CF 105066A - It's Time to Submit

CF 105066A - It's Time to Submit

Rating: -
Tags: -
Solve time: 54s
Verified: yes

Solution

Problem Understanding

The task is intentionally minimal: we are given a single integer T and must decide whether it is possible to obtain the string "YES" by simply printing the sample output provided in the problem statement. In other words, the problem is not asking us to compute anything from T, but to determine whether the existence of the sample output being something specific affects the validity of a trivial submission strategy.

The input consists of one integer T with a very small range from 0 to 10. Despite this, the value of T is irrelevant to the final decision in any meaningful computational sense, because no transformation or condition is defined based on it. The output is either "YES" or "NO", depending on whether a particular meta-condition about the sample output holds.

The only subtlety lies in the note: the sample output is not "NO". This matters because the intended joke structure of the problem is that if the sample output were "NO", then any submission would be contradictory, making AC impossible. Since the sample output is not "NO", there is no contradiction preventing a valid submission.

Edge cases are essentially nonexistent from a computational perspective, but a careless reader might still attempt to branch on T. For example, for input 0, one might incorrectly assume that only 0 yields "YES" because it appears in the sample. However, no such dependency exists. The correct behavior is consistent for all valid inputs.

Approaches

A brute-force interpretation would try to model what “outputting the sample output is enough to get AC” could mean, perhaps simulating different outputs or checking conditions depending on T. But since the problem never defines any transformation or constraint involving T, any such simulation is purely artificial. Even if one enumerated all possible interpretations of “possible to AC”, the decision reduces to a constant check about whether a contradiction exists in the statement.

The key observation is that the value of T is irrelevant to the output logic. The only meaningful condition is whether the statement rules out the possibility of a valid submission strategy. The note explicitly guarantees that the sample output is not "NO", which removes the only pathological case where the problem would become impossible. Therefore, every input must yield "YES".

The brute-force view would require O(1) per hypothetical interpretation but with unnecessary branching logic. The optimal solution collapses everything into a constant-time answer.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force Interpretation	O(1)	O(1)	Overthinking
Optimal Constant Answer	O(1)	O(1)	Accepted

Algorithm Walkthrough

1. Read the integer T from input. It is not used further, but must still be consumed to match input format.
2. Immediately output "YES" because the problem statement guarantees no contradictory condition that would invalidate a submission-by-printing strategy.

Why it works

The problem reduces to a single global property of the statement: whether there exists any contradiction that would make all submissions invalid. The note explicitly removes the only such contradiction case. Since nothing else depends on T, the answer cannot vary across inputs, and a constant output is correct for all cases.

Python Solution

import sys
input = sys.stdin.readline

T = input().strip()
print("YES")

The solution reads the input line to satisfy format requirements, even though T is never used in computation. This is important in competitive programming environments where ignoring input entirely can lead to runtime errors due to unread buffered input.

The decision logic is reduced to a single print statement. There are no edge conditions, loops, or branches because the problem definition does not introduce any.

Worked Examples

Example 1

Input:

0

Execution trace:

Step	Action	State
1	Read input	T = 0
2	Decide output	result = "YES"
3	Print	"YES"

This confirms that even for the smallest possible input, the output remains unchanged. The value 0 has no influence on computation.

Example 2 (constructed)

Input:

7

Execution trace:

Step	Action	State
1	Read input	T = 7
2	Decide output	result = "YES"
3	Print	"YES"

This demonstrates that even for a different valid integer, the algorithm behaves identically. The invariance across inputs confirms that no hidden dependency exists on T.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	Only a single input read and one print operation
Space	O(1)	No auxiliary data structures are used

The constraints allow up to 10, which is trivial. The solution executes in constant time regardless of input size, well within limits.

Test Cases

# helper: run solution on input string, return output string
import sys, io

def run(inp: str) -> str:
    sys.stdin = io.StringIO(inp)
    import sys as _sys
    input = _sys.stdin.readline
    T = input().strip()
    return "YES"

# provided sample
assert run("0\n") == "YES", "sample 1"

# custom cases
assert run("1\n") == "YES", "any small input should work"
assert run("10\n") == "YES", "upper bound input"
assert run("5\n") == "YES", "middle value"
assert run("0\n") == "YES", "minimum boundary"

Test input	Expected output	What it validates
0	YES	minimum input case
10	YES	maximum constraint boundary
5	YES	generic mid-range value
1	YES	smallest positive value

Edge Cases

The only implicit edge case is whether the logic incorrectly depends on T. For input 0, the algorithm reads T = 0 and still prints "YES", showing no conditional branching exists.

For input 10, the same flow occurs: the value is read, ignored, and "YES" is printed. This confirms that no hidden constraints or parity checks exist in the problem logic, and the solution is stable across the entire input domain.