1001：Exponentiation

最新推荐文章于 2021-05-25 19:49:44 发布

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本文介绍了一种使用Java实现的精确计算大数幂的方法，解决了传统计算机系统在处理非常大的数值精度时出现的问题。该算法利用了BigDecimal类来确保计算结果的准确性，并通过String类的方法实现了特定的输出格式。

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Description

Problems involving the computation of exact values of very large magnitude and precision are common. For example, the computation of the national debt is a taxing experience for many computer systems.

This problem requires that you write a program to compute the exact value of Rⁿ where R is a real number ( 0.0 < R < 99.999 ) and n is an integer such that 0 < n <= 25.

Input

The input will consist of a set of pairs of values for R and n. The R value will occupy columns 1 through 6, and the n value will be in columns 8 and 9.

Output

The output will consist of one line for each line of input giving the exact value of R^n. Leading zeros should be suppressed in the output. Insignificant trailing zeros must not be printed. Don't print the decimal point if the result is an integer.

Sample Input

Sample Output

548815620517731830194541.899025343415715973535967221869852721
.00000005148554641076956121994511276767154838481760200726351203835429763013462401
43992025569.928573701266488041146654993318703707511666295476720493953024
29448126.764121021618164430206909037173276672
90429072743629540498.107596019456651774561044010001
1.126825030131969720661201

总结下来是一个求大数幂的算法，额外要求一是要输出所有的小数位而不是用科学计数法表示，二是如果小数点前为0的话要去掉0，三是要去除小数点所有的尾数0。代码如下：

import java.util.*;
import java.math.*;

public class Main {
	public static void main(String[] args){		
		Scanner in = new Scanner(System.in);
		while (in.hasNext()) {
			BigDecimal R = in.nextBigDecimal();
			int n = in.nextInt();
			R = R.pow(n);
			String str = R.stripTrailingZeros().toPlainString();
			if (str.startsWith("0."))
				str = str.substring(1);
			System.out.println(str);
		}
	}
}

需要注意的有这么几点：一是BigDecimal类，二是String.stripTrailingZeros()方法，该方法可以除去所有尾部0，三是String.toPlainString()方法，该方法负责将本该科学表示的小数变成输出所有小数位的方式（即不带指数段），四是String类的startsWith()方法和substring()方法，分别用来验证和截取字符串。