题目内容

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 0.123×10⁵ 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 ,  and  , where (＜100) is the number of significant digits, and  and  are the two float numbers to be compared. Each float number is non-negative, no greater than 10¹⁰⁰, 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:

Sample Output 1:

Sample Input 2:

Sample Output 2:

题目要点

本题 25 分，是一道比较复杂的模拟题，既要考虑一些边界情况又要考虑浮点数带来的精度损失，因此处理起来异常棘手。

如果使用Python解这道题，强烈建议使用下面代码中标准库的 decimal 模块。因为题设中已知精确度范围在100以内，如果是小于1的小数，那么可能会精确到小数点百位，对于浮点数来说极易失去精度。如果直接使用输入的字符串类型数据分析，也会遇到麻烦。比如，输入数据可能是如0003.120这样有前导零的不规范数字，还要先将不需要的零去掉。

经过测试，测试点3、5的数据就是需要严格精度的。因此，在做这道题时会出现一个诡异的情况，在通过网上收集的许多测试点后仍然无法完全通过PTA的测试。所以，使用 decimal 模块以定点数存储数据，并充分利用模块提供的一些方法可以极大地提高效率，直接针对问题的核心，避免陷入处理细枝末节的窘境。

源代码

额外测试点

本题有许多边界情况需要考虑，这里提供一些测试点以供参考。