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

https://sjzezoj.com/submission/63900

S2OJ/1738/1738.cpp

@@ -0,0 +1,108 @@
+#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;
+}