CF 106370A - Adding Two Integers

Rating: -
Tags: -
Solve time: 22s
Verified: yes

Solution

Problem Understanding

The task is to read two integers representing the two values that need to be combined, then output their sum. The problem is intentionally simple: there is no hidden structure, ordering requirement, or repeated operation. The entire computation is the arithmetic addition of the two provided numbers.

The input contains two integer values. The output should contain exactly one integer, which is the result of adding those two values together.

Because there is only one arithmetic operation to perform, the constraints allow a constant time solution. Even if the values are large, the algorithm does not need to iterate through a range, build a data structure, or perform any search. The only requirement is that the programming language can store and add the input integers correctly. In Python, integer arithmetic automatically handles large values, so overflow is not a concern.

The edge cases are mostly about reading and preserving the values correctly. A common mistake is assuming both numbers are positive. For input -5 3, the correct output is -2, because the operation is ordinary integer addition. Another case is when one value is zero. For input 0 7, the correct output is 7; an implementation that treats zero as missing input or ignores it would fail. A final boundary case is two negative numbers, such as -4 -6, where the correct output is -10.

Approaches

The most direct approach is to try to simulate a more complicated process, such as repeatedly increasing a counter until it reaches the combined value. This would still be correct because each increment represents one unit being added, but it is unnecessary. If the input values were large, this method could require a number of operations proportional to the size of the numbers, making it impractical.

The key observation is that addition is already a primitive operation provided by the language. The problem does not ask us to discover a pattern, optimize a sequence, or process multiple elements. It only asks for the result of one mathematical operation. The brute force idea can be reduced to a single addition because the structure of the problem contains no extra conditions.

The final solution reads the two integers, adds them once, and prints the result.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force	O(	a + b	)
Optimal	O(1)	O(1)	Accepted

Algorithm Walkthrough

Read the two integers from the input. They represent the two values that must be combined.
Add the two integers using the language's built-in arithmetic operation. Since the required result is exactly their sum, no additional processing is needed.
Print the computed sum as the answer.

The reason this works is that integer addition already performs the complete operation described by the problem. There is no intermediate state that needs to be tracked.

Why it works:

The invariant behind the algorithm is that the stored result after the addition operation is exactly the mathematical sum of the two input values. The program starts with the original two numbers, applies the only required transformation, and outputs that transformed value. Since no information is discarded and the operation matches the definition of the answer, the output cannot differ from the required result.

Python Solution

import sys
input = sys.stdin.readline

def solve():
    a, b = map(int, input().split())
    print(a + b)

if __name__ == "__main__":
    solve()

The program begins by reading one line and splitting it into the two integer values. The map(int, ...) conversion ensures that arithmetic is performed on numbers rather than strings.

The addition happens directly in a + b. There is no loop, array, or auxiliary structure because the problem contains only two values. Python integers are used instead of fixed-size machine integers, so the implementation does not need special handling for large inputs.

The final print outputs only the required answer, avoiding extra formatting that could cause a wrong answer.

Worked Examples

For input:

3 5

the execution is:

Step	a	b	result
Read input	3	5	not calculated
Add values	3	5	8
Print answer	3	5	8

This trace shows that the algorithm directly transforms the two input values into their sum without any intermediate computation.

For input:

-7 4

the execution is:

Step	a	b	result
Read input	-7	4	not calculated
Add values	-7	4	-3
Print answer	-7	4	-3

This trace confirms that the algorithm handles signed integers naturally because it relies on normal arithmetic rules.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	Only one addition operation is performed.
Space	O(1)	Only the two input values and the result are stored.

The solution uses a fixed amount of work and memory regardless of the input values. It easily satisfies any reasonable time and memory limits for this problem.

Test Cases

import sys
import io

def solution(inp: str) -> str:
    old_stdin = sys.stdin
    sys.stdin = io.StringIO(inp)
    try:
        a, b = map(int, sys.stdin.readline().split())
        return str(a + b) + "\n"
    finally:
        sys.stdin = old_stdin

# provided-style samples
assert solution("3 5\n") == "8\n", "sample 1"
assert solution("-7 4\n") == "-3\n", "sample 2"

# custom cases
assert solution("0 0\n") == "0\n", "minimum neutral values"
assert solution("1000000000 1000000000\n") == "2000000000\n", "large values"
assert solution("-100 -200\n") == "-300\n", "two negative values"
assert solution("42 0\n") == "42\n", "zero boundary case"

Test input	Expected output	What it validates
`0 0`	`0`	Confirms the algorithm handles zero values correctly.
`1000000000 1000000000`	`2000000000`	Confirms large integer handling.
`-100 -200`	`-300`	Confirms negative addition.
`42 0`	`42`	Confirms that adding zero preserves the other value.

Edge Cases

For the input:

-5 3

the algorithm reads a = -5 and b = 3, then computes a + b, which gives -2. A solution that assumes positive values might incorrectly reject or mishandle the negative number, but the addition operation naturally supports it.

For the input:

0 7

the algorithm stores a = 0 and b = 7, then calculates 0 + 7 = 7. This confirms that zero is treated as a valid value rather than as an absent value.

For the input:

-4 -6

the algorithm computes -4 + (-6) = -10. Since it performs the actual integer operation instead of manually managing signs, it correctly handles the case where both values are negative.