"Turn" calculation Geometry topic recommendation

I'm going to turn around and do a good job of calculating geometry.

Original address: http://blog.sina.com.cn/s/blog_49c5866c0100f3om.html

In fact, it is not recommended, just the topic they have done, and even some of the topic has not AC, let in the struggle. The reason why we recommend computational geometry is that I feel that the computational geometry of various ACM algorithms is a more practical algorithm and has important uses in many fields.
The characteristics of computational geometry problems and the essentials of doing them:
1. Most of them will not be very difficult, and a few questions are ingenious
2. To do computational geometry problems, templates are important and templates must be highly reliable.
3. Pay attention to the organization of the Code, because the topic of computational geometry is easy to 200 lines of code, most of which are templates. If the code is chaotic, it will seriously affect the correct rate of the problem.
4. Attention to accuracy control.
5. To use integers wherever possible, think of ways to expand the data (one-fold, or expand Sqrt2). Because integers do not consider floating-point errors, and operations are faster than floating-point.

One. Understanding of point, line, polygon, shape basic relation, dot product cross product

POJ 2318 TOYS (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=2318
POJ 2398 Toy Storage (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=2398
A rectangle, which is divided into n squares by a number of lines, gives the coordinates of a point and asks you which point the point is in.
Knowledge Point: In fact, the point in the convex quadrilateral within the judgment, if the use of cross product properties, can be two-point solution.

POJ 3304 Segments
http://acm.pku.edu.cn/JudgeOnline/problem?id=3304
Knowledge Points: Line segments intersect with lines, note the handling of coincident points at enumeration

POJ 1269 Intersecting Lines
http://acm.pku.edu.cn/JudgeOnline/problem?id=1269
Knowledge Points: The intersection of lines to determine the intersection intersection

POJ 1556 the Doors (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1556
Knowledge Point: Simple graph theory + simple calculation geometry, first to find the intersection of line segments, and then use the DIJ to find the shortest way.

POJ 2653 Pick-up Sticks
http://acm.pku.edu.cn/JudgeOnline/problem?id=2653
Knowledge Point: or segment intersection judgment

POJ 1066 Treasure Hunt
http://acm.pku.edu.cn/JudgeOnline/problem?id=1066
Knowledge Points: Segment intersection judgment, but must first understand "the door of the least" is what the matter.

POJ 1410 Intersection
http://acm.pku.edu.cn/JudgeOnline/problem?id=1410
Knowledge Points: segments intersect with rectangles. Correctly understand the definition of intersection in test instructions.
See: http://hi.baidu.com/novosbirsk/blog/item/68c682c67e8d1f1d9d163df0.html

POJ 1696 Space Ant (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1696
A good topic for the Tehran Division. Need to understand the properties of dot product

POJ 3347 Kadj Squares
http://acm.pku.edu.cn/JudgeOnline/problem?id=3347
My method is extremely wretched. Complex intersection of segments. This topic is a typical application of the computational geometry of expanded data operations, and the enlargement of the square root is twice times the number of decimal places avoided.

POJ 2826 an easy problem?! Recommended
http://acm.pku.edu.cn/JudgeOnline/problem?id=2826
Q: The two lines form a graph that can hold much rain. Very simple easy problem, to consider all the circumstances. You don't look at discuss to see if you can AC. (I can hardly) hint that the water is falling vertically from the sky.

POJ 1039 Pipe
http://acm.pku.edu.cn/JudgeOnline/problem?id=1039
It is also the judgment of line and line intersection, plus the idea of enumeration.

POJ 3449 Geometric Shapes
http://acm.pku.edu.cn/JudgeOnline/problem?id=3449
Determines whether the geometry intersects, but the input output is disgusting.
In addition, there is a knowledge point, is to give a square (side not parallel to the axis) of the two diagonal vertices, you need to find two other points. Must master its methods.

POJ 1584 a Round Peg in A Ground Hole
http://acm.pku.edu.cn/JudgeOnline/problem?id=1584
Knowledge Points: Point to line distance, circle intersects Polygon, polygon is convex

POJ 2074 Line of Sight (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=2074
The key to solving the problem of line of sight is to find the linear equation with two points and the intersection point of Line and line. Data has a trick, be careful.

Two. Convex hull problem

POJ 1113 Wall
http://acm.pku.edu.cn/JudgeOnline/problem?id=1113
Knowledge points: Bare convex hull problem, convex hull circumference plus circumference.

POJ scrambled Polygon
http://acm.pku.edu.cn/JudgeOnline/problem?id=2007
Knowledge point: Convex hull, output scheme by polar angle sequence

POJ 1873 the fortified Forest (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1873
World Final water problem, first convex bag, and then search. Because of the small size, you can use bit operation enumeration.
See: http://hi.baidu.com/novosbirsk/blog/item/333abd54c7f22c52574e0067.html

POJ 1228 Grandpa ' s Estate (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1228
To find the number of convex hull, many people find convex hull template is more out of the point, although the area can get the correct answer, but in this topic will be problematic. In addition, the properties of convex hull should be understood correctly.

