PAT 1060. Are They Equal (25)

1060. Are They Equal (25)

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 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 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.d₁...d_N*10^k" (d₁>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

 需要注意的是的情况为0.00， 0012.3 0.00123等等

#include <iostream>
#include <string>

using namespace std;

int CalculateRadix(string &num)
{
    int i = 0;
    while (i < num.size())
    {
        if (num[i] == '.')
        {
            num.erase(i, 1);
            break;
        }
        i++;
    }

    return i;
}

int erasezero(string &num)
{
    int cnt = 0;
    string::iterator it = num.begin();
    while (it!=num.end()&& (*it) == '0')
    {
        it = num.erase(it);
        cnt++;
    }
    return cnt;
}

string CalculateCoeff(string num, int significantNum, int &radix)
{
    string coeff;
    radix -= erasezero(num);
    if (num.empty())
        radix = 0;
    if (num.size() >= significantNum)
        coeff.assign(num.begin(), num.begin() + significantNum);
    else
        coeff = num + string(significantNum - num.size(), '0');

    return "0." + coeff;
}

int main()
{
    string num1, num2;
    int significantNum;
    cin >> significantNum >> num1 >> num2;

    int radix1, radix2;
    radix1 = CalculateRadix(num1);
    radix2 = CalculateRadix(num2);
    
    string coeff1 = CalculateCoeff(num1, significantNum, radix1);
    string coeff2 = CalculateCoeff(num2, significantNum, radix2);

    if (coeff1 == coeff2&&radix1 == radix2)
        cout << "YES" << " " << coeff1 << "*10^" << radix1;
    else
        cout << "NO" << " " << coeff1 << "*10^" << radix1 << " " << coeff2 << "*10^" << radix2;
}