xor range

content/various/chapter.tex

@@ -3,6 +3,10 @@ \chapter{Various}
 \kactlimport{GaussianElimination.hpp}
 \kactlimport{BinaryTrie.hpp}
 \kactlimport{InfixPropostfix.hpp}
+\kactlinport{xor_range.hpp}
+
+\section{LP Duality}
+	\import{lp_dual.tex}
 
 \section{Optimization tricks}
 	\verb@__builtin_ia32_ldmxcsr(40896);@ disables denormals (which make floats 20x slower near their minimum value).

content/various/lp_dual.tex

@@ -0,0 +1,10 @@
+\begin{tabular}{c|c}
+Maximization & Minimization \\
+\hline
+Inequality constraint $\le$ & Nonnegative variable $\ge$ \\
+Inequality constraint $\ge$ & Nonpositive variable $\le$ \\
+Equality constraint $=$ & Free variable \\
+Nonnegative variable $\ge$ & Inequality constraint $\ge$ \\
+Nonpositive variable $\le$ & Inequality constraint $\le$ \\
+Free variable & Equality constraint $=$ \\
+\end{tabular}

content/various/xor_range.hpp

@@ -0,0 +1,26 @@
+#pragma once
+
+/**
+ * Author: Teetat T.
+ * Date: 2024-11-27
+ * Description: find all range of $x$ such that $l \le x$ xor $p < r$.
+ */
+
+template<class F>
+void xor_range(ll p,ll l,ll r,const F &query){
+    for(int i=0;i<60;i++){
+        if(l==r)break;
+        ll b=1LL<<i;
+        if(l&b){
+            query(l^p,(l^p)+b);
+            l+=b;
+        }
+        if(r&b){
+            r-=b;
+            query(r^p,(r^p)+b);
+        }
+        if(p&b){
+            p^=b;
+        }
+    }
+}