P1306 斐波那契公约数

https://www.luogu.com.cn/record/80117613

Luogu/P1306/P1306.cpp

@@ -0,0 +1,79 @@
+#include <iostream>
+#include <algorithm>
+#include <cstring>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 10;
+const int mod = 1e8;
+
+class Matrix {
+  private:
+    long long data[N][N];
+
+  public:
+    Matrix() {
+        memset(data, 0x00, sizeof(data));
+    }
+
+    long long* operator[](int i) {
+        return data[i];
+    }
+
+    Matrix operator*(Matrix b) const {
+        Matrix c;
+
+        int n = 2;
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= n; j++) {
+                for (int k = 1; k <= n; k++) {
+                    c[i][j] = (c[i][j] + data[i][k] * b[k][j] % mod) % mod;
+                }
+            }
+        }
+
+        return c;
+    }
+} base, ans;
+
+Matrix binpow(Matrix a, int k) {
+    Matrix res;
+    res[1][1] = 1;
+    res[1][2] = 1;
+
+    while (k) {
+        if (k & 1) res = res * a;
+        a = a * a;
+        k >>= 1;
+    }
+
+    return res;
+}
+
+long long fib(int n) {
+    if (n <= 2) {
+        return !!n;
+    }
+
+    Matrix tmp;
+
+    tmp[1][1] = 1, tmp[1][2] = 1;
+    tmp[2][1] = 1, tmp[2][2] = 0;
+
+    return binpow(tmp, n - 2)[1][1];
+}
+
+int n, m;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+
+    cin >> n >> m;
+
+    cout << fib(std::__gcd(n, m)) % mod << endl;
+
+    return 0;
+}