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Many people actually know that the secondary derivative of the function can be used to judge the concave and convex of the function, but many people forget how to prove it. Here I will prove it again. Proof: If f (x) is continuous in (A, B) and can be imported twice, if f'' (x)> 0, the function is concave. If f (x) is greater than 0, the function is convex. Preface: First, we will give several theorems and
Grandpa's estate Time limit:1000 ms Memory limit:10000 K Total submissions:10851 Accepted:2953 DescriptionBeing the only living descendant of his grandfather, Kamran the believer inherited all of the grandpa's belongings. the most valuable one was a piece of Convex Polygon shaped farm in the grandpa's birth village. the farm was originally separated from the neighboring farms by a thick rope hooked to some spikes
Link: http://poj.org/problem? Id = 2079 triangle Time limit:3000 Ms Memory limit:30000 K Total submissions:8173 Accepted:2423 DescriptionGiven n distinct points on a plane, your task is to find the triangle that have the maximum area, whose vertices are from the given points. InputThe input consists of several test cases. the first line of each test case contains an integer N, indicating the number of points on the plane. each of the following n lines contai
glass is like the polygon in Figure 1, you have just two ways to put it on the table, since all the other ways are not stable. however, the glass like the polygon in Figure 2 has three ways to be appreciated. Pay attention to the cases in Figure 3. We consider that those glasses are not stable. Inputthe input file contains several test cases. the first line of the file contains an integer t representing the number of test cases. For each test case, the first line is an integer n
Link: http://acm.sgu.ru/problem.php? Contest = 0 problem = 253 http://acm.hust.edu.cn/vjudge/contest/view.action? Cid = 27464 # Problem/a253. Theodore roosevelttime limit per test: 0.5 sec. Memory limit per test: 65536 kbinput: Standard Output: Standard Danger! Sudden attack on Russia! These are Americans "again", but this time they are serious. giant aircraft-carrier "Theodore Roosevelt" is entering the Baltic Sea. at one o 'clock American aircraft launched from the carrier bombed Petrozavodsk
Original question connection: http://poj.org/problem? Id = 1113 Give N points. You can see a wall so that the distance between all points and the wall is no less than l. Length of the wall .. Idea: first obtain the convex hull of N points, and then build a wall based on the convex hull. One part of the wall is the convex hull length, and the other part is a circl
Title Address: http://acm.hdu.edu.cn/showproblem.php?pid=3685Idea: First, the polygon center of gravity, placed on the edge must be convex edge. Determine if the center of gravity falls between the edges (find the distance between the line and the point to the line).40 04 08 44 4Note that the center of gravity cannot be on the perpendicular of the convex edge end.#include Hdu 3685 Rotational Painting (Polyg
the estimates. Sample Input 9 100200 400300 400300 300400 300400 400500 400500 200350 200200 200 Sample Output 1628 HintThe result is rounded to the nearest integer. Code: This question is to find a convex hull based on the given points and calculate its perimeter, plus the four extra 1/4 circles, that is, the circumference of a circle. Gift Wrapping is to tie a rope to a point and wrap around the outermost point. The key step is 1. Determine a st
Http://poj.org/problem? Id = 1228 The question is to give you n points and ask if you can determine the unique convex hull; Because these vertices are all boundary points, you only need to determine whether each boundary has> = 3 vertices. If yes, no. Why? It is assumed that there are two points, that is, there are only two endpoints of a line segment, so there can be any point out of the line to form a new convex
Http://acm.hdu.edu.cn/showproblem.php? PID = 1, 1392 Question: Given N points in a two-dimensional plane, use a shortest rope to enclose all points and find the length of the rope. Solution: Convex Hull template. There are many algorithms for Convex packets. Adrew is used here. Note these groups of test data 1 1 1 3 0 0 1 0 2 0 Output Data 0.00 2.00 1 # include HDU 1392 surround the trees (Geometric
Question: http://poj.org/problem? Id = 3348 Convex Hull area Algorithm: first sort the horizontal coordinates of the point, calculate the lower convex edge from left to right, and then calculate the upper convex edge from right to left. the complexity is slightly higher than the Graham scan method (traversing the point set twice), but it is easier to implement #i
Link: http://acm.hdu.edu.cn/showproblem.php? PID = 1, 4946 There are n people. In the position (XI, Yi), the speed is vi. If one person can come to that point before all others, this point is contracted by this person. The number of contracted (fish ponds) area is infinite. Idea: Find out the maximum speed. Only the person with the maximum speed can contract an infinite area (because the high-speed person will catch up with the low-speed person sooner or later ). The boundary between two people
Poj 3990 Fermat Point in Quadrangle convex hull and Fermat Point Question: Evaluate the Fermat point of a quadrilateral. Analysis: The simulated annealing either times out or wa, and the data in this question does not want to pass the random algorithm .. In fact, the fenma point of the quadrilateral is very simple. If it is a convex quadrilateral, The fenma point is the diagonal intersection point, and if i
After finding the convex hull, the violent enumeration edge is $check$, note that the convex hull is a line (or two lines) of the case to output $no$#include That's it."POJ 1228" Grandpa ' s Estate convex bag
containing a single integer n (3 OutputPrint exactly one line for each test case. The line should contain exactly and numbers separated by one space. These numbers is the coordinates of the centre of gravity. Round the coordinates to the nearest number with exactly, digits after the decimal point (0.005 rounds up to 0.01). Note that the centre of gravity may outside the polygon, if it shape is not convex. If There is such a case in the
Topic PortalTest instructions: To find the shortest route, so that any point on the line away from the castle at least L distanceAnalysis: Convex hull First, answer = length of convex hull + circumference of circle with L as radius/************************************************* author:running_time* Created time:2015/10/25 11:00:48* File N Ame:P oj_1113.cpp ************************************************
Test instructions is a world with many countries, each with n buildings, including a power station and N-1 buildings, all of which are surrounded by a convex hull that is the size of the country. A missile that explodes within a country can cause the country to power down.Step 1: Find the convex hull of each country (I use the horizontal sort is all kinds of pits, change the fork by the sort before, mainly
RescueTime limit:2000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)Total submission (s): 398 Accepted Submission (s): 296Problem descriptioni work at NASA Outer Space Rescue team which needs much courage and patient. In daily life, I always receive a lot of mission, and I must complete it right now.Today, team leader announced me that there are a huge spaceship dropping anchor in the out space, and we should reach there For rescue. As a working principle, at first, we should c
input contains several test cases, each of the which describes a hypothetical forest. Each test case is begins with a line containing a single integer n, 2 The input ends with a empty test case (n = 0).OutputFor each test case, compute a subset of the trees such that, using the wood from that subset, the remaining trees can E Nclosed in a single fence. Find the subset with minimum value. If more than one such minimum-value subset exists, choose one with the smallest number of trees. For simplic
Determines whether a polygon can be placed in a convex hull. Perform a convex hull for all vertices, and add both the key and common vertices to the convex hull set. If a vertex in the graph storm set is a polygon vertex, no is output. Else Yes View code # Include # Include # Include # Include Using Namespace STD;Typedef _ int64 LLD; Const Double
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