結果
問題 | No.1750 ラムドスウイルスの感染拡大-hard |
ユーザー | kohei2019 |
提出日時 | 2023-06-13 00:57:15 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,725 ms / 2,000 ms |
コード長 | 7,430 bytes |
コンパイル時間 | 269 ms |
コンパイル使用メモリ | 87,148 KB |
実行使用メモリ | 85,404 KB |
最終ジャッジ日時 | 2023-09-02 17:39:25 |
合計ジャッジ時間 | 20,130 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge15 |
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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 | 86 ms
71,676 KB |
testcase_01 | AC | 84 ms
71,780 KB |
testcase_02 | AC | 82 ms
71,700 KB |
testcase_03 | AC | 93 ms
76,624 KB |
testcase_04 | AC | 128 ms
77,696 KB |
testcase_05 | AC | 81 ms
71,780 KB |
testcase_06 | AC | 83 ms
71,756 KB |
testcase_07 | AC | 88 ms
71,692 KB |
testcase_08 | AC | 248 ms
78,032 KB |
testcase_09 | AC | 224 ms
78,476 KB |
testcase_10 | AC | 244 ms
78,496 KB |
testcase_11 | AC | 244 ms
78,228 KB |
testcase_12 | AC | 321 ms
78,536 KB |
testcase_13 | AC | 306 ms
78,472 KB |
testcase_14 | AC | 1,725 ms
84,948 KB |
testcase_15 | AC | 1,680 ms
85,040 KB |
testcase_16 | AC | 1,714 ms
85,148 KB |
testcase_17 | AC | 1,328 ms
85,320 KB |
testcase_18 | AC | 1,219 ms
85,404 KB |
testcase_19 | AC | 1,279 ms
84,884 KB |
testcase_20 | AC | 1,042 ms
83,368 KB |
testcase_21 | AC | 1,305 ms
84,592 KB |
testcase_22 | AC | 259 ms
78,916 KB |
testcase_23 | AC | 1,535 ms
84,824 KB |
testcase_24 | AC | 207 ms
79,084 KB |
testcase_25 | AC | 386 ms
80,356 KB |
testcase_26 | AC | 167 ms
78,712 KB |
testcase_27 | AC | 95 ms
77,372 KB |
testcase_28 | AC | 100 ms
77,332 KB |
testcase_29 | AC | 94 ms
77,344 KB |
testcase_30 | AC | 242 ms
79,296 KB |
testcase_31 | AC | 236 ms
78,864 KB |
testcase_32 | AC | 238 ms
78,728 KB |
testcase_33 | AC | 242 ms
78,448 KB |
ソースコード
import copy class matrix(): def __init__(self): self.mod = 998244353 def multiplication(self,arr1,arr2): ''' 例 arr1 2 3 4 5 6 7 8 9 arr2 1 2 3 4 5 6 7 8 ''' H = len(arr1) W = len(arr2[0]) arr3 = [[0]*W for i in range(H)] for i in range(H): for j in range(W): val = 0 for k in range(len(arr1[0])): val += arr1[i][k]*arr2[k][j] arr3[i][j] = val return arr3 def determinant(self,arr): ''' 正方行列N*Nの行列式 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) N = len(arr_calc) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]/d for k in range(i,N): arr_calc[j][k] -= e*arr_calc[i][k] #arr_calc 上△行列 det = 1 for i in range(N): det *= arr_calc[i][i] return det def invarr(self,arr): ''' 正方行列N*Nの逆行列 det == 0ならreturn False 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) if self.determinant(arr_calc) == 0: return False N = len(arr_calc) for i in range(N): v = [0]*(N) v[i] = 1 arr_calc[i].extend(v) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]/d for k in range(i,2*N): arr_calc[j][k] -= e*arr_calc[i][k] for i in range(N-1,-1,-1): d = arr_calc[i][i] for k in range(i,2*N): arr_calc[i][k] /= d for j in range(i-1,-1,-1): c = arr_calc[j][i] for k in range(i,2*N): arr_calc[j][k] -= c*arr_calc[i][k] inv = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): inv[i][j] = arr_calc[i][j+N] return inv def SimultaneousE(self,arr): ''' 3x+2y+z = 4 4x+5y+6z = 3 7x+8y+9z = 2 -> 3 2 1 4 4 5 6 3 7 8 9 2 ''' N = len(arr) arr1 = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): arr1[i][j] = arr[i][j] v = [[0] for i in range(N)] for i in range(N): v[i][0] = arr[i][-1] if self.determinant(arr1) == 0: return False inva = self.invarr(arr1) return self.multiplication(inva,v) def invmod(self,a):#mod逆元 if a == 0: return 0 if a == 1: return 1 return (-self.invmod(self.mod % a) * (self.mod // a)) % self.mod def multiplication_mod(self,arr1,arr2): H = len(arr1) W = len(arr2[0]) arr3 = [[0]*W for i in range(H)] for i in range(H): for j in range(W): val = 0 for k in range(len(arr1[0])): val += arr1[i][k]*arr2[k][j] arr3[i][j] = val%self.mod return arr3 def determinant_mod(self,arr): ''' 正方行列N*Nの行列式 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) N = len(arr_calc) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]*self.invmod(d) e %= self.mod for k in range(i,N): arr_calc[j][k] -= e*arr_calc[i][k] arr_calc[j][k] %= self.mod #arr_calc 上△行列 det = 1 for i in range(N): det *= arr_calc[i][i] det %= self.mod return det def invarr_mod(self,arr): ''' 正方行列N*Nの逆行列 det == 0ならreturn False 計算量O(N**3) ''' arr_calc = copy.deepcopy(arr) det = self.determinant_mod(arr_calc) if det == 0: return False N = len(arr_calc) for i in range(N): v = [0]*(N) v[i] = det arr_calc[i].extend(v) for i in range(N-1): d = arr_calc[i][i] for j in range(i+1,N): e = arr_calc[j][i]*self.invmod(d) for k in range(i,2*N): arr_calc[j][k] -= e*arr_calc[i][k] arr_calc[j][k] %= self.mod for i in range(N-1,-1,-1): d = arr_calc[i][i] for k in range(i,2*N): arr_calc[i][k] *= self.invmod(d) for j in range(i-1,-1,-1): c = arr_calc[j][i] for k in range(i,2*N): arr_calc[j][k] -= c*arr_calc[i][k] arr_calc[j][k] %= self.mod inv = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): inv[i][j] = arr_calc[i][j+N]*self.invmod(det)%self.mod return inv def SimultaneousE_mod(self,arr): ''' 3x+2y+z = 4 4x+5y+6z = 3 7x+8y+9z = 2 -> 3 2 1 4 4 5 6 3 7 8 9 2 ''' N = len(arr) arr1 = [[0]*(N) for i in range(N)] for i in range(N): for j in range(N): arr1[i][j] = arr[i][j] v = [[0] for i in range(N)] for i in range(N): v[i][0] = arr[i][-1] det = self.determinant_mod(arr1) if det == 0: return False inva = self.invarr_mod(arr1) v2 = self.multiplication_mod(inva,v) for i in range(N): v2[i][0] %= self.mod return v2 def modPow_matrix(self,arr,n): ''' N*Nの正方行列arrをn乗する。 ''' N = len(arr) if n==0: arr1 = [[0]*(N) for i in range(N)] for i in range(N): arr1[i][i] = 1 return arr1 if n==1: for i in range(N): for j in range(N): arr[i][j] %= self.mod return arr if n % 2 == 1: arr2 = self.multiplication_mod(arr,self.modPow_matrix(arr,n-1)) return arr2 arr3 = self.modPow_matrix(arr,n//2) return self.multiplication_mod(arr3,arr3) def Pow_matrix(self,arr,n): ''' N*Nの正方行列arrをn乗する。 ''' N = len(arr) if n==0: arr1 = [[0]*(N) for i in range(N)] for i in range(N): arr1[i][i] = 1 return arr1 if n==1: return arr if n % 2 == 1: arr2 = self.multiplication(arr,self.Pow_matrix(arr,n-1)) return arr2 arr3 = self.Pow_matrix(arr,n//2) return self.multiplication(arr3,arr3) mod = 998244353 N,M,T = map(int,input().split()) lsar = [[0]*N for i in range(N)] for i in range(M): s,t = map(int, input().split()) lsar[s][t] = 1 lsar[t][s] = 1 ML = matrix() arn = ML.modPow_matrix(lsar, T) vec = [[0] for i in range(N)] vec[0][0] = 1 anl = ML.multiplication_mod(arn, vec) print(anl[0][0])