Add 4529

4000-4999/4529 - Остання цифра числа Фібоначчі.cpp

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+#include <bits/stdc++.h>
+
+using namespace std;
+using ull = unsigned long long;
+
+const ull MODULE = 10;
+
+using mat_t = ull[2][2];
+using vec_t = ull[2];
+
+mat_t fibomat = {
+	{ 0, 1 },
+	{ 1, 1 },
+};
+
+ull mod(ull v) {
+	return v % MODULE;
+}
+
+void mulmat(mat_t a, mat_t b, mat_t &r) {
+	r[0][0] = mod(mod(a[0][0] * b[0][0]) + mod(a[0][1] * b[1][0]));
+	r[0][1] = mod(mod(a[0][0] * b[0][1]) + mod(a[0][1] * b[1][1]));
+	r[1][0] = mod(mod(a[1][0] * b[0][0]) + mod(a[1][1] * b[1][0]));
+	r[1][1] = mod(mod(a[1][0] * b[0][1]) + mod(a[1][1] * b[1][1]));
+}
+
+void mulvec(vec_t a, mat_t b, vec_t &r) {
+	r[0] = mod(mod(a[0] * b[0][0]) + mod(a[1] * b[1][0]));
+	r[1] = mod(mod(a[0] * b[0][1]) + mod(a[1] * b[1][1]));
+}
+
+void matpow(mat_t m, ull n, mat_t &r) {
+	if (n == 1) {
+		r[0][0] = m[0][0];
+		r[0][1] = m[0][1];
+		r[1][0] = m[1][0];
+		r[1][1] = m[1][1];
+	} else if (n % 2 == 1) {
+		mat_t t;
+		matpow(m, n - 1, t);
+		mulmat(m, t, r);
+	} else {
+		mat_t t;
+		matpow(m, n / 2, t);
+		mulmat(t, t, r);
+	}
+}
+
+int main() {
+	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
+
+	ull n;
+	while (cin >> n) {
+		if (n == 0) {
+			out << 1 << endl;
+		} else if (n == 1) {
+			out << 1 << endl;
+		} else {
+			vec_t start = {1, 1}, v;
+			mat_t m;
+			matpow(fibomat, n - 1, m);
+
+			mulvec(start, m, v);
+			out << v[1] << endl;
+		}
+	}
+
+	return 0;
+}