mzuenni tests

11 files changed, 183 insertions, 0 deletions

diff --git a/content/math/transforms/andTransform.cpp b/content/math/transforms/andTransform.cpp
new file mode 100644
index 0000000..1fd9f5c
--- /dev/null
+++ b/content/math/transforms/andTransform.cpp
@@ -0,0 +1,8 @@
+void fft(vector<ll>& a, bool inv = false) {
+	int n = sz(a);
+	for (int s = 1; s < n; s *= 2) {
+		for (int i = 0; i < n; i += 2 * s) {
+			for (int j = i; j < i + s; j++) {
+				ll& u = a[j], &v = a[j + s];
+				tie(u, v) = inv ? pair(v - u, u) : pair(v, u + v);
+}}}}
diff --git a/content/math/transforms/bitwiseTransforms.cpp b/content/math/transforms/bitwiseTransforms.cpp
new file mode 100644
index 0000000..28561da
--- /dev/null
+++ b/content/math/transforms/bitwiseTransforms.cpp
@@ -0,0 +1,12 @@
+void bitwiseConv(vector<ll>& a, bool inv = false) {
+	int n = sz(a);
+	for (int s = 1; s < n; s *= 2) {
+		for (int i = 0; i < n; i += 2 * s) {
+			for (int j = i; j < i + s; j++) {
+				ll& u = a[j], &v = a[j + s];
+				tie(u, v) = inv ? pair(v - u, u) : pair(v, u + v); // AND
+				//tie(u, v) = inv ? pair(v, u - v) : pair(u + v, u); //OR
+				//tie(u, v) = pair(u + v, u - v); // XOR
+	}}}
+	//if (inv) for (ll& x : a) x /= n; // XOR (careful with MOD)
+}
diff --git a/content/math/transforms/fft.cpp b/content/math/transforms/fft.cpp
new file mode 100644
index 0000000..2bd95b2
--- /dev/null
+++ b/content/math/transforms/fft.cpp
@@ -0,0 +1,23 @@
+using cplx = complex<double>;
+
+void fft(vector<cplx>& a, bool inv = false) {
+	int n = sz(a);
+	for (int i = 0, j = 1; j < n - 1; ++j) {
+		for (int k = n >> 1; k > (i ^= k); k >>= 1);
+		if (j < i) swap(a[i], a[j]);
+	}
+	static vector<cplx> ws(2, 1);
+	for (static int k = 2; k < n; k *= 2) {
+		ws.resize(n);
+		cplx w = polar(1.0, acos(-1.0) / k);
+		for (int i=k; i<2*k; i++) ws[i] = ws[i/2] * (i % 2 ? w : 1);
+	}
+	for (int s = 1; s < n; s *= 2) {
+		for (int j = 0; j < n; j += 2 * s) {
+			for (int k = 0; k < s; k++) {
+				cplx u = a[j + k], t = a[j + s + k];
+				t *= (inv ? conj(ws[s + k]) : ws[s + k]);
+				a[j + k] = u + t;
+				a[j + s + k] = u - t;
+				if (inv) a[j + k] /= 2, a[j + s + k] /= 2;
+}}}}
diff --git a/content/math/transforms/fftMul.cpp b/content/math/transforms/fftMul.cpp
new file mode 100644
index 0000000..660ed79
--- /dev/null
+++ b/content/math/transforms/fftMul.cpp
@@ -0,0 +1,15 @@
+vector<cplx> mul(vector<ll>& a, vector<ll>& b) {
+	int n = 1 << (__lg(sz(a) + sz(b) - 1) + 1);
+	vector<cplx> c(all(a)), d(n);
+	c.resize(n);
+	for (int i = 0; i < sz(b); i++) c[i] = {real(c[i]), b[i]};
+	fft(c);
+	for (int i = 0; i < n; i++) {
+		int j = (n - i) & (n - 1);
+		cplx x = (c[i] + conj(c[j])) / cplx{2, 0}; //fft(a)[i];
+		cplx y = (c[i] - conj(c[j])) / cplx{0, 2}; //fft(b)[i];
+		d[i] = x * y;
+	}
+	fft(d, true);
+	return d;
+}
diff --git a/content/math/transforms/multiplyBitwise.cpp b/content/math/transforms/multiplyBitwise.cpp
new file mode 100644
index 0000000..f7cf169
--- /dev/null
+++ b/content/math/transforms/multiplyBitwise.cpp
@@ -0,0 +1,8 @@
+vector<ll> mul(vector<ll> a, vector<ll> b) {
+	int n = 1 << (__lg(2 * max(sz(a), sz(b)) - 1));
+	a.resize(n), b.resize(n);
+	bitwiseConv(a), bitwiseConv(b);
+	for (int i=0; i<n; i++) a[i] *= b[i]; // MOD?
