem?id=3675Common areas of circles and polygonsPOJ 1259 the Picnichttp://poj.org/problem?id=1259Maximum convex hole, computed geometry + DPPOJ 1586 three Sides make a Trianglehttp://poj.org/problem?id=1586The topic content is very simple, the method is also very obvious, but want to AC not easy, the accuracy is very disgusting of a question, I was looked discuss only then had 　　 HDU 3629 Convex (recommended)http://acm.hdu.edu.cn/showproblem.php?pid=3629A good topic, this question has two kinds of ideas:1) http://apps.topcoder.com/wiki/display/tc/TCO%2710+Online+Round+42) 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 game)http://acm.hdu.edu.cn/showproblem.php?pid=3644Originally wanted to use simulated annealing water, the result hovering between WA and tle cannot acFzu 1973 how many stars (recommended) (2010 Fuzhou online game)http://acm.fzu.edu.cn/problem.php?pid=1973A more classic topicPOI2007 axis of symmetry OSIhttp://www.zybbs.org/JudgeOnline/problem.php?id=1100A very sharp topic, test instructions is to judge the number of symmetrical axis polygon, the original do this problem is the complexity of O (n^2) to solve,This time O (n^2) resolute not, plus randomization also can not, finally in the guidance of the problem solving report to solve this problem. First time to find computational geometryProblem can still be solved by the method of string.Online Search of Problem solving report: http://hi.baidu.com/nplusnplusnplu/blog/item/d260baef2e9e9c5879f055cb.html

"Turn" [thematic learning] [computational geometry]