結果
問題 | No.1410 A lot of Bit Operations |
ユーザー |
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提出日時 | 2021-02-27 08:12:50 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 120 ms / 2,000 ms |
コード長 | 3,261 bytes |
コンパイル時間 | 165 ms |
コンパイル使用メモリ | 82,300 KB |
実行使用メモリ | 77,332 KB |
最終ジャッジ日時 | 2024-10-02 17:05:39 |
合計ジャッジ時間 | 5,935 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 44 |
ソースコード
def extgcd(x,y):if y==0: return 1,0r0,r1,s0,s1 = x,y,1,0while r1 != 0:r0,r1, s0,s1 = r1,r0%r1, s1,s0-r0//r1*s1return s0,(r0-s0*x)//ydef modinv(a,MOD):x,y = extgcd(a,MOD)return x%MODdef divmod_poly(f,g,MOD): #MODは素数とするassert g != [] and g != [0]ainv = modinv(g[-1],MOD)df,dg = len(f),len(g)if df < dg: return [0], f[:]gg = [gi*ainv%MOD for gi in g]r = f[:]q = [0]*(df-dg+1)for i in range(df-dg,-1,-1):q[i] = c = r[-1]if c:for j in range(dg-1,-1,-1):r[j+i] -= c*gg[j]r[j+i] %= MODr.pop()for i in range(df-dg+1): # g を monic にするq[i] = q[i]*ainv%MODwhile r and r[-1]==0: r.pop()if not r: r = [0]return q,rdef mul_poly(f,g,MOD):df,dg = len(f),len(g)res = [0]*(df+dg-1)for i in range(df):for j in range(dg):res[i+j] += f[i]*g[j]res[i+j] %= MODreturn resdef sub_poly(f,g,MOD):df,dg = len(f),len(g)m = max(df,dg)res = f[:]+[0]*(m-df)for i in range(m):if i < dg:res[i] -= g[i]if res[i] < 0: res[i] += MODreturn resdef bm(x,MOD):assert len(x)%2==0L = len(x)//2x.reverse()while x and x[-1]==0: x.pop()if not x: return [0] # all zero の場合r0,r1,s0,s1 = x,[0]*(2*L-1)+[1],[1],[0]while len(s1) <= L and r1 != [0]:q,r = divmod_poly(r0,r1,MOD)#print(r0,r1,q,r)#assert mul_poly(q,r1,MOD)==sub_poly(r0,r,MOD)r0,r1 = r1,rs0,s1 = s1, sub_poly(s0,mul_poly(q,s1,MOD),MOD)#print(q,r0,r1,s0,s1)while s0 and s0[-1]==0: s0.pop()ainv = modinv(s0[-1],MOD)return [si*ainv%MOD for si in s0]def f(n,op,I):ans = 0for p in range(1<<n):for q in range(1<<n):L = 0for i in range(n):L |= op(p>>i&1,q>>i&1,I)<<iR = (1<<n)-1-Lassert L >= 0 and R >= 0#print(L,R,1<<n)ans += max(L,R) - min(L,R) + 1return ans%MODdef fps_nth_term(f,g,N):assert g[0] != 0while N:h = g[:]for i in range(1,len(g),2):h[i] = -h[i]f = polymul(f,h)[N%2:N+1:2]g = polymul(g,h)[:N+1:2]N //= 2return f[0]*pow(g[0],MOD-2,MOD)%MOD# a[0],...,a[L-2] とL-1次特性多項式 g が与えられているL項間漸化式の第N項def rec_nth_term(a,g,N):L = len(g)assert len(a) == L-1f = polymul(a,g)[:L-1]return fps_nth_term(f,g,N)MOD = 10**9+7def polymul(x,y):return mul_poly(x,y,MOD)n = int(input())k = input()ans = 0for i in range(8):if k[i] == "-": continueif n==0: ans += 1;continuedef op(x,y,i):if x==0 and y==0: return i>>0&1if x==0 and y: return i>>1&1if x and y==0: return i>>2&1return 0lst = [f(k,op,i) for k in range(1,7)]#print(lst)a = bm(lst[:],MOD)[::-1]#for i in range(10):# x = rec_nth_term(lst[:len(a)-1],a,i)# print(lst,a,x)#for i,j in zip(lst,lst[1:]):# print(i*12-j*32)ans += rec_nth_term(lst[:len(a)-1],a,n-1)print(ans%MOD)