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#1738. 【2022.11.7 NOIP 模拟赛】序列(sequence)

https://sjzezoj.com/submission/63900
This commit is contained in:
Baoshuo Ren 2022-11-07 22:04:27 +08:00
parent 01e14ba3fc
commit 0a6f04d059
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
66 changed files with 303 additions and 0 deletions

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#include <iostream>
#include <algorithm>
#include <cstring>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e6 + 5,
K = 105;
const int mod = 1e9 + 7;
int n, k, a[N];
long long m, f[N], s, ans;
std::pair<long long, int> sum[N];
class Matrix {
private:
long long data[K][K];
public:
Matrix() {
memset(data, 0x00, sizeof(data));
};
void build() {
for (int i = 1; i <= k; i++) data[i][i] = 1;
}
long long *operator[](int x) {
return data[x];
}
Matrix operator*(Matrix b) {
Matrix res;
for (int i = 1; i <= k; i++) {
for (int j = 1; j <= k; j++) {
for (int l = 1; l <= k; l++) {
res[i][j] = (res[i][j] + data[i][l] * b[l][j]) % mod;
}
}
}
return res;
}
} z, res;
Matrix binpow(Matrix a, long long b) {
Matrix res;
res.build();
while (b) {
if (b & 1) res = res * a;
a = a * a;
b >>= 1;
}
return res;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> k;
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
for (int i = 1; i <= n; i++) {
f[i] = (s + 1) % mod;
s = ((s - sum[a[i]].first) % mod + mod) % mod;
sum[a[i]].first = f[i];
s = (s + sum[a[i]].first) % mod;
sum[a[i]].second = i;
}
std::sort(sum + 1, sum + 1 + k, [&](auto a, auto b) -> bool { return a.second < b.second; });
for (int i = 1; i <= k; i++) {
res[1][i] = sum[i].first;
}
res[1][k + 1] = s;
res[1][k + 2] = 1;
for (int i = 1; i < k; i++) {
z[i + 1][i] = 1;
}
z[1][k + 1] = mod - 1;
z[k + 1][k] = 1;
z[k + 1][k + 1] = 2;
z[k + 2][k] = 1;
z[k + 2][k + 1] = 1;
z[k + 2][k + 2] = 1;
k += 2;
res = res * binpow(z, m);
cout << res[1][k - 1] << endl;
return 0;
}

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