C++ Program to Floating Point Comparison with Epsilon with Explanation
C++
Hard
C++ Data Types
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This problem helps you practice core C++ fundamentals in a practical way. It builds intuition around floating, point, equal. Let’s break it down step by step so you can implement it confidently.
Problem Statement
Compare floating point numbers correctly considering precision errors. This teaches floating point arithmetic issues.
Logic: Check if absolute difference is less than small epsilon value
Input Format
Two floating-point numbers a and b.
Output Format
Print whether the two numbers are equal or not equal (considering precision).
Constraints
• Floating point values
• Direct == comparison should be avoided
Concept Explanation
Floating point numbers are stored in approximate binary form.
Because of this, calculations like 0.1 + 0.2 may not give exactly 0.3.
So direct comparison using == can fail.
Step-by-Step Logic
1.Define a small value called epsilon (example: 0.000001).
2.Calculate the absolute difference between a and b.
3.If abs(a - b) < epsilon:
• Treat the numbers as equal.
4.Otherwise:
• Treat them as not equal.
Code Solution
This explanation is written for learning purposes and to help beginners understand the concept clearly.
void question13_float_comparison() {
float a = 0.1f + 0.1f + 0.1f;
float b = 0.3f;
float epsilon = 0.0001f;
cout << "a = " << a << ", b = " << b << endl;
if(a == b) {
cout << "Equal (using ==)" << endl;
} else {
cout << "Not equal (using ==)" << endl;
}
if(abs(a - b) < epsilon) {
cout << "Equal (using epsilon method)" << endl;
} else {
cout << "Not equal (using epsilon method)" << endl;
}
}
Output Example
Input:
a = 0.1 + 0.2
b = 0.3
Common Mistakes
- Misreading input/output format.
- Not handling constraints and edge cases.
- Off-by-one errors in loops.
- Forgetting to reset variables between test cases (if any).
Solution Guide
Problem
Compare floating point numbers correctly considering precision errors. This teaches floating point arithmetic issues.
Logic: Check if absolute difference is less than small epsilon value
Input / Output
Input
Two floating-point numbers a and b.
Output
Print whether the two numbers are equal or not equal (considering precision).
Constraints
• Floating point values
• Direct == comparison should be avoided
Examples
Input:
a = 0.1 + 0.2
b = 0.3
Explanation
Concept Explanation
Floating point numbers are stored in approximate binary form.
Because of this, calculations like 0.1 + 0.2 may not give exactly 0.3.
So direct comparison using == can fail.
Step-by-Step Explanation
1.Define a small value called epsilon (example: 0.000001).
2.Calculate the absolute difference between a and b.
3.If abs(a - b) < epsilon:
• Treat the numbers as equal.
4.Otherwise:
• Treat them as not equal.
Details
Common Mistakes
- Misreading input/output format.
- Not handling constraints and edge cases.
- Off-by-one errors in loops.
- Forgetting to reset variables between test cases (if any).
Official Solution
void question13_float_comparison() {
float a = 0.1f + 0.1f + 0.1f;
float b = 0.3f;
float epsilon = 0.0001f;
cout << "a = " << a << ", b = " << b << endl;
if(a == b) {
cout << "Equal (using ==)" << endl;
} else {
cout << "Not equal (using ==)" << endl;
}
if(abs(a - b) < epsilon) {
cout << "Equal (using epsilon method)" << endl;
} else {
cout << "Not equal (using epsilon method)" << endl;
}
}
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