#997935 (PyPy3) No.2823 PEX (Predecessing Excluded Value) Game

• 問題: No.2823 PEX (Predecessing Excluded Value) Game
• ユーザー: navel_tos
• 提出日時: 2024-07-26 23:27:58
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 401 ms / 2,000 ms
• コード長: 2,808 bytes
• コンパイル時間: 452 ms
• コンパイル使用メモリ: 82,168 KB
• 実行使用メモリ: 125,276 KB
• 最終ジャッジ日時: 2024-07-27 21:24:14
• 合計ジャッジ時間: 5,355 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 51

ソースコード

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#yukicoder 2823 PEX Game
from random import randint
#適当に実験  Grundy数を計算する
def brute(S):
    D = dict()
    E = dict()
    Q = [tuple(sorted(S))]
    while Q:
        T = Q.pop()
        if T not in D:  #入りがけの処理
            Q.append(T)
            D[T] = -1
            E[T] = []
            #遷移先を全探索する
            R = [0] * (max(T) + 1)
            for i in T:
                R[i] = 1
            if sum(R[1: len(T) + 1]) == len(T):
                D[T] = 0
                continue
            for i in range(1, max(T) + 1):
                if R[i] == 0: continue
                for j in range(i - 1, -1, -1):
                    if R[j] == 0: break
                if j == 0: continue
                R[i], R[j] = R[j], R[i]
                nT = tuple([i for i in range(1, len(R)) if R[i] == 1])
                R[i], R[j] = R[j], R[i]
                Q.append(nT)
                E[T].append(nT)
        elif D[T] != -1:
            continue
        elif D[T] == -1:  #帰りがけの処理
            X = set()
            for nT in E[T]:
                assert D[nT] >= 0
                X.add(D[nT])
            for i in range(10 ** 7):
                if i not in X:
                    D[T] = i
                    break
    return D[tuple(sorted(S))]
#規則性しかない  適当にエスパーする
#x: これより左側にある値の個数
def esper(Lt, Rt, x = 0):
    d = Rt - Lt + 1
    return 0 if (Lt - x) & 1 == 1 else d
def test(Lt, Rt):
    D = [i for i in range(Lt, Rt + 1)]
    assert brute(D) == esper(Lt, Rt)
#適当にテストケース乱択
def make_test(maxN = 12):
    P = []
    while len(P) == 0 or randint(0, 3):
        back = P[-1] if len(P) else 0
        if back >= maxN - 1: break
        Lt = randint(back + 1, maxN - 1)
        Rt = randint(Lt + 1, maxN)
        P.append(Lt)
        P.append(Rt)
    assert len(P) > 0 and len(P) & 1 == 0
    Q = []
    for i in range(len(P) // 2):
        Q.append((P[i << 1], P[i << 1 | 1]))
    return Q
def solve(P):
    #圧縮
    bL, bR = P[0]
    Q = []
    for i in range(1, len(P)):
        Lt, Rt = P[i]
        if bR + 1 == Lt:
            bR = Rt
            continue
        else:
            Q.append((bL, bR))
            bL, bR = Lt, Rt
    Q.append((bL, bR))
    ans = 0
    cnt = 0
    for Lt, Rt in Q:
        ans ^= esper(Lt, Rt, cnt)
        cnt += Rt - Lt + 1
    return ans
        
#実験
def act(time = 1000):
    for _ in range(1, time + 1):
        P = make_test(15)
        Q = []
        for Lt, Rt in P:
            for i in range(Lt, Rt + 1): Q.append(i)
        assert brute(Q) == solve(P), P
      
#実行
N = int(input())
P = [tuple(map(int, input().split())) for _ in range(N)]
ans = solve(P)
print('First' if ans else 'Second')
 
 
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