CF 1029368 - A+B
The task is to read two integer values and compute their sum. The input consists of two numbers presented in a simple textual format, and the output is a single integer representing their arithmetic addition. There is no hidden structure such as graphs, sequences, or queries.
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Solve time: 33s
Verified: yes
Solution
Problem Understanding
The task is to read two integer values and compute their sum. The input consists of two numbers presented in a simple textual format, and the output is a single integer representing their arithmetic addition.
There is no hidden structure such as graphs, sequences, or queries. The entire problem reduces to correctly parsing integer input and producing their sum as output.
From a constraints perspective, this kind of problem is designed to be trivial in computational complexity. Even if the integers are large, standard 32-bit or 64-bit integer arithmetic is sufficient in Python because Python integers are unbounded. The limiting factor is not computation but correctness of input parsing and output formatting. Any algorithm beyond O(1) time is unnecessary.
The main edge cases are not algorithmic but representational. If the two integers are large or negative, a naive implementation that assumes positive values or fixed-width integers in lower-level languages could fail. For example, an input like -5 10 must correctly produce 5, and 10^18 10^18 must not overflow in languages without big integer support. Another subtle case is formatting: printing extra spaces or lines would be considered incorrect even though the arithmetic is correct.
Approaches
A brute-force interpretation of the problem might involve simulating addition digit by digit, as one would do manually on paper. This would read both numbers as strings, align them from the least significant digit, and compute a carry across positions. This approach is correct and mirrors how addition is defined, but it is unnecessary overhead for a problem that already provides numbers in machine-readable integer form. It also introduces avoidable complexity in parsing and edge handling.
The key observation is that the input is already in a form that the language runtime can interpret directly as integers. Once parsed, the addition operation is a single constant-time instruction in Python. The entire problem collapses into input parsing followed by one arithmetic operation.
The brute-force digit simulation becomes redundant because the structure of the problem does not require handling arbitrary representations or malformed numeric strings. The abstraction level is already at the arithmetic domain.
| Approach | Time Complexity | Space Complexity | Verdict |
|---|---|---|---|
| Digit-by-digit simulation | O(d) | O(d) | Correct but unnecessary |
| Direct integer addition | O(1) | O(1) | Accepted |
Algorithm Walkthrough
- Read the first integer from input. This represents the first operand in the sum.
- Read the second integer from input. This represents the second operand.
- Compute the sum of the two integers using the built-in arithmetic operator.
- Output the computed result as a single integer.
Each step is direct because the problem does not require transformation or intermediate data structures. The only real responsibility is ensuring that input tokens are correctly interpreted as integers.
The reason step ordering matters is purely related to input consumption. Reading must happen before arithmetic, and output must happen after both values are fully parsed.
Why it works
The correctness comes from the fact that integer addition is a well-defined total operation over the set of integers. Since the inputs are guaranteed to be valid integers in textual form, parsing converts them into exact mathematical values. The final operation is then identical to computing $a + b$ in arithmetic, without approximation or truncation. No intermediate state or invariant beyond correct parsing is required.
Python Solution
import sys
input = sys.stdin.readline
a = int(input().strip())
b = int(input().strip())
print(a + b)
The solution reads two lines from standard input and converts each line into an integer using Python’s built-in parsing. The .strip() call ensures that trailing newline characters do not interfere with conversion, although int() would also handle whitespace correctly.
The final print statement outputs the sum directly. There is no need for formatting adjustments because the problem expects a single integer output.
A subtle implementation detail is that reading with sys.stdin.readline avoids unnecessary overhead compared to input() in tight competitive programming environments, although for this problem it is not performance-critical.
Worked Examples
Consider an input where the first number is 3 and the second number is 5.
| Step | a | b | a + b |
|---|---|---|---|
| After reading input | 3 | - | - |
| After reading input | 3 | 5 | - |
| After computation | 3 | 5 | 8 |
This trace shows that the algorithm simply accumulates the two parsed integers and produces their sum without any transformation.
Now consider a case with negative numbers, such as -4 and 10.
| Step | a | b | a + b |
|---|---|---|---|
| After reading input | -4 | - | - |
| After reading input | -4 | 10 | - |
| After computation | -4 | 10 | 6 |
This confirms that sign handling is inherently supported by integer parsing and arithmetic, requiring no additional logic.
Complexity Analysis
| Measure | Complexity | Explanation |
|---|---|---|
| Time | O(1) | Only two integer parses and one arithmetic operation are performed |
| Space | O(1) | No auxiliary data structures are used beyond two integer variables |
The constant-time nature of the solution makes it trivially efficient under any reasonable constraints. Memory usage is also constant since no input scaling affects storage requirements.
Test Cases
import sys, io
def run(inp: str) -> str:
sys.stdin = io.StringIO(inp)
a = int(sys.stdin.readline().strip())
b = int(sys.stdin.readline().strip())
return str(a + b)
# provided samples (hypothetical)
assert run("3\n5\n") == "8", "sample 1"
assert run("-4\n10\n") == "6", "sample 2"
# custom cases
assert run("0\n0\n") == "0", "zero case"
assert run("1000000000\n1000000000\n") == "2000000000", "large numbers"
assert run("-1\n-1\n") == "-2", "negative numbers"
assert run("1\n-100\n") == "-99", "mixed sign"
| Test input | Expected output | What it validates |
|---|---|---|
| 0, 0 | 0 | identity behavior |
| large positive integers | sum | no overflow issues conceptually |
| negative inputs | correct sign handling | correctness of parsing |
| mixed signs | correct arithmetic cancellation | general correctness |
Edge Cases
One important case is when both inputs are zero. The algorithm reads both values correctly and produces zero, since integer parsing preserves exact values and addition identity holds.
Another case involves large integers that exceed typical 32-bit limits. For example, inputs like 1000000000000000000 and 1000000000000000000 are safely handled in Python because integer arithmetic automatically promotes to arbitrary precision, and the algorithm still performs a single addition operation.
Negative values are also straightforward. For an input like -7 and 3, parsing preserves the sign and the addition operator correctly applies integer arithmetic rules, producing -4 without any special-case logic.