✨ adds matrix exponentiation isolated function

algorithms/math/matrix-exponentiation.cpp

@@ -0,0 +1,33 @@
+ll MOD = 1'000'000'007;
+
+template <typename T>
+vector<vector<T>> prod(vector<vector<T>> &a,
+                       vector<vector<T>> &b) {
+  int n = len(a);
+  vector<vector<T>> c(n, vector<T>(n));
+
+  for (int i = 0; i < n; i++) {
+    for (int j = 0; j < n; j++) {
+      for (int k = 0; k < n; k++) {
+        c[i][j] =
+          (c[i][j] + ((a[i][k] * b[k][j]) % MOD)) % MOD;
+      }
+    }
+  }
+
+  return c;
+}
+
+template <typename T>
+vector<vector<T>> fpow(vector<vector<T>> &xs, ll p) {
+  vector<vector<T>> ans(len(xs), vector<T>(len(xs)));
+  for (int i = 0; i < len(xs); i++) ans[i][i] = 1;
+
+  auto b = xs;
+  while (p) {
+    if (p & 1) ans = prod(ans, b);
+    p >>= 1;
+    b = prod(b, b);
+  }
+  return ans;
+}