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.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
思路:
关键是找到小数点移动的方向和距离。规律如下
浮点数 小数点下标 第一个非0数的下标 指数
12345 5 0 5 (5-0)
123.45 3 0 3 (3-0)
0.00123· 1 4 -2 (1 - 4 + 1)
0.000345 1 5 -3 (1 - 5 + 1)
坑点:0要写成0.000*10^0的形式。
/*
浮点数 小数点下标 第一个非0数的下标 指数
12345 5 0 5 (5-0)
123.45 3 0 3 (3-0)
0.00123· 1 4 -2 (1 - 4 + 1)
0.000345 1 5 -3 (1 - 5 + 1)
*/
#include <cstdio>
#include <cstring>
#include <string>
#include <iostream>
using namespace std;
// 返回第一个小数点的位置
int indexOfPoint(char num[])
{
for(int i = 0; i < strlen(num); i++)
{
if(num[i] == '.')
return i;
}
return strlen(num);
}
//返回第一个非零整数的位置
int indexOfFirst(char num[])
{
for(int i = 0; i < strlen(num); i++)
{
if(num[i] > '0' && num[i] <= '9')
return i;
}
return -1; //返回-1表示是0
}
// 得到标准格式
string get(char n1[], int n)
{
int point; // 小数点的下标
int first; // 第一个非零数字的下标
//先计算第一个浮点数
point = indexOfPoint(n1); //小数点的位置
first = indexOfFirst(n1); //第一个非零数字的位置
string s1 = "0.";
if(first != -1)
{
// 标准格式的指数
int index = point - first;
index = index > 0 ? index : index + 1;
// 计算有效位上的数字
int i = 0;
while(i < n)
{
if(first < strlen(n1) && n1[first] != '.')
{
s1 += n1[first];
i++;
}
else if(first >= strlen(n1))
{
s1 += "0";
i++;
}
first++;
}
s1 += "*10^";
s1 += to_string(index);
}
else
{
for(int i = 0; i < n; i++)
s1 += "0";
s1 += "*10^";
s1 += "0"; // 0.000要求为0.000*10^0
}
return s1;
}
int main()
{
char n1[110], n2[110];
int n;
scanf("%d", &n);
scanf("%s", n1);
scanf("%s", n2);
string s1 = get(n1, n);
string s2 = get(n2, n);
if(s1 == s2)
printf("YES %s\n", s1.c_str());
else
printf("NO %s %s\n", s1.c_str(), s2.c_str());
return 0;
}