結果

問題 No.3059 Range Tournament
ユーザー qwewe
提出日時 2025-05-14 13:00:57
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 2,319 bytes
コンパイル時間 389 ms
コンパイル使用メモリ 82,064 KB
実行使用メモリ 73,484 KB
最終ジャッジ日時 2025-05-14 13:02:56
合計ジャッジ時間 5,046 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample RE * 2
other RE * 27
権限があれば一括ダウンロードができます

ソースコード

diff # 

import sys

# Set input function to read lines from stdin for potentially faster I/O
input = sys.stdin.readline

def solve():
    """
    Solves the problem for T test cases.
    Reads T, then for each test case reads an integer angle x (in degrees),
    determines if tan(x degrees) is rational, and collects the results.
    Finally, prints all results, each on a new line.
    """
    # Read the total number of test cases.
    T = int(input())
    
    # A list to store the 'Y' or 'N' result string for each test case.
    results = []
    
    # Iterate T times, processing one test case per iteration.
    for _ in range(T):
        # Read the angle x (an integer representing degrees).
        # The problem statement guarantees 0 <= x < 90.
        x = int(input())
        
        # Mathematical background:
        # It can be shown that for an integer angle x (in degrees), 
        # tan(x degrees) is rational if and only if x is a multiple of 45 degrees,
        # excluding angles where tan is undefined (like 90 degrees, 270 degrees, etc.).
        # The relevant theorem involves roots of unity in the field of Gaussian rationals Q(i).
        # If tan(x degrees) is rational, then exp(i * x * pi / 90) must be one of {1, -1, i, -i}.
        # Analyzing these cases for x in the range [0, 90):
        # 1. exp(i * x * pi / 90) = 1  => x = 0. tan(0 deg) = 0 (rational).
        # 2. exp(i * x * pi / 90) = -1 => x = 90 (not in range).
        # 3. exp(i * x * pi / 90) = i   => x = 45. tan(45 deg) = 1 (rational).
        # 4. exp(i * x * pi / 90) = -i => x = 135 (not in range).
        # Therefore, within the specified range 0 <= x < 90, tan(x degrees) is rational
        # if and only if x is 0 or 45.
        
        if x == 0 or x == 45:
            # If x is 0 or 45, tan(x degrees) is rational.
            results.append('Y')
        else:
            # For all other integer values of x in the range [0, 90), tan(x degrees) is irrational.
            results.append('N')
            
    # Print the collected results. 
    # Using "\n".join(results) efficiently prints each result on a separate line.
    print("\n".join(results))

# The standard Python entry point check.
# Ensures that solve() is called only when the script is executed directly.
if __name__ == '__main__':
    solve()
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