【PAT】A1060 Are They Equal【数字处理】

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 0.123×10^​5
​​ 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 (<100) 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 10
​100
​​ , 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 0.12010^3 0.12810^3

题意

求两个数的科学记数法，如果相同，则输出YES和相应的表达式，如果不相同则输出NO和它们不同的表达式。

思路

因为题目输入少，使用stl库的string类处理会比较方便。对一个字符串执行去除前导0，对小数进行移位使其变成0.a1a2…an(其中a1>0)的形式，对带小数整数通过查找“.”的位置计算它的指数，对于长度不够的形式需要补“0”（如要求输出精度为5，而原有效数字长度只有3的情况，就需要补2个0）等等，经过这些操作得到科学记数法。要注意的点是不能丢失精度，即120的科学记数法是0.12010^3而不是0.1210^3。具体过程看代码注释。

代码

#include <iostream>
#include <string>
#include <cmath>
using namespace std;
string format(string s, int N){
   
   
    long