81 lines
1.9 KiB
C++
81 lines
1.9 KiB
C++
#include <cstdio>
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#include <iostream>
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#include <cstring>
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#include <cmath>
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using namespace std;
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double ch[200];
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const double PI = 4 * atan( double( 1 ) );
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//const double PI = 3.1415926;
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int num;
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double is_triangle( double a, double b, double c )
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{
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if( c > a + b )
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return 100;
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else if( c < fabs( a - b ) )
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return -100;
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else
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return acos( ( a * a + b * b - c * c ) / ( 2 * a * b ) );
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}
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double Acos( double a, double b, double c )
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{
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return is_triangle( a, b, c );
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}
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double total_angle( double mid )
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{
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double ans = 0;
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for( int i = 2; i <= num; ++i )
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{
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double t = Acos( ch[i], ch[i-1], mid );
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if( fabs( t ) == 100 )
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return t;
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else
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ans += Acos( ch[i], ch[i-1], mid );
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}
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return ans;
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}
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double Bsearch( double ss, double ee )
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{
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double left = ss, right = ee, mid, sum_angle;
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while( right - left >= 1e-9 )
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{
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mid = ( left + right ) / 2.0;
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double t = total_angle( mid );
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if( fabs( t ) == 100 )
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{
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if( t > 0 )
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right = mid;
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else
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left = mid;
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}
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else
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{
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sum_angle = t + Acos( ch[1] , ch[num], mid );
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if( sum_angle - 2 * PI > 1e-9 )
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right = mid;
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else if( sum_angle - 2 * PI < -1e-9 )
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left = mid;
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else
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return mid;
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}
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}
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return 0;
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}
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int main( )
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{
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int i,j,k,T;
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cin>>T;
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for(i = 1; i <= T; ++i )
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{
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cin>>num;
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for(j = 1; j <= num; ++j )
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cin>>ch[j];
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double ans = Bsearch( fabs( ch[num] - ch[1] ), ch[1] + ch[num] );
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printf( "Case %d: ", i );
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if( ans == 0 )
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puts( "impossible" );
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else
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printf( "%.3lf\n", ans );
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}
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return 0;
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}
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