Programming Exercises(using POJ)

本文探讨了在Java中处理高精度数学运算的方法,重点介绍了使用BigDecimal类进行精确计算的技巧,包括去除尾数无效零、转换为字符串及幂运算等功能。同时,文章提供了输入输出的示例,如使用Scanner类读取整数和浮点数,以及如何正确处理输入中的特殊字符。


[2020/05/21]

Problem 1000

coefficient of difficulty:simple input and output

A+B Problem

  • Time Limit: 1000MS
  • Memory Limit: 10000K
  • Total Submissions: 504351
  • Accepted: 284571

Description: Calculate a+b
Input: Two integer a,b (0<=a,b<=10)
Output :Outputa+b
Sample Input :1 2
Sample Output :3

Java Points:

Class Scanner for reading interger:

Scanner in = new Scanner(System.in);
int a = in.nextInt();
int b = in.nextInt();

Problem 1001

coeficient of difficulty: simple input and master of some basic class

Exponentiation

  • Time Limit: 500MS
  • Memory Limit: 10000K
  • otal Submissions: 193661
  • Accepted: 46400

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
95.123 12
0.4321 20
5.1234 15
6.7592 9
98.999 10
1.0100 12

Sample Output

548815620517731830194541.899025343415715973535967221869852721
.00000005148554641076956121994511276767154838481760200726351203835429763013462401
43992025569.928573701266488041146654993318703707511666295476720493953024
29448126.764121021618164430206909037173276672
90429072743629540498.107596019456651774561044010001
1.126825030131969720661201

Solution

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


public class Main {
    public static void main(String[] args) throws InterruptedException {
        // write your code here
        Scanner cin = new Scanner(System.in);
        while(cin.hasNext()){
            BigDecimal a = cin.nextBigDecimal();
            int b = cin.nextInt();
            String res = a.pow(b).stripTrailingZeros().toPlainString();
            res = (res.indexOf("0.")==0)?(res.substring(1)):res;
            System.out.println(res);
        }
    }
}

Java Points

1. Function next() in Class Scanner:
The result of code below :

Scanner in = new Scanner(System.in);
String a = in.next();
String b = in.next();

When getting an input:

Great commodities!

Variables a and b will respectively storage:

a : "Great"
b : "commodities!"

Summary: in.next() can read strings devided by space into corresponding variables.

2. Class in Java for accurate calculation:
Java provides a class BigDecimal for precise compute, and this class has some useful functions:

  1. stripTrailingZeros(): strip Insignificant zeros at the tail of a big decimal.
  2. toPlainString(): convert BigDecimal to String not formatted with scientific notation .
  3. pow(): power function of the BigDecimal.

Notation: Use function nextBigDecimal() in class Scanner to read a big decimal.

3. Tips of input in the question stem:
Here it requires a set of pairs of values rather than a pair of values, so we need give it a circulation to read.
4. Spliting a string with “.”:
Use escape character to accomplish it as follow:

String[] strings = resultBigDecimal.split("\\.");

Otherwise strings array’s length will be zero.
Notation: When matching “. { [ ( ? $ ^ *” these peculiar character, add "\"before them.
5. Presentation Error:
It means your data is correct but is not formatted in proper way.

(Mathcad+Simulink仿真)基于扩展描述函数法的LLC谐振变换器小信号分析设计内容概要:本文围绕“基于扩展描述函数法的LLC谐振变换器小信号分析设计”展开,结合Mathcad与Simulink仿真工具,系统研究LLC谐振变换器的小信号建模方法。重点利用扩展描述函数法(Extended Describing Function Method, EDF)对LLC变换器在非线性工作条件下的动态特性进行线性化近似,建立适用于频域分析的小信号模型,并通过Simulink仿真验证模型准确性。文中详细阐述了建模理论推导过程,包括谐振腔参数计算、开关网络等效处理、工作模态分析及频响特性提取,最后通过仿真对比验证了该方法在稳定性分析与控制器设计中的有效性。; 适合人群:具备电力电子、自动控制理论基础,熟悉Matlab/Simulink和Mathcad工具,从事开关电源、DC-DC变换器或新能源变换系统研究的研究生、科研人员及工程技术人员。; 使用场景及目标:①掌握LLC谐振变换器的小信号建模难点与解决方案;②学习扩展描述函数法在非线性系统线性化中的应用;③实现高频LLC变换器的环路补偿与稳定性设计;④结合Mathcad进行公式推导与参数计算,利用Simulink完成动态仿真验证。; 阅读建议:建议读者结合Mathcad中的数学推导与Simulink仿真模型同步学习,重点关注EDF法的假设条件与适用范围,动手复现建模步骤和频域分析过程,以深入理解LLC变换器的小信号行为及其在实际控制系统设计中的应用。
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