Problem Understanding

The problem asks us to calculate the perimeter and area of a rectangle given its length (d) and width (r).

Input:

• Two space-separated integers d and r representing the length and width respectively.
• Constraints: 0 < r, d ≤ 5000.

Output:

• First line: the perimeter of the rectangle.
• Second line: the area of the rectangle.

Formulas:

• Perimeter = 2 * (length + width) = 2 * (d + r)
• Area = length * width = d * r

The problem is straightforward, requiring basic arithmetic operations. The main considerations are ensuring correct implementation and handling potential integer overflow, although the given constraints make overflow unlikely for 32-bit integers.

Solution Approaches

Approach 1: Basic Arithmetic with Intermediate Variables

This approach uses intermediate variables to store the inputs and calculated values, making the code extremely readable and easy to understand.

Explanation:

1. Read the two integers d and r from standard input.
2. Calculate the perimeter c using the formula 2 * (d + r).
3. Calculate the area s using the formula d * r.
4. Print c followed by s, each on a new line.

Code:

d, r = map(int, input().split())
c = 2 * (d + r)
s = d * r
print(c)
print(s)

Analysis: This solution is clean and follows a direct translation of the mathematical formulas. It uses descriptive variable names (d for length, r for width, c for perimeter, s for area). It's the most educational and readable version for beginners.

Complexity:

• Time: O(1) - Constant time operations.
• Space: O(1) - Uses a fixed number of variables.

Approach 2: Direct Calculation in Output

This approach minimizes the use of intermediate variables by performing the calculations directly within the print statements.

Explanation:

1. Read the two integers a and b (using generic names) from standard input.
2. Calculate the perimeter (a + b) * 2 and print it immediately.
3. Calculate the area a * b and print it immediately.

Code:

a, b = map(int, input().split())
print((a + b) * 2)
print(a * b)

Analysis: This is a more concise version. It avoids storing the calculated results in separate variables, which can slightly reduce memory usage (though negligible here). It's functionally identical to Approach 1 but written in a more compact style.

Complexity:

• Time: O(1)
• Space: O(1)

Approach 3: C++ with Explicit Casting (Advanced)

This approach uses C++ instead of Python and explicitly handles potential integer overflow by casting to long long.

Explanation:

1. Read two integers a and b using cin.
2. Calculate the perimeter. The expression (a + b) * 2 is cast to long long to ensure the calculation is performed with 64-bit precision, preventing any potential overflow (though not strictly necessary here given the constraints).
3. Calculate the area a * b and cast it to long long for the same reason.
4. Print the results using cout.

Code:

#include <bits/stdc++.h>

using namespace std;

int main()
{
    int a, b;
    cin >> a >> b;
    cout << (long long) (a + b) * 2  << endl;
    cout << (long long ) a * b << endl;
    return 0; 
}

Analysis: This C++ solution demonstrates good practice for competitive programming where input constraints can sometimes be larger than expected. The explicit casting to long long is a defensive programming technique to avoid integer overflow bugs. In Python, integers have arbitrary precision, so this is not a concern, but it's crucial in languages like C++ or Java.

Complexity:

• Time: O(1)
• Space: O(1)

Complexity Analysis

Key Insights

1. Direct Translation: The problem is a direct translation of mathematical formulas into code. There are no complex algorithms or data structures required.
2. Integer Arithmetic: All operations are basic integer arithmetic (addition, multiplication).
3. Input/Output: The focus is on correctly reading two integers and printing two integers.
4. Language Nuances: Python handles large integers automatically, while C++ requires careful attention to data types (int vs long long) to prevent overflow, even if it's not strictly necessary for these specific constraints.

Common Pitfalls

1. Order of Operations: Forgetting parentheses in the perimeter calculation. Writing 2 * d + r would be incorrect (it would calculate 2*d + r instead of 2*(d+r)).
2. Input Parsing: Incorrectly reading the input. Forgetting to convert strings to integers (int() in Python) would cause errors or incorrect output types.
3. Variable Naming: Using confusing variable names can lead to implementation errors, although for this simple problem, it's less likely.
4. Integer Overflow: While not an issue with Python or the given constraints, using int in C++ for much larger values (e.g., up to 2 * 10^9) could cause overflow in the area calculation a * b if a and b are both large. Casting to long long (as in Approach 3) mitigates this.

Practice Problems

1. Circle Calculations: Given the radius r of a circle, calculate its circumference (2 * π * r) and area (π * r^2). This extends the concept to floating-point arithmetic and using a constant for π.
2. Right Triangle: Given the base a and height b of a right-angled triangle, calculate its area (0.5 * a * b) and hypotenuse (sqrt(a^2 + b^2)).
3. Trapezoid: Given the lengths of the two parallel sides a and b and the height h, calculate the area of a trapezoid ((a + b) / 2 * h).