From 52ba871e0de9399f77da4b5b0d2c33a2dd6eb6a1 Mon Sep 17 00:00:00 2001
From: Gloria Mundi <gloria@gloria-mundi.eu>
Date: Sat, 18 Jan 2025 03:05:17 +0100
Subject: 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
---
 content/math/math.tex                         | 6 ++++--
 content/math/transforms/andTransform.cpp      | 2 +-
 content/math/transforms/bitwiseTransforms.cpp | 4 ++--
 content/math/transforms/orTransform.cpp       | 2 +-
 content/other/other.tex                       | 5 ++---
 content/other/sos.cpp                         | 6 ------
 6 files changed, 10 insertions(+), 15 deletions(-)
 delete mode 100644 content/other/sos.cpp

(limited to 'content')

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];
-}}}
-- 
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