結果

問題 No.8031 （物理学）長距離相互作用
ユーザー 37zigen
提出日時 2018-02-28 17:07:50
言語 Java
(openjdk 23)
結果
AC  
実行時間 691 ms / 10,000 ms
コード長 4,567 bytes
コンパイル時間 2,957 ms
コンパイル使用メモリ 84,432 KB
実行使用メモリ 46,196 KB
最終ジャッジ日時 2024-12-25 21:07:35
合計ジャッジ時間 10,556 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 11
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ソースコード

diff # 

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws CloneNotSupportedException {
		new Main().run();
	}

	void run() throws CloneNotSupportedException {
		solver();
	}

	void solver() throws CloneNotSupportedException {
		Scanner sc = new Scanner(System.in);
		double potential = 0;
		double balancer = 1;
		double volume = 1;
		// 単位構造は(1,0,0),(0,1,0),(0,0,1)
		// 逆格子ベクトルは(1,0,0),(0,1,0),(0,0,1)

		double[][] rt = new double[16][];
		for (int i = 0; i < 8; i++) {
			rt[i] = new double[] { (i >> 2) % 2 / 2.0, (i >> 1) % 2 / 2.0, i % 2 / 2.0 };
		}
		for (int i = 0; i < 8; i++) {
			rt[i + 8] = new double[] { (i >> 2) % 2 / 2.0 + 1.0 / 4.0, (i >> 1) % 2 /2.0 + 1.0 / 4.0,
					i % 2 / 2.0 + 1.0 / 4.0 };
		}
		double[] qt = new double[16];
		for (int i = 0; i < 16; i++) {
			qt[i] = sc.nextDouble();
		}
		potential += shortRangeInteraction(rt, qt, balancer);
		potential += longRangeInteracion(rt, qt, balancer, 1).real;

		System.out.println(potential);
	}

	double shortRangeInteraction(double[][] rt, double[] qt, double balancer) {
		double ret = 0;
		int L = 50;
		for (int x = -L; x <= L; x++) {
			for (int y = -L; y <= L; y++) {
				for (int z = -L; z <= L; z++) {
				    if(Math.sqrt(x*x+y*y+z*z)>L)continue;
					for (int i = 0; i < qt.length; i++) {
						double[] nrt = new double[] { rt[i][0] + x, rt[i][1] + y, rt[i][2] + z };
						if (nrt[0] == 0 && nrt[1] == 0 && nrt[2] == 0)
							continue;
						ret += qt[i] / norm(nrt) * erfc(Math.sqrt(balancer) * norm(nrt));
					}
				}
			}
		}
		return ret;
	}

	Complex longRangeInteracion(double[][] rt, double[] qt, double balancer, double volume)
			throws CloneNotSupportedException {
		Complex ret = new Complex(0, 0);
		int L = 50;
		for (int x = 0; x < L; x++) {
			for (int y = 0; y < L; y++) {
				for (int z = 0; z < L; z++) {
					if (x == 0 && y == 0 && z == 0)
						continue;
					if(Math.sqrt(x*x+y*y+z*z)>L)continue;
					// Gは逆格子ベクトル
					double[] G = new double[] { 2 * Math.PI * x, 2 * Math.PI * y, 2 * Math.PI * z };
					// r2=G^2
					double r2 = 4 * Math.PI * Math.PI * (x * x + y * y + z * z);
					ret.add(structuralFactor(qt, G, rt).multiply(1 / r2 * Math.exp(-r2 / (4 * balancer))));
				}
			}
		}
		ret = ret.multiply(4 * Math.PI / volume);
		// consider the effect of the self potential
		ret.add(new Complex(-2 * qt[0] * Math.sqrt(balancer / Math.PI), 0));
		return ret;
	}

	double norm(double[] vector) {
		double ret = 0;
		for (int i = 0; i < vector.length; i++) {
			ret += vector[i] * vector[i];
		}
		ret = Math.sqrt(ret);
		return ret;
	}

	Complex structuralFactor(double[] qt, double[] G, double[][] rt) throws CloneNotSupportedException {
		Complex ret = new Complex(0, 0);
		for (int i = 0; i < qt.length; i++) {
			ret.add(exp(dotProduct(G, rt[i])).multiply(qt[i]));
		}
		return ret;
	}

	// =exp(-i(theta))
	Complex exp(double theta) {
		return new Complex(-Math.cos(theta), -Math.sin(theta));
	}

	double dotProduct(double[] v1, double[] v2) {
		double ret = 0;
		for (int i = 0; i < v1.length; i++) {
			ret = v1[i] * v2[i];
		}
		return ret;
	}

	// fractional error in math formula less than 1.2 * 10 ^ -7.
	// although subject to catastrophic cancellation when z in very close to 0
	// from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2
	public static double erf(double z) {
		double t = 1.0 / (1.0 + 0.5 * Math.abs(z));

		// use Horner's method
		double ans = 1 - t * Math.exp(-z * z - 1.26551223
				+ t * (1.00002368 + t * (0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (0.27886807
						+ t * (-1.13520398 + t * (1.48851587 + t * (-0.82215223 + t * (0.17087277))))))))));
		if (z >= 0)
			return ans;
		else
			return -ans;
	}

	public static double erfc(double z) {
		return 1 - erf(z);
	}

	class Complex implements Cloneable {
		double real;
		double imaginal;

		public Complex(double real, double imaginal) {
			this.real = real;
			this.imaginal = imaginal;
		}

		void add(Complex c) {
			this.real += c.real;
			this.imaginal += c.imaginal;
		}

		void show() {
			System.out.println("real:" + real + " comples:" + imaginal);
		}

		Complex multiply(double a) throws CloneNotSupportedException {
			this.real *= a;
			this.imaginal *= a;
			return (Complex) this.clone();
		}
	}

	Complex add(Complex... c) {
		Complex ret = new Complex(0, 0);
		for (int i = 0; i < c.length; i++) {
			ret.add(c[i]);
		}
		return ret;
	}

	void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}
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