POJ 3348 Cows
http://acm.pku.edu.cn/JudgeOnline/problem?id=3348
Convex hull Area calculation

Three. Area problem, formula problem

POJ 1654 Area
http://acm.pku.edu.cn/JudgeOnline/problem?id=1654
Knowledge point: Calculate polygon area with a forward area (cross product)

POJ 1265 Area
http://acm.pku.edu.cn/JudgeOnline/problem?id=1265
POJ 2954 Triangle
http://acm.pku.edu.cn/JudgeOnline/problem?id=2954
Pick the application of the formula, the relationship between the polygon and the whole hour. (There is a gcd relationship)

Four. Semi-planar Cross

The main application of semi-planar intersection is to determine whether the polygon has a kernel, and also to solve some problems related to the feasible region of the linear equation group (that is, those in high school).

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.
Semi-planar intersection + binary solution 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.

Five. To calculate the geometric background, the key to solving the problem is other problems (data structure, combinatorial mathematics, or enumeration ideas).
If the main road of the classic discretization + scan line of the topic, ACM Players must do the problem

POJ 1151 Atlantis (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1151
POJ 1389 area of simple polygons
http://acm.pku.edu.cn/JudgeOnline/problem?id=1389
Rectangular discretization, Segment tree processing, rectangular area intersection

POJ 1177 Picture (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1177
Rectangular discretization, Segment tree processing, the circumference of the rectangular intersection, the data of this topic is relatively strong. The segment tree must be efficient.

POJ 3565 Ants (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3565
The idea of adjustment in computational geometry is somewhat like a sort. The judgment to use to intersect the segment.
See: http://hi.baidu.com/novosbirsk/blog/item/fb668cf0f362bec47931aae2.html

POJ 3695 rectangles
http://acm.pku.edu.cn/JudgeOnline/problem?id=3695
Is the area of the rectangular intersection, but because it is a number of queries, and the rectangle is not many, the use of combinatorial mathematics in the principle of tolerance to solve the most suitable. The line tree is a pass-through method, but there are other possible ways to do it, except for the line segment tree.

POJ 2002 Squares
http://acm.pku.edu.cn/JudgeOnline/problem?id=2002
Enumeration idea, the number of points on the plane can be composed of the maximum number of squares, points of the hash

POJ 1434 Fill The cisterns! (recommended)
http://acm.pku.edu.cn/JudgeOnline/problem?id=1434
At first, I was dizzy, ready to get a line tree. Actually, it's just a simple two-point.

Six. Stochastic algorithm
POJ 2420 A Star not a Tree?
http://acm.pku.edu.cn/JudgeOnline/problem?id=2420
The Fermat point of the polygon. The so-called fee horse Point, is a polygon in a point P, the point to other points of the shortest distance. The polygon above the quadrilateral has no formula to calculate the cost of the horse point, so the random variable step-size greedy method can be used.
See: http://hi.baidu.com/novosbirsk/blog/item/75983f138499f825dd54019b.html

Seven. Analytic geometry
This kind of topic I am not good at, so do not have much, the template is very important. Of course, it is useful to use the properties of cross product and dot product skillfully.
POJ 1375 Intervals
http://acm.pku.edu.cn/JudgeOnline/problem?id=1375
Knowledge Points: A point in the outside circle to seek the tangent of a circle

POJ 1329 Circle Through three Points
http://acm.pku.edu.cn/JudgeOnline/problem?id=1329
Seeking Triangle circumscribed circle

POJ 2354 Titanic
http://acm.pku.edu.cn/JudgeOnline/problem?id=2354
The distance of two points on the spherical surface is obtained, and the coordinates of geographical latitude and longitude are given.

POJ 1106 Transmitters
http://acm.pku.edu.cn/JudgeOnline/problem?id=1106
Angle sort, know slope angle, use atan function.

POJ 1673 Exocenter of A TRIANGLE
http://acm.pku.edu.cn/JudgeOnline/problem?id=1673
can be transformed into a triangular vertical heart problem.

Eight. Rotating Jam

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 (difficult)
http://acm.pku.edu.cn/JudgeOnline/problem?id=3608
The nearest distance of two convex bags. My jam is always WA. Depressed.

Nine. Other questions
POJ 1981 Circle and Points
http://acm.pku.edu.cn/JudgeOnline/problem?id=1981
To find the maximum number of points on a plane that can be covered by a unit circle

"Turn" calculation Geometry topic recommendation