Problem H
Scientific Grading
You recently started working as a TA (teaching assistant) for your university’s Scientific Computing class. Today, Professor introduced the scientific notation, where numbers are written in the form $m \times 10^ n$ with a real number $m$ (the significand) and an integer $n$ (the exponent). At the end of class, she gave students the following assignment.
Given two numbers $x$, $y$ in scientific notation, perform the following four arithmetic operations:
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$x + y$
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$x - y$
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$x \times y$
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$x / y$
As a strict grader, you decided to write a program to grade students’ answers. You mark a solution correct if and only if both relative and absolute errors are less than $10^{-9}$ (not including $10^{-9}$). If the correct answer is $0$, then $0$ is the only acceptable answer. Otherwise, a student’s answer $z$ will be compared to the correct answer $\tilde{z}$, and the relative and absolute errors are computed as $\frac{|z - \tilde{z}|}{|\tilde{z}|}$ and $|z - \tilde{z}|$, respectively.
Input
The first line of input contains the value of $x$, and the second line contains the value of $y$. The next four lines contain a student’s answer to $x+y$, $x-y$, $x \times y$, and $x/y$. All numbers are in the form of <SIGNIFICAND>e<EXPONENT>. The significand $m$ starts with a sign (+ or -), followed by one digit, a period (.), and exactly nine digits. The exponent $n$ also starts with a sign (+ or -) and is followed by an integer between $0$ and $10^9$, inclusively. The value is computed by $m \times 10^ n$. The value $0$ is always represented as +0.000000000e+0, and for any nonzero values the first digit of their significand is not $0$. It is guaranteed that $x$ and $y$ are both nonzero.
Output
For each student solution, output Correct if it is considered correct and Incorrect otherwise. The first line of output indicates if the student’s solution to $x+y$ is correct, the second line indicates if their solution to $x-y$ is correct, the third line indicates if their solution to $x \times y$ is correct, and the fourth line indicates if their solution to $x/y$ is correct.
| Sample Input 1 | Sample Output 1 |
|---|---|
+2.000000000e+1 +3.000000000e+2 +3.200000000e+2 -2.800000000e+2 +6.000000000e+3 +6.666666667e-2 |
Correct Correct Correct Correct |
| Sample Input 2 | Sample Output 2 |
|---|---|
+1.000000000e-1 +1.000000000e-1 +2.000000003e-1 +1.000000000e-18 +1.000000002e-2 +1.000000001e+0 |
Incorrect Incorrect Incorrect Incorrect |
