結果

問題 No.1648 Sum of Powers
ユーザー SSRSSSRS
提出日時 2021-08-13 22:42:37
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 99 ms / 2,000 ms
コード長 2,673 bytes
コンパイル時間 2,186 ms
コンパイル使用メモリ 193,044 KB
実行使用メモリ 11,216 KB
最終ジャッジ日時 2023-07-27 05:57:23
合計ジャッジ時間 10,229 ms
ジャッジサーバーID
(参考情報)
judge12 / judge14
このコードへのチャレンジ(β)

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 82 ms
11,216 KB
testcase_01 AC 29 ms
4,736 KB
testcase_02 AC 71 ms
10,108 KB
testcase_03 AC 63 ms
10,168 KB
testcase_04 AC 72 ms
10,188 KB
testcase_05 AC 63 ms
10,284 KB
testcase_06 AC 64 ms
10,392 KB
testcase_07 AC 71 ms
10,156 KB
testcase_08 AC 72 ms
10,280 KB
testcase_09 AC 74 ms
10,128 KB
testcase_10 AC 73 ms
10,104 KB
testcase_11 AC 70 ms
10,124 KB
testcase_12 AC 68 ms
10,152 KB
testcase_13 AC 68 ms
10,124 KB
testcase_14 AC 65 ms
10,172 KB
testcase_15 AC 65 ms
10,168 KB
testcase_16 AC 67 ms
10,160 KB
testcase_17 AC 71 ms
10,160 KB
testcase_18 AC 61 ms
10,116 KB
testcase_19 AC 60 ms
10,280 KB
testcase_20 AC 62 ms
10,220 KB
testcase_21 AC 63 ms
10,108 KB
testcase_22 AC 87 ms
10,952 KB
testcase_23 AC 76 ms
11,076 KB
testcase_24 AC 74 ms
11,080 KB
testcase_25 AC 81 ms
10,956 KB
testcase_26 AC 80 ms
10,992 KB
testcase_27 AC 81 ms
10,988 KB
testcase_28 AC 83 ms
11,008 KB
testcase_29 AC 86 ms
10,960 KB
testcase_30 AC 80 ms
10,964 KB
testcase_31 AC 92 ms
10,900 KB
testcase_32 AC 81 ms
10,960 KB
testcase_33 AC 80 ms
10,944 KB
testcase_34 AC 81 ms
10,944 KB
testcase_35 AC 77 ms
10,896 KB
testcase_36 AC 83 ms
11,040 KB
testcase_37 AC 95 ms
11,048 KB
testcase_38 AC 92 ms
10,944 KB
testcase_39 AC 99 ms
10,908 KB
testcase_40 AC 88 ms
10,992 KB
testcase_41 AC 97 ms
10,956 KB
testcase_42 AC 83 ms
10,904 KB
testcase_43 AC 80 ms
10,952 KB
testcase_44 AC 79 ms
10,964 KB
testcase_45 AC 87 ms
10,992 KB
testcase_46 AC 88 ms
10,908 KB
testcase_47 AC 69 ms
10,276 KB
testcase_48 AC 30 ms
4,572 KB
testcase_49 AC 63 ms
10,120 KB
testcase_50 AC 69 ms
10,124 KB
testcase_51 AC 17 ms
4,380 KB
testcase_52 AC 73 ms
10,988 KB
testcase_53 AC 75 ms
11,180 KB
testcase_54 AC 75 ms
10,968 KB
testcase_55 AC 81 ms
10,904 KB
testcase_56 AC 85 ms
11,216 KB
testcase_57 AC 1 ms
4,376 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 #

#include <bits/stdc++.h>
using namespace std;
const int SQRT = 100000;
const long long MOD = 998244353;
long long modpow(long long a, long long b){
	long long ans = 1;
	while (b > 0){
		if (b % 2 == 1){
			ans *= a;
			ans %= MOD;
		}
		a *= a;
		a %= MOD;
		b /= 2;
	}
	return ans;
}
long long modinv(long long a){
	return modpow(a, MOD - 2);
}
vector<vector<long long>> matmul(vector<vector<long long>> A, vector<vector<long long>> B){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		for (int j = 0; j < N; j++){
			for (int k = 0; k < N; k++){
				ans[i][k] += A[i][j] * B[j][k];
				ans[i][k] %= MOD;
			}
		}
	}
	return ans;
}
vector<vector<long long>> matexp(vector<vector<long long>> A, long long b){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		ans[i][i] = 1;
	}
	while (b > 0){
		if (b % 2 == 1){
			ans = matmul(ans, A);
		}
		A = matmul(A, A);
		b /= 2;
	}
	return ans;
}
int main(){
  long long A, B, P, Q;
  cin >> A >> B >> P >> Q;
  if (B == 0){
    if (A == 0){
      cout << 2 << endl;
    } else {
      vector<long long> a(SQRT);
      a[0] = P;
      for (int i = 0; i < SQRT - 1; i++){
        a[i + 1] = a[i] * modinv(A) % MOD;
      }
      map<long long, int> mp;
      for (int i = 0; i < SQRT; i++){
        mp[a[i]] = i;
      }
      long long A2 = modpow(A, SQRT);
      long long X = A * A % MOD, N = 2;
      while (true){
        if (mp.count(X) == 1){
          cout << N + mp[X] << endl;
          break;
        }
        X *= A2;
        X %= MOD;
        N += SQRT;
      }
    }
  } else {
    vector<vector<long long>> C = {{A, MOD - B}, {1, 0}};
    vector<vector<long long>> Cinv = {{0, 1}, {(MOD - 1) * modinv(B) % MOD, A * modinv(B) % MOD}};
    vector<pair<long long, long long>> a(SQRT);
    vector<vector<long long>> tmp = {{1, 0}, {0, 1}};
    a[0] = make_pair(P, Q);
    for (int i = 0; i < SQRT - 1; i++){
      tmp = matmul(tmp, Cinv);
      a[i + 1] = make_pair((tmp[0][0] * P + tmp[0][1] * Q) % MOD, (tmp[1][0] * P + tmp[1][1] * Q) % MOD);
    }
    map<pair<long long, long long>, int> mp;
    for (int i = 0; i < SQRT; i++){
      mp[a[i]] = i;
    }
    vector<vector<long long>> C2 = matexp(C, SQRT);
    long long X = (A * A - B * 2 + MOD % MOD) % MOD, Y = A;
    long long N = 2;
    while (true){
      if (mp.count(make_pair(X, Y)) == 1){
        cout << N + mp[make_pair(X, Y)] << endl;
        break;
      }
      long long X2 = (C2[0][0] * X + C2[0][1] * Y) % MOD;
      long long Y2 = (C2[1][0] * X + C2[1][1] * Y) % MOD;
      X = X2;
      Y = Y2;
      N += SQRT;
    }
  }
}
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