[UVa] 10233 - Dermuba Triangle

題目網址: http://goo.gl/sx05kx

題意:

(from luckycat)

解 法: 找出所求正方形為第幾層，設第 0 個三角形上方頂點為座標原點，配合三角形重心的性質，就可以找出三角形重心的座標。

TAG: Math,

注意:

程式碼:

	/**
	* Tittle: 10233 - Dermuba Triangle
	* Author: Cheng-Shih, Wong
	* Date: 2015/05/22
	*/
	// 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) )
	typedef long long ll;
	// declarations
	ll a, b;
	ll la, lb;
	double ax, ay, bx, by;
	// functions
	// main function
	int main( void )
	{
	double r3d2 = sqrt(3)/2.0;
	// input
	while( scanf( "%lld%lld", &a, &b )==2 ) {
	// solve
	++a; ++b;
	la = sqrt(a);
	lb = sqrt(b);
	if( la*la < a ) ++la;
	if( lb*lb < b ) ++lb;
	a -= (la-1)*(la-1);
	b -= (lb-1)*(lb-1);
	ay = ((la-1) + ((a&1LL) ? 2:1)/3.0)*r3d2;
	by = ((lb-1) + ((b&1LL) ? 2:1)/3.0)*r3d2;
	ax = 0.5*(a-la);
	bx = 0.5*(b-lb);
	double dx = ax-bx;
	double dy = ay-by;
	// output
	printf( "%.3lf\n", sqrt( dx*dx+dy*dy ) );
	}
	return 0;
	}

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