+	bitwiseConv(a, true);
+	return a;
+}
diff --git a/content/math/transforms/multiplyFFT.cpp b/content/math/transforms/multiplyFFT.cpp
new file mode 100644
index 0000000..0022d1f
--- /dev/null
+++ b/content/math/transforms/multiplyFFT.cpp
@@ -0,0 +1,12 @@
+vector<ll> mul(vector<ll>& a, vector<ll>& b) {
+	int n = 1 << (__lg(sz(a) + sz(b) - 1) + 1);
+	vector<cplx> a2(all(a)), b2(all(b));
+	a2.resize(n), b2.resize(n);
+	fft(a2), fft(b2);
+	for (int i=0; i<n; i++) a2[i] *= b2[i];
+	fft(a2, true);
+
+	vector<ll> ans(n);
+	for (int i=0; i<n; i++) ans[i] = llround(a2[i].real());
+	return ans;
+}
diff --git a/content/math/transforms/multiplyNTT.cpp b/content/math/transforms/multiplyNTT.cpp
new file mode 100644
index 0000000..806d124
--- /dev/null
+++ b/content/math/transforms/multiplyNTT.cpp
@@ -0,0 +1,8 @@
+vector<ll> mul(vector<ll> a, vector<ll> b) {
+	int n = 1 << (__lg(sz(a) + sz(b) - 1) + 1);
+	a.resize(n), b.resize(n);
+	ntt(a), ntt(b);
+	for (int i=0; i<n; i++) a[i] = a[i] * b[i] % mod;
+	ntt(a, true);
+	return a;
+}
diff --git a/content/math/transforms/ntt.cpp b/content/math/transforms/ntt.cpp
new file mode 100644
index 0000000..ca605d3
--- /dev/null
+++ b/content/math/transforms/ntt.cpp
@@ -0,0 +1,23 @@
+constexpr ll mod = 998244353, root = 3;
+
+void ntt(vector<ll>& a, bool inv = false) {
+	int n = sz(a);
+	auto b = a;
+	ll r = inv ? powMod(root, mod - 2, mod) : root;
+
+	for (int s = n / 2; s > 0; s /= 2) {
+		ll ws = powMod(r, (mod - 1) / (n / s), mod), w = 1;
+		for (int j = 0; j < n / 2; j += s) {
+			for (int k = j; k < j + s; k++) {
+				ll u = a[j + k], t = a[j + s + k] * w % mod;
+				b[k] = (u + t) % mod;
+				b[n/2 + k] = (u - t + mod) % mod;
+			}
+			w = w * ws % mod;
+		}
+		swap(a, b);
+	}
+	if (inv) {
+		ll div = powMod(n, mod - 2, mod);
+		for (auto& x : a) x = x * div % mod;
+}}
diff --git a/content/math/transforms/orTransform.cpp b/content/math/transforms/orTransform.cpp
new file mode 100644
index 0000000..eb1da44
--- /dev/null
+++ b/content/math/transforms/orTransform.cpp
@@ -0,0 +1,8 @@
+void fft(vector<ll>& a, bool inv = false) {
+	int n = sz(a);
+	for (int s = 1; s < n; s *= 2) {
+		for (int i = 0; i < n; i += 2 * s) {
+			for (int j = i; j < i + s; j++) {
+				ll& u = a[j], &v = a[j + s];
+				tie(u, v) = inv ? pair(v, u - v) : pair(u + v, u);
+}}}}
diff --git a/content/math/transforms/seriesOperations.cpp b/content/math/transforms/seriesOperations.cpp
new file mode 100644
index 0000000..4743674
--- /dev/null
+++ b/content/math/transforms/seriesOperations.cpp
@@ -0,0 +1,56 @@
+vector<ll> poly_inv(const vector<ll>& a, int n) {
+	vector<ll> q = {powMod(a[0], mod-2, mod)};
+	for (int len = 1; len < n; len *= 2){
+		vector<ll> a2 = a, q2 = q;
+		a2.resize(2*len), q2.resize(2*len);
+		ntt(q2);
+		for (int j : {0, 1}) {
+			ntt(a2);
+			for (int i = 0; i < 2*len; i++) a2[i] = a2[i]*q2[i] % mod;
+			ntt(a2, true);
+			for (int i = 0; i < len; i++) a2[i] = 0;
+		}
+		for (int i = len; i < min(n, 2*len); i++) {
+			q.push_back((mod - a2[i]) % mod);
+	}}
+	return q;
+}
+
+vector<ll> poly_deriv(vector<ll> a) {
+	for (int i = 1; i < sz(a); i++)
+		a[i-1] = a[i] * i % mod;
+	a.pop_back();
+	return a;
+}
+
+vector<ll> poly_integr(vector<ll> a) {
+	if (a.empty()) return {0};
+	a.push_back(a.back() * powMod(sz(a), mod-2, mod) % mod);
+	for (int i = sz(a)-2; i > 0; i--)
+		a[i] = a[i-1] * powMod(i, mod-2, mod) % mod;
+	a[0] = 0;
+	return a;
+}
+
+vector<ll> poly_log(vector<ll> a, int n) {
+	a = mul(poly_deriv(a), poly_inv(a, n));
+	a.resize(n-1);
+	a = poly_integr(a);
+	return a;
+}
+
+vector<ll> poly_exp(vector<ll> a, int n) {
+	vector<ll> q = {1};
+	for (int len = 1; len < n; len *= 2) {
+		vector<ll> p = poly_log(q, 2*len);
+		for (int i = 0; i < 2*len; i++)
+			p[i] = (mod - p[i] + (i < sz(a) ? a[i] : 0)) % mod;
+		vector<ll> q2 = q;
+		q2.resize(2*len);
+		ntt(p), ntt(q2);
+		for (int i = 0; i < 2*len; i++) p[i] = p[i] * q2[i] % mod;
+		ntt(p, true);
+		for (int i = len; i < min(n, 2*len); i++) q.push_back(p[i]);
+	}
+	return q;
+}
diff --git a/content/math/transforms/xorTransform.cpp b/content/math/transforms/xorTransform.cpp
new file mode 100644
index 0000000..f9d1d82
--- /dev/null
+++ b/content/math/transforms/xorTransform.cpp
@@ -0,0 +1,10 @@
+void fft(vector<ll>& a, bool inv = false) {
+	int n = sz(a);
+	for (int s = 1; s < n; s *= 2) {
+		for (int i = 0; i < n; i += 2 * s) {
+			for (int j = i; j < i + s; j++) {
+				ll& u = a[j], &v = a[j + s];
+				tie(u, v) = pair(u + v, u - v);
+	}}}
+	if (inv) for (ll& x : a) x /= n;
+}