changes to bitwise convolutions

- modify or/and transform to remove unnecessary reversal
- or transform is now sum over subsets, add note about this
- remove old sum over subsets DP

7 files changed, 10 insertions, 65 deletions

diff --git a/content/math/math.tex b/content/math/math.tex
index d59da54..fdf7081 100644
--- a/content/math/math.tex
+++ b/content/math/math.tex
@@ -321,6 +321,7 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 \end{algorithm}

 

 \begin{algorithm}{Polynome, FFT, NTT \& andere Transformationen}

+	\label{fft}

 	Multipliziert Polynome $A$ und $B$.

 	\begin{itemize}

 		\item $\deg(A \cdot B) = \deg(A) + \deg(B)$

@@ -328,14 +329,15 @@ sich alle Lösungen von $x^2-ny^2=c$ berechnen durch:
 		$\deg(A \cdot B) + 1$ haben.

 		Größe muss eine Zweierpotenz sein.

 		\item Für ganzzahlige Koeffizienten: \code{(ll)round(real(a[i]))}

-		\item \emph{xor}, \emph{or} und \emph{and} Transform funktioniert auch mit \code{double} oder modulo einer Primzahl $p$ falls $p \geq 2^{\texttt{bits}}$

+		\item \emph{or} Transform berechnet sum over subsets

+			$\rightarrow$ inverse für inclusion/exclusion

 	\end{itemize}

 	%\sourcecode{math/fft.cpp}

 	%\sourcecode{math/ntt.cpp}

 	\sourcecode{math/transforms/fft.cpp}

 	\sourcecode{math/transforms/ntt.cpp}

 	\sourcecode{math/transforms/bitwiseTransforms.cpp}

-	Multiplikation mit 2 transforms statt 3: (nur benutzten wenn nötig!)

+	Multiplikation mit 2 Transforms statt 3: (nur benutzen wenn nötig!)

 	\sourcecode{math/transforms/fftMul.cpp}

 \end{algorithm}

 

diff --git a/content/math/transforms/andTransform.cpp b/content/math/transforms/andTransform.cpp
index 1e9cfc0..9e40c74 100644
--- a/content/math/transforms/andTransform.cpp
+++ b/content/math/transforms/andTransform.cpp
@@ -4,5 +4,5 @@ void fft(vector<ll>& a, bool inv = false) {
 		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);
+				tie(u, v) = inv ? pair(u - v, v) : pair(u + v, v);
 }}}}
diff --git a/content/math/transforms/bitwiseTransforms.cpp b/content/math/transforms/bitwiseTransforms.cpp
index b98ea94..17f3163 100644
--- a/content/math/transforms/bitwiseTransforms.cpp
+++ b/content/math/transforms/bitwiseTransforms.cpp
@@ -4,8 +4,8 @@ void bitwiseConv(vector<ll>& a, bool inv = false) {
 		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) = inv ? pair(u - v, v) : pair(u + v, v); // AND
+				//tie(u, v) = inv ? pair(u, v - u) : 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/orTransform.cpp b/content/math/transforms/orTransform.cpp
index d0122bf..6503a68 100644
--- a/content/math/transforms/orTransform.cpp
+++ b/content/math/transforms/orTransform.cpp
@@ -4,5 +4,5 @@ void fft(vector<ll>& a, bool inv = false) {
 		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);
+				tie(u, v) = inv ? pair(u, v - u) : pair(u, v + u);
 }}}}
diff --git a/content/other/other.tex b/content/other/other.tex
index 2519427..8896962 100644
--- a/content/other/other.tex
+++ b/content/other/other.tex
@@ -67,9 +67,7 @@
 	\paragraph{Quadrangle inequality} Die Bedingung  $\forall a\leq b\leq c\leq d:

 	C[a][d] + C[b][c] \geq C[a][c] + C[b][d]$ ist hinreichend für beide Optimierungen.

 	

-	\paragraph{Sum over Subsets DP} $\text{res}[\text{mask}]=\sum_{i\subseteq\text{mask}}\text{in}[i]$.

-	Für Summe über Supersets \code{res} einmal vorher und einmal nachher reversen.

-	\sourcecode{other/sos.cpp}

+	\paragraph{Sum over Subsets DP} Siehe \emph{or} Transform, Seite \pageref{fft}.

 \end{algorithm}

 

 \begin{algorithm}{Fast Subset Sum}

@@ -82,6 +80,7 @@
 	\sourcecode{other/pbs.cpp}

 \end{algorithm}

 

+\columnbreak

 \begin{algorithm}{Josephus-Problem}

 	$n$ Personen im Kreis, jeder $k$-te wird erschossen.

 	\begin{description}

diff --git a/content/other/sos.cpp b/content/other/sos.cpp
deleted file mode 100644
index 892a47c..0000000
--- a/content/other/sos.cpp
+++ /dev/null
@@ -1,6 +0,0 @@
-vector<ll> res(in);
-for (int i = 1; i < ssize(res); i *= 2) {
-	for (int mask = 0; mask < ssize(res); mask++){
-		if (mask & i) {
-			res[mask] += res[mask ^ i];
-}}}
diff --git a/test/other/sos.cpp b/test/other/sos.cpp
deleted file mode 100644
index 3ab34ea..0000000
--- a/test/other/sos.cpp
+++ /dev/null
@@ -1,50 +0,0 @@
-#include "../util.h"
-
-vector<ll> sos(const vector<ll>& in) {
-	#include <other/sos.cpp>
-	return res;
-}
-
-vector<ll> naive(const vector<ll>& in) {
-	vector<ll> res(ssize(in));
-	for (ll i = 0; i < ssize(in); i++) {
-		for (ll j = 0; j <= i; j++) {
-			if ((i | j) == i) {
-				res[i] += in[j];
-			}
-		}
-	}
-	return res;
-}
-
-void stress_test() {
-	ll tests = 0;
-	for (ll i = 0; i < 1000; i++) {
-		int n = Random::integer<int>(1, 100);
-		auto in = Random::integers<ll>(n, -1000, 1000);
-		auto got = sos(in);
-		auto expected = naive(in);
-		if (got != expected) cerr << "error: " << i << FAIL;
-		tests += n;
-	}
-	cerr << "tested random queries: " << tests << endl;
-}
-
-constexpr int N = 10'000'000;
-void performance_test() {
-	timer t;
-	auto in = Random::integers<ll>(N, -1000, 1000);
-	t.start();
-	auto res = sos(in);
-	t.stop();
-	hash_t hash = 0;
-	for (ll x : res) hash += x;
-	if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
-	cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
-}
-
-int main() {
-	stress_test();
-	performance_test();
-}
-