PAT Advanced 1060 Are They Equal (25分)

Posted 2021-03-12 littlepage

If a machine can save only 3 significant digits, the float numbers 12300 and 12358.9 are considered equal since they are both saved as 0 with simple chopping. Now given the number of significant digits on a machine and two float numbers, you are supposed to tell if they are treated equal in that machine.

Input Specification:

Each input file contains one test case which gives three numbers N, A and B, where N (<) is the number of significant digits, and A and B are the two float numbers to be compared. Each float number is non-negative, no greater than 1, and that its total digit number is less than 100.

Output Specification:

For each test case, print in a line YES if the two numbers are treated equal, and then the number in the standard form 0.d[1]...d[N]*10^k (d[1]>0 unless the number is 0); or NO if they are not treated equal, and then the two numbers in their standard form. All the terms must be separated by a space, with no extra space at the end of a line.

Note: Simple chopping is assumed without rounding.

Sample Input 1:

3 12300 12358.9

 

Sample Output 1:

YES 0.123*10^5

 

Sample Input 2:

3 120 128

 

Sample Output 2:

NO 0.120*10^3 0.128*10^3

大数题用Java解决比较简便，我们要注意的是，4和6测试点，这两个case中，

4测试点是 0.00000001和0.1，这样有没有考虑小数的测试点呢？

6测试点是0和00000.000，有没有考虑这样的数字呢？

import java.math.BigDecimal;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt(), expo1 = 0, expo2 = 0; 
        BigDecimal b1 = sc.nextBigDecimal();
        BigDecimal b2 = sc.nextBigDecimal();
        BigDecimal num = new BigDecimal("1");
        BigDecimal num2 = new BigDecimal("0.1");
        BigDecimal num3 = new BigDecimal("0");
        BigDecimal ten = new BigDecimal("10");
        while(b1.compareTo(num) > 0) {
            b1 = b1.divide(ten);
            expo1++;
        }
        while(b1.compareTo(num2) < 0 && b1.compareTo(num3) > 0) {
            b1 = b1.multiply(ten);
            expo1--;
        }
        while(b2.compareTo(num) > 0) {
            b2 = b2.divide(ten);
            expo2++;
        }
        while(b2.compareTo(num2) < 0 && b2.compareTo(num3) > 0) {
            b2 = b2.multiply(ten);
            expo2--;
        }
        String s = "";
        for(int i = 0; i < N + 2; i++) s += "0";
        String sub1 = b1.toString(), sub2 = b2.toString();
        if(!b1.toString().contains(".")) sub1 += ".";
        if(!b2.toString().contains(".")) sub2 += ".";
        sub1 = (sub1 + s).substring(0, N + 2);
        sub2 = (sub2 + s).substring(0, N + 2);
        if(expo1 == expo2 && sub1.equals(sub2)) {
            System.out.printf("YES %s*10^%d", sub1, expo1);
        }
        else {
            System.out.printf("NO %s*10^%d %s*10^%d", sub1, expo1, sub2, expo2);
        }
    }
}