結果

問題 No.1881 Everything is the same...
ユーザー colognecologne
提出日時 2022-03-18 02:55:22
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 374 ms / 2,000 ms
コード長 2,506 bytes
コンパイル時間 328 ms
コンパイル使用メモリ 82,168 KB
実行使用メモリ 82,768 KB
最終ジャッジ日時 2024-10-02 13:33:20
合計ジャッジ時間 13,865 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 48 ms
55,296 KB
testcase_01 AC 50 ms
55,296 KB
testcase_02 AC 48 ms
55,424 KB
testcase_03 AC 49 ms
55,296 KB
testcase_04 AC 47 ms
55,296 KB
testcase_05 AC 54 ms
55,296 KB
testcase_06 AC 188 ms
78,932 KB
testcase_07 AC 46 ms
55,296 KB
testcase_08 AC 48 ms
54,912 KB
testcase_09 AC 48 ms
55,040 KB
testcase_10 AC 327 ms
80,504 KB
testcase_11 AC 313 ms
81,392 KB
testcase_12 AC 351 ms
81,324 KB
testcase_13 AC 338 ms
81,088 KB
testcase_14 AC 366 ms
81,776 KB
testcase_15 AC 368 ms
81,680 KB
testcase_16 AC 354 ms
81,356 KB
testcase_17 AC 348 ms
80,316 KB
testcase_18 AC 342 ms
81,472 KB
testcase_19 AC 374 ms
82,740 KB
testcase_20 AC 356 ms
82,064 KB
testcase_21 AC 340 ms
80,668 KB
testcase_22 AC 341 ms
81,252 KB
testcase_23 AC 351 ms
80,912 KB
testcase_24 AC 345 ms
81,000 KB
testcase_25 AC 340 ms
81,028 KB
testcase_26 AC 336 ms
80,964 KB
testcase_27 AC 345 ms
81,100 KB
testcase_28 AC 333 ms
80,772 KB
testcase_29 AC 334 ms
80,980 KB
testcase_30 AC 361 ms
82,768 KB
testcase_31 AC 350 ms
81,488 KB
testcase_32 AC 323 ms
80,884 KB
testcase_33 AC 360 ms
81,996 KB
testcase_34 AC 373 ms
81,428 KB
testcase_35 AC 357 ms
81,908 KB
testcase_36 AC 336 ms
80,940 KB
testcase_37 AC 352 ms
81,224 KB
testcase_38 AC 347 ms
81,868 KB
testcase_39 AC 358 ms
82,124 KB
testcase_40 AC 351 ms
81,796 KB
testcase_41 AC 344 ms
80,872 KB
testcase_42 AC 48 ms
55,296 KB
testcase_43 AC 48 ms
54,912 KB
testcase_44 AC 47 ms
55,424 KB
testcase_45 AC 49 ms
55,296 KB
testcase_46 AC 48 ms
55,296 KB
testcase_47 AC 47 ms
55,296 KB
testcase_48 AC 47 ms
55,296 KB
testcase_49 AC 47 ms
55,296 KB
testcase_50 AC 47 ms
55,040 KB
testcase_51 AC 48 ms
55,424 KB
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 # 

from functools import reduce
from itertools import count
from operator import xor


def factorize(N):
    ret = []
    for p in count(2):
        if p*p > N:
            break
        if N % p == 0:
            k = 0
            while N % p == 0:
                k += 1
                N //= p
            ret.append((p, k))
    if N != 1:
        ret.append((N, 1))
    return ret


memo = {}


def bktk(A):
    if len(A) == 0:
        yield []
        return

    for i in range(A[-1]):
        for a in bktk(A[:-1]):
            a.append(i)
            yield a
    return


def calc(A):
    # Calculate grundy number of cyclic group, prod(Cp^a)
    # A should be sorted
    if A in memo:
        return memo[A]
    if len(A) == 0:
        return 0

    grundy = set()

    # for group C = prod(Cp^ai), backtrack for B / <x>
    # B = prod(Cp^bi), then a_{i-1} <= b_i <= a_i holds.
    # this means, 0 <= ai-bi <= a_i-a_{i-1}
    cA = [1 + A[i] - (0 if i == 0 else A[i-1]) for i in range(len(A))]
    for dA in bktk(cA):
        if max(dA) == 0:
            continue
        B = tuple(a-da for a, da in zip(A, dA) if a != da)
        grundy.add(calc(B))

    for i in count(0):
        if i not in grundy:
            memo[A] = i
            return i


def solve(x):
    # express G as product of cyclic group
    # C[p] = [a, b, ...] denotes (Z/xZ)* = Cp^a*Cp^b*...
    C = {}
    for p, k in factorize(x):
        if p not in C:
            C[p] = []
        if p == 2:
            if k >= 2:
                C[p].append(1)
            if k >= 3:
                C[p].append(k-2)
        else:
            if k >= 2:
                C[p].append(k-1)
            for q, t in factorize(p-1):
                if q not in C:
                    C[q] = []
                C[q].append(t)

    # simple transpose algorithm
    def T(arr):
        if len(arr) == 0:
            return ()
        ret = [0] * max(arr)
        for i in arr:
            for j in range(i):
                ret[j] += 1
        return tuple(ret)

    # Here, uses transpose trick.
    # grundy number of cyclic group quotient can be transposed into game where
    # arbitary positive number of decks were chosen, and -1 from chosen numbers
    part = []
    for v in C.values():
        part.extend(T(v))
    part = T(part)

    return calc(part[::-1])


def main():
    int(input())  # N
    A = map(int, input().split())
    G = reduce(xor, map(solve, A))
    print('X' if G == 0 else 'Y')


if __name__ == '__main__':
    main()
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