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            Temple of Dune
            Time Limit: 1000MS Memory Limit: 65536K
            Total Submissions: 211 Accepted: 82

            Description

            The Archaeologists of the Current Millenium (ACM) now and then discover ancient artifacts located at the vertices of regular polygons. In general it is necessary to move one sand dune to uncover each artifact. After discovering three artifacts, the archaeologists wish to compute the minimum number of dunes that must be moved to uncover all of them.

            Input

            The first line of input contains a positive integer n, the number of test cases. Each test case consists of three pairs of real numbers giving the x and y coordinates of three vertices from a regular polygon.

            Output

            For each line of input, output a single integer stating the fewest vertices that such a polygon might have. You may assume that each input case gives three distinct vertices of a regular polygon with at most 200 vertices.

            Sample Input

            4
            10.00000 0.00000 0.00000 -10.00000 -10.00000 0.00000
            22.23086 0.42320 -4.87328 11.92822 1.76914 27.57680
            156.71567 -13.63236 139.03195 -22.04236 137.96925 -11.70517
            129.400249 -44.695226 122.278798 -53.696996 44.828427 -83.507917
            

            Sample Output

            4
            6
            23
            100
            

            Source



            題目大意是給出三個(gè)點(diǎn)的(x,y)坐標(biāo),要求輸出一個(gè)邊數(shù)最小的正多邊形的邊數(shù),使這三個(gè)點(diǎn)恰好在

            這個(gè)正多邊形上面。其實(shí)這個(gè)三角形和這個(gè)正多邊形是共外接圓,由外接圓的圓心出發(fā),三角形的三

            條邊可以把圓分成三份,每份圓弧所對(duì)應(yīng)的圓心角分別為arg[0],arg[1]和arg[2],正多邊形把圓弧

            分成相等的n份,每份對(duì)應(yīng)的圓心角為2*pi/n。其實(shí)三角形的三個(gè)角就分別占用了若干等份正多邊形

            所劃分的圓弧,最后也就只要求arg[0],arg[1],arg[2]和2*pi的最大公約數(shù)(gcd)即可。但是這里是

            個(gè)角度都是浮點(diǎn)數(shù),所以還定義一個(gè)浮點(diǎn)數(shù)的gcd,計(jì)算浮點(diǎn)數(shù)的gcd可以利用math.h的函數(shù)fmod

            (x,y)表示x%y。例如3.5%0.3=0.2,x%y的結(jié)果為不超過y的一個(gè)浮點(diǎn)數(shù)。下面寫了一個(gè)fmod(x,y)自己

            的實(shí)現(xiàn)。
            double fmod(double x, double y)
            {
             return x-floor(x/y)*y;
            }
            有了fmod函數(shù)以后,就可以用它來求gcd了!
            double fgcd(double a, double b)
            {
             double t;
             if(dblcmp(a-b) == 1)  //a>b
             {
              t=a;
              a=b;
              b=t;
             }
             if(dblcmp(a) == 0) return b;
             return fgcd(fmod(b,a),a);
            }

            posted on 2008-06-28 15:18 飛飛 閱讀(1297) 評(píng)論(3)  編輯 收藏 引用 所屬分類: ACM/ICPC

            FeedBack:
            # re: POJ 2335 浮點(diǎn)數(shù)的gcd
            2008-08-16 04:56 | ecnu_zp
            果然能從alpc大牛這里學(xué)到東東。。。(*^__^*) 嘻嘻……  回復(fù)  更多評(píng)論
              
            # re: POJ 2335 浮點(diǎn)數(shù)的gcd
            2008-11-24 23:06 | 11
            大牛啊。。最近我都在學(xué)習(xí)你的blog呢。。。

            寫的不錯(cuò)啊!!!  回復(fù)  更多評(píng)論
              
            # re: POJ 2335 浮點(diǎn)數(shù)的gcd
            2008-12-04 23:44 | yumi
            敬愛的……都不更新了  回復(fù)  更多評(píng)論
              
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