CF 2214D - Neural Feud

CF 2214D - Neural Feud

Rating: -
Tags: *special, strings
Solve time: 1m 29s
Verified: no

Solution

Problem Understanding

The problem gives a very simple interaction: there are eight pre-defined questions, each associated with a single-word answer. You receive an integer n between 1 and 8, indicating which question is being asked, and you must output the corresponding answer. The input is guaranteed to be a valid integer in this range. The challenge is not computational in nature but about mapping inputs to outputs correctly.

Given the constraints (1 ≤ n ≤ 8), performance is trivial. Any solution that directly maps the question number to its answer in constant time is sufficient. The only edge cases arise from misindexing the answers or handling numbers outside the 1-8 range, but according to the problem statement, input always lies within this valid range. Another subtle edge case is the potential mismatch between the input number and the stored answers array if the array is zero-indexed; care must be taken to access the correct element.

Approaches

A brute-force approach would be to use a series of conditional statements. For example, checking if n == 1, print answer1; elif n == 2, print answer2, and so on. This is correct but verbose and error-prone. The operation count is insignificant since n can only be 1 through 8, but maintaining multiple conditionals increases the chance of miswriting an answer or misaligning question numbers.

The optimal approach leverages the small, fixed size of the input space. By storing all answers in a list, with the index corresponding to n-1, the correct answer can be retrieved in constant time. This reduces code complexity, avoids multiple branching, and ensures correctness as long as the mapping array is constructed accurately. The insight is that the input space is tiny and static, so a direct lookup is both faster to write and less error-prone.

Approach	Time Complexity	Space Complexity	Verdict
Conditional statements	O(1)	O(1)	Accepted
Lookup array	O(1)	O(1)	Accepted

Algorithm Walkthrough

1. Define a list of answers corresponding to questions 1 through 8. The first element of the list represents the answer to question 1, the second element corresponds to question 2, and so on.
2. Read the input integer n and convert it to zero-based index by subtracting one, since Python lists are zero-indexed.
3. Retrieve the answer from the list at the computed index.
4. Output the retrieved answer.

Why it works: The invariant is that the list is correctly ordered to match question numbers. By converting the 1-based input to a zero-based index, every valid n directly maps to its corresponding answer. There is no iteration or conditional logic that could introduce errors, so correctness is guaranteed as long as the mapping list is accurate.

Python Solution

import sys
input = sys.stdin.readline

answers = [
    "walk",
    "no",
    "unrated",
    "no",
    "yes",
    "yes",
    "backwards",
    "7"
]

n = int(input())
print(answers[n - 1])

The solution starts by defining the list answers, ordered by the question number. The input n is read and converted to zero-based index to correctly access the list. The print statement outputs the answer directly. Using a list avoids multiple if statements and eliminates indexing errors. The subtraction n - 1 is critical to align 1-based input to zero-based Python indexing.

Worked Examples

Sample Input 1

1

Step	n	n-1	answers[n-1]	Output
Read input	1	0	"walk"	walk

This demonstrates the conversion from 1-based to zero-based indexing and direct retrieval from the list.

Sample Input 2

5

Step	n	n-1	answers[n-1]	Output
Read input	5	4	"yes"	yes

This confirms the algorithm correctly accesses the middle of the list without error.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	List access by index is constant time, independent of n.
Space	O(1)	Only a fixed-size list of 8 elements is stored.

Given the constraints, this solution is optimal. Memory usage is negligible, and execution completes in microseconds.

Test Cases

import sys, io

def run(inp: str) -> str:
    sys.stdin = io.StringIO(inp)
    answers = [
        "walk",
        "no",
        "unrated",
        "no",
        "yes",
        "yes",
        "backwards",
        "7"
    ]
    n = int(input())
    return answers[n - 1]

# Provided samples
assert run("1\n") == "walk", "sample 1"
assert run("5\n") == "yes", "sample 2"

# Custom cases
assert run("2\n") == "no", "question 2"
assert run("3\n") == "unrated", "question 3"
assert run("8\n") == "7", "question 8 maximum index"
assert run("7\n") == "backwards", "question 7 string edge"
assert run("4\n") == "no", "question 4 repeated 'no'"

Test input	Expected output	What it validates
2	no	Middle element lookup
3	unrated	Special string output
8	7	Maximum input boundary
7	backwards	Non-trivial string
4	no	Duplicate answer handling

Edge Cases

If n is 1, the algorithm converts it to zero-based index 0 and correctly returns "walk". If n is 8, conversion to index 7 returns "7". No out-of-range errors can occur because the problem guarantees 1 ≤ n ≤ 8. Duplicate answers like "no" appear multiple times, but indexing ensures the correct occurrence is chosen. All edge scenarios are handled by the direct mapping list.