#1789. 【2017.3 长乐省选集训 Day15 T1】斐波那契

https://sjzezoj.com/submission/65549

S2OJ/1789/1789.cpp

@@ -0,0 +1,88 @@
+#include <iostream>
+#include <array>
+#include <cstring>
+#include <numeric>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+const int mod = 1e9 + 7;
+
+class Matrix {
+  private:
+    long long data[10][10];
+
+  public:
+    Matrix() {
+        memset(data, 0x00, sizeof(data));
+    }
+
+    long long* operator[](long long i) {
+        return data[i];
+    }
+
+    Matrix operator*(Matrix b) const {
+        Matrix c;
+
+        for (int i = 0; i < 3; i++) {
+            for (int j = 0; j < 3; j++) {
+                for (int k = 0; k < 3; k++) {
+                    c[i][j] = (c[i][j] + data[i][k] * b[k][j] % mod) % mod;
+                }
+            }
+        }
+
+        return c;
+    }
+
+    Matrix operator-(Matrix b) const {
+        Matrix c;
+
+        for (int i = 0; i < 3; i++) {
+            for (int j = 0; j < 3; j++) {
+                c[i][j] = (data[i][j] - b[i][j] + mod) % mod;
+            }
+        }
+
+        return c;
+    }
+} base, ans;
+
+Matrix binpow(Matrix a, long long k) {
+    Matrix res;
+
+    res[1][1] = 1;
+    res[2][2] = 1;
+
+    while (k) {
+        if (k & 1) res = res * a;
+        a = a * a;
+        k >>= 1;
+    }
+
+    return res;
+}
+
+int t, n, k;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> t;
+
+    while (t--) {
+        cin >> n >> k;
+
+        Matrix tmp;
+
+        tmp[1][1] = 0, tmp[1][2] = 1;
+        tmp[2][1] = 1, tmp[2][2] = 1;
+
+        cout << binpow(binpow(tmp, n + 1) - tmp, k)[2][2] << endl;
+    }
+
+    return 0;
+}