[UVa] 10215 - The Largest/Smallest Box ...

題目網址: http://goo.gl/84B3cM

題意:
(from luckycat)


解 法: 盒子的體積是 (L-2*x)*(W-2*x)*x，微分等於零的時候會有極大/小值，然後 x 等於 0，盒子體積也最小。

TAG: Math

注意: 輸出要加上 machine epsilon 喔~

程式碼:

	/**
	* Tittle: 10215 - The Largest/Smallest Box ...
	* Author: Cheng-Shih, Wong
	* Date: 2015/05/20
	*/
	// include files
	#include <iostream>
	#include <cstdio>
	#include <cstring>
	#include <cmath>
	using namespace std;
	// definitions
	#define FOR(i,a,b) for( int i=(a),_n=(b); i<=_n; ++i )
	#define clr(x,v) memset( x, v, sizeof(x) )
	#define EPS 1e-8
	// declarations
	double l, w;
	// functions
	inline double volume( double x )
	{
	return x*(l-2*x)*(w-2*x);
	}
	// main function
	int main( void )
	{
	double a, b;
	double lpw, lmw;
	// input
	while( scanf( "%lf%lf", &l, &w )==2 ) {
	// solve
	lpw = l+w;
	lmw = l*w;
	a = (lpw + sqrt(lpw*lpw-3*lmw))/6;
	b = (lpw - sqrt(lpw*lpw-3*lmw))/6;
	if( volume(a) < volume(b) ) swap( a, b );
	// output
	printf( "%.3lf 0.000 %.3lf\n", a+EPS, min(l,w)/2.0+EPS );
	}
	return 0;
	}

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