new linear recurrence kthTerm code

1 files changed, 33 insertions, 0 deletions

diff --git a/content/math/linearRecurrenceOld.cpp b/content/math/linearRecurrenceOld.cpp
new file mode 100644
index 0000000..2501e64
--- /dev/null
+++ b/content/math/linearRecurrenceOld.cpp
@@ -0,0 +1,33 @@
+constexpr ll mod = 1'000'000'007;
+vector<ll> modMul(const vector<ll>& a, const vector<ll>& b,
+                  const vector<ll>& c) {
+	ll n = sz(c);
+	vector<ll> res(n * 2 + 1);
+	for (int i = 0; i <= n; i++) { //a*b
+		for (int j = 0; j <= n; j++) {
+			res[i + j] += a[i] * b[j];
+			res[i + j] %= mod;
+	}}
+	for (int i = 2 * n; i > n; i--) { //res%c
+		for (int j = 0; j < n; j++) {
+			res[i - 1 - j] += res[i] * c[j];
+			res[i - 1 - j] %= mod;
+	}}
+	res.resize(n + 1);
+	return res;
+}
+
+ll kthTerm(const vector<ll>& f, const vector<ll>& c, ll k) {
+	assert(sz(f) == sz(c));
+	vector<ll> tmp(sz(c) + 1), a(sz(c) + 1);
+	tmp[0] = a[1] = 1; //tmp = (x^k) % c
+
+	for (k++; k > 0; k /= 2) {
+		if (k & 1) tmp = modMul(tmp, a, c);
+		a = modMul(a, a, c);
+	}
+
+	ll res = 0;
+	for (int i = 0; i < sz(c); i++) res += (tmp[i+1] * f[i]) % mod;
+	return res % mod;
+}