結果

問題 No.2226 Hello, Forgotten World!
ユーザー chineristACchineristAC
提出日時 2023-02-24 22:10:42
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 133 ms / 2,000 ms
コード長 11,745 bytes
コンパイル時間 364 ms
コンパイル使用メモリ 82,364 KB
実行使用メモリ 86,888 KB
最終ジャッジ日時 2024-09-13 05:33:55
合計ジャッジ時間 2,147 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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 80 ms
77,932 KB
testcase_01 AC 133 ms
86,616 KB
testcase_02 AC 110 ms
86,584 KB
testcase_03 AC 104 ms
86,888 KB
testcase_04 AC 89 ms
82,280 KB
testcase_05 AC 105 ms
86,620 KB
testcase_06 AC 98 ms
86,576 KB
testcase_07 AC 102 ms
86,780 KB
testcase_08 AC 87 ms
81,292 KB
testcase_09 AC 100 ms
86,556 KB
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ソースコード

diff # 

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0

def _ntt(f,L,reverse=False):
    F=[f[i] for i in range(L)]
    n = L.bit_length() - 1
    base = omega
    if reverse:
        base = rev_omega

    if not n:
        return F

    size = 2**n
    wj = pow(base,2**22,mod)
    res = [0]*2**n

    for i in range(n,0,-1):
        use_omega = pow(base,2**(22+i-n),mod)
        res = [0]*2**n
        size //= 2
        w = 1
        for j in range(0,L//2,size):
            for a in range(size):
                res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
                t = (w * wj) % mod
                res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
            w = (w * use_omega) % mod
        F = res

    return res

def ntt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L)
    return F

def intt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L,reverse=True)
    inv = pow(L,mod-2,mod)
    for i in range(L):
        F[i] *= inv
        F[i] %= mod
    return F

def convolve(_f,_g,limit):
    f = [v for v in _f]
    g = [v for v in _g]
    l = len(f)+len(g)-1
    L = 1<<((l-1).bit_length())

    F = ntt(f,L)
    G = ntt(g,L)

    H = [(F[i] * G[i]) % mod for i in range(L)]

    h = intt(H,L)

    return h[:limit]

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0

_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
              183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
               771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
 
 
def _butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = 0
    while len_ < h:
        if h - len_ == 1:
            p = 1 << (h - len_ - 1)
            rot = 1
            for s in range(1 << len_):
                offset = s << (h - len_)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot % _fft_mod
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 1
        else:
            p = 1 << (h - len_ - 2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot * rot % _fft_mod
                rot3 = rot2 * rot % _fft_mod
                offset = s << (h - len_)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % _fft_mod * _fft_imag
                    a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 2
 
 
def _butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = h
    while len_:
        if len_ == 1:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 1)):
                offset = s << (h - len_ + 1)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p]
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) * irot % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 1
        else:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 2)):
                irot2 = irot * irot % _fft_mod
                irot3 = irot2 * irot % _fft_mod
                offset = s << (h - len_ + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * _fft_iimag % _fft_mod
                    a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
                    a[i + offset + p] = (a0 - a1 +
                                         a2na3iimag) * irot % _fft_mod
                    a[i + offset + p * 2] = (a0 + a1 -
                                             a2 - a3) * irot2 % _fft_mod
                    a[i + offset + p * 3] = (a0 - a1 -
                                             a2na3iimag) * irot3 % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 2
 
 
def _convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    return ans
 
 
def _convolution_fft(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    b += [0] * (z - m)
    _butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def _convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def convolution(a, b):
    """It calculates (+, x) convolution in mod 998244353. 
    Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], 
    it calculates the array c of length n + m - 1, defined by
 
    >   c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
 
    It returns an empty list if at least one of a and b are empty.
 
    Constraints
    -----------
 
    >   len(a) + len(b) <= 8388609
 
    Complexity
    ----------
 
    >   O(n log n), where n = len(a) + len(b).
    """
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 0:
        return _convolution_naive(a, b)
    if a is b:
        return _convolution_square(a)
    return _convolution_fft(a, b)

import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

def Z_algorithm(s):
    N = len(s)
    Z_alg = [0]*N

    Z_alg[0] = N
    i = 1
    j = 0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        Z_alg[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < N and k + Z_alg[k]<j:
            Z_alg[i+k] = Z_alg[k]
            k += 1
        i += k
        j -= k
    return Z_alg

def solve(N,M,S,T):
    Sa = S.replace("?","a")
    
    SaT = T + "#" + Sa
    check = Z_algorithm(SaT)
    for i in range(N):
        if check[i+M+1] == M:
            return Sa
    
    
    """
    Sの?を置き換える際は
    ・かならず?->a以外にするとこがある（->?を置き換える部分がある）
    S[i:i+M] と S[j:j+M] (i < j) の置き換えを比較するとき、
    i+M < j のとき、jが小さい
    S[i:j] に ? があった場合、jが小さい
    ない場合、S[j:i+M] を T[j-i:M] と T[:i+M-j] の比較
    これで決着がつかない場合、iが小さい
    """

    wild_cnt = [0] + [S[i]=="?" for i in range(N)]
    for i in range(N):
        wild_cnt[i+1] += wild_cnt[i]

    T_Z = Z_algorithm(T)

    def compare(i,j):
        if i+M <= j:
            return j
        
        cnt = wild_cnt[j-1] - wild_cnt[i-1]
        if cnt > 0:
            return j
        
        if T_Z[j-i]==M+i-j:
            return i

        if T[j-i+T_Z[j-i]] > T[T_Z[j-i]]:
            return j
        return i
    
    hash = [k+1 for k in range(26)]
    f = [0] * N
    for i in range(N):
        if S[i]!="?":
            f[i] = hash[ord(S[i])-ord("a")]
    
    g = [0] * M
    for i in range(M):
        if T[i]!="?":
            g[i] = hash[ord(T[i])-ord("a")]


    p = convolution([f[i]**3 % mod for i in range(N)],g[::-1])
    q = convolution([f[i]**2 % mod for i in range(N)],[g[i]**2 % mod for i in range(M)][::-1])
    r = convolution([f[i] % mod for i in range(N)],[g[i]**3 % mod for i in range(M)][::-1])

    cand = []
    for i in range(N-M+1):
        if (p[i+M-1]-2*q[i+M-1]+r[i+M-1]) % mod == 0:
            cand.append(i)
    
    if not cand:
        return -1
    
    k = cand[0]
    for i in cand[1:]:
        k = compare(k,i)
    
    res = "".join([S[:k].replace("?","a") , T , S[k+M:].replace("?","a")])
    return res

for _ in range(int(input())):
    N = int(input())
    S = input()
    M = 10
    T = "helloworld"

    res = "z" * (N+1)
    for i in range(N-10+1):
        flag = True
        for j in range(10):
            if S[i+j]!="?" and S[i+j]!=T[j]:
                flag = False
        
        if flag:
            tmp = S[:i].replace("?","a") + T + S[i+10:].replace("?","a")
            res = min(res,tmp)
    
    if len(res) == N + 1:
        print(-1)
    else:
        print(res)
0