Problem Understanding

The problem asks us to read two integers a and b from the input, calculate their sum c = a + b, and print the result in a specific format: a + b = c. The output must include spaces between the numbers and the operators. The constraints are that the absolute values of a and b can be up to $10^9$.

This is a very basic problem that tests fundamental I/O (Input/Output) operations and arithmetic in a programming language.

Solution Approaches

All three provided solutions follow the same fundamental logic:

1. Read the input line.
2. Parse the two integers a and b.
3. Calculate the sum c = a + b.
4. Print the formatted string.

The differences lie in the syntax and specific functions used for I/O and string formatting, which correspond to the programming language used.

Approach 1: C++ with iostream (Simple & Efficient)

This approach uses the standard C++ input/output library <iostream> (often included via the convenience header <bits/stdc++.h>). It reads the integers directly into variables using the extraction operator >> and prints the result using the insertion operator <<.

Explanation:

• cin >> a >> b; reads whitespace-separated tokens from standard input and parses them as integers, storing them in a and b.
• cout << ... ; prints a sequence of variables and string literals to standard output. The << operator is chained to build the output line. String literals like " + " are used to insert the required formatting characters.

Code:

#include <bits/stdc++.h>

using namespace std;

int main()
{
    int a, b;
    cin >> a >> b;
    int c = a + b;
    cout << a << " + " << b << " = " << c;
    return 0; 
}

Complexity:

• Time Complexity: $O(1)$ - The operations (reading 2 integers, one addition, printing) take constant time.
• Space Complexity: $O(1)$ - Only three integer variables are stored.

Analysis: This is a standard, idiomatic C++ solution. It is efficient and concise. The use of #include <bits/stdc++.h> is common in competitive programming for convenience, though it's technically non-standard. The code is straightforward and easy to read.

Approach 2: Python with f-string (Concise & Readable)

This approach uses Python's modern f-string formatting to create the output string in a single, highly readable line.

Explanation:

• input().split() reads a line from standard input and splits it into a list of strings based on whitespace.
• map(int, ...) applies the int() function to each item in the list, converting them to integers.
• print(f"{a} + {b} = {a + b}") uses an f-string (formatted string literal). The expressions inside the curly braces {} are evaluated and their string representations are embedded directly into the string. This avoids the need for multiple arguments to print or manual string conversion.

Code:

a, b = map(int, input().split())
print(f"{a} + {b} = {a + b}")

Complexity:

• Time Complexity: $O(1)$ - The operations are constant time relative to the number of integers (2).
• Space Complexity: $O(1)$ - A few variables are stored.

Analysis: This is the most elegant and "Pythonic" solution among the three. F-strings are the preferred method for string formatting in modern Python (3.6+). This code is not only short but also very clear about what the final output will look like.

Approach 3: Python with print's Separator (Idiomatic Python)

This approach uses the built-in capabilities of Python's print function to handle the formatting, avoiding explicit string interpolation.

Explanation:

• a, b = map(int,input().split()) is identical to Approach 2 for reading input.
• print(a,"+",b,"=",c) passes multiple arguments to the print function. By default, print separates these arguments with a single space. This perfectly matches the required output format.

Code:

a, b = map(int,input().split())
c = a+b
print(a,"+",b,"=",c)

Complexity:

• Time Complexity: $O(1)$
• Space Complexity: $O(1)$

Analysis: This is another excellent, idiomatic Python solution. It leverages the default behavior of the print function, making the code extremely simple and direct. It is just as good as the f-string approach for this specific problem.

Complexity Analysis

All three approaches are optimal for this problem, as the constraints are very small and the problem itself is computationally trivial.

Key Insights

• Fundamental I/O: The core of this problem is mastering how to read from standard input (stdin) and write to standard output (stdout) in your chosen language.
• String Formatting: Most languages provide multiple ways to format strings (e.g., concatenation, placeholders, f-strings, stream insertion). Knowing the idiomatic way in your language makes code cleaner and more maintainable.
• Problem Decomposition: Even simple problems can be broken down into steps: Input -> Process -> Output. This structure is fundamental to all programming.

Common Pitfalls

• Incorrect Spacing: The problem requires specific spacing (a + b = c). A common mistake is to print without spaces (e.g., a+b=c) or with an incorrect number of spaces. Using language features like C++'s cout << " + " << or Python's print with multiple arguments helps avoid this.
• Data Type Overflow: The constraints state |a|, |b| <= 10^9. Their sum can be up to $2 \times 10^9$. In C++, a standard 32-bit int can hold values up to approx. $2.14 \times 10^9$, so it is sufficient here. However, if the limits were higher, one would need to use a 64-bit integer type (e.g., long long in C++ or the default int in Python 3, which has arbitrary precision).
• Input Parsing Errors: Not handling the input format correctly (e.g., failing to split the string on whitespace) can lead to runtime errors or incorrect values.

Practice Problems

1. CB02 - Tính tổng 2 số: The original problem this is based on. It likely has a simpler output format without the full expression.
2. Hello, World!: A classic first problem on many platforms to test basic output.
3. A + B: The "Hello, World!" of competitive programming, found on many online judges. It requires reading two integers and printing their sum.