http://acm.hdu.edu.cn/showproblem.php?pid=3918 一个如上图所示的杯子,一开始为空,且杯子的重量不计,沿着杯壁往里面慢慢地倒水,直到杯子倒了为止,最高能往里面倒多少水,求最后水的高度。 做法:将杯身分割成梯形,每个梯形中,重心是在x轴的分量,是往一个方向偏移,也就是有单调性。求出从下往上枚举每个梯形,求出第一个使得杯子倒掉的梯形,然后在这个梯形内部二分,求出水的最高位置
1 /**//* 2 author: AmazingCaddy 3 time: 2011-08-04 15:25:53 4 */ 5 #include <iostream> 6 #include <cstdio> 7 #include <cstring> 8 #include <string> 9 #include <vector> 10 #include <algorithm> 11 #include <stack> 12 #include <queue> 13 #include <complex> 14 #include <cstdlib> 15 #include <cmath> 16 #include <ctime> 17 #include <map> 18 using namespace std; 19 20 const int maxn = 204; 21 const int inf = 0x3fffffff; 22 const double eps = 1e-8; 23 const double pi = acos( -1.0 ); 24 25 int D( double x ) { return ( x < -eps ? -1 : x > eps ); } 26 27 struct point 28  { 29 double x, y; 30 point( ) { } 31 point( double _x, double _y ) : x( _x ), y( _y ) { } 32 void input( ) { scanf( "%lf%lf", &x, &y ); } 33 }; 34 35 point p[ maxn ], q[ maxn ]; 36 double Y[ maxn << 1 ]; 37 38 double mass, ypre, ynow; 39 double x1, x2, x3, x4, Gx, LGx; 40 int pid, qid; 41 42 int myUnique( int n ) 43  { 44 int len = 1; 45 for( int i = 1; i < n; i++ ) 46 if( D( Y[ i ] - Y[ i - 1 ] ) != 0 ) 47 Y[ len++ ] = Y[ i ]; 48 return len; 49 } 50 51 double insection( double y, const point &a, const point &b ) 52  { 53 return ( b.x - a.x ) * ( y - a.y ) / ( b.y - a.y ) + a.x; 54 } 55 56 double get_Gx( double y ) 57  { 58 x3 = insection( y, p[ pid - 1 ], p[ pid ] ); 59 x4 = insection( y, q[ qid - 1 ], q[ qid ] ); 60 double tmp = ( ( x1 + x2 + x3 ) * ( x2 - x1 ) + ( x2 + x4 + x3 ) * ( x4 - x3 ) ) * ( y - ypre ) / 6; 61 tmp = ( tmp + LGx * mass ); 62 return tmp / ( mass + ( x2 - x1 + x4 - x3 ) * ( y - ypre ) / 2 ); 63 } 64 65 66 int main(int argc, char *argv[]) 67  { 68 // freopen( "data.in", "r", stdin ); 69 // freopen( "out", "w", stdout ); 70 int cas, n, m; 71 scanf( "%d", &cas ); 72 while( cas-- ) 73 { 74 scanf( "%d%d", &m, &n ); 75 for( int i = 0; i < m; i++ ) 76 { 77 p[ i ].input( ); 78 Y[ i ] = p[ i ].y; 79 } 80 for( int j = 0; j < n; j++ ) 81 { 82 q[ j ].input( ); 83 Y[ j + m ] = q[ j ].y; 84 } 85 double ans = min( p[ m - 1 ].y, q[ n - 1 ].y ); 86 87 sort( Y, Y + m + n ); 88 int len = myUnique( m + n ); 89 90 pid = 1, qid = 1; 91 92 x1 = p[ 0 ].x, x2 = q[ 0 ].x; 93 mass = 0, LGx = 0, ypre = 0; 94 95 for( int i = 1; i < len && D( Y[ i ] - ans ) <= 0; i++ ) 96 { 97 ynow = Y[ i ]; 98 while( D( p[ pid ].y - ynow ) < 0 ) pid++; 99 while( D( q[ qid ].y - ynow ) < 0 ) qid++; 100 101 Gx = get_Gx( ynow ); 102 // printf( "Gx = %.3lf\n" ); 103 if( D( Gx - p[ 0 ].x ) < 0 || D( Gx - q[ 0 ].x ) > 0 ) 104 { 105 double l = ypre, r = ynow, mid; 106 while( r - l > eps ) 107 { 108 mid = ( l + r ) * 0.5; 109 double gx = get_Gx( mid ); 110 if( D( gx - p[ 0 ].x ) < 0 || D( gx - q[ 0 ].x ) > 0 ) r = mid; 111 else l = mid; 112 } 113 ans = mid; 114 break; 115 } 116 117 mass = mass + ( x2 - x1 + x4 - x3 ) * ( ynow - ypre ) / 2; 118 x1 = x3; 119 x2 = x4; 120 LGx = Gx; 121 ypre = ynow; 122 } 123 printf( "%.3lf\n", ans ); 124 } 125 return 0; 126 } 。
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