Added subset stuff to handbook

ACM-UCI · Jan 1, 2022 · a888bb3 · a888bb3
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diff --git a/acm_uci_handbook/main.pdf b/acm_uci_handbook/main.pdf
diff --git a/acm_uci_handbook/main.tex b/acm_uci_handbook/main.tex
@@ -140,6 +140,13 @@
 
 
     \PartDivider{Algorithms}
+        \section{Dynamic Programming}
+            \subsection{Sum over Subsets}
+                Given an array \verb|A|, sum over subsets fills array \verb|S| such that \verb|S[mask]| is the sum of all values at indices \verb|s| where $s \subseteq mask$ in \verb|A|.
+                This algorithm is $O(N2^{N})$
+                \lstinputlisting[language=C++]{snippets/sum_over_subsets.cpp}
+                \lstinputlisting[language=Python]{snippets/sum_over_subsets.py}
+
         \section{Geometry}
             \subsection{Closest Points}
             \subsection{Convex Hull}
@@ -238,6 +245,11 @@
                 Returns $\sum_{k=0}^{end} k^{3} = \frac{n^{2}(n+1)^{2}}{4}$
                 \lstinputlisting[language=C++]{snippets/sum_of_cubes.cpp}
                 \lstinputlisting[language=Python]{snippets/sum_of_cubes.py}
+        \section{Miscellaneous}
+            \subsection{Subset Enumeration}
+                Given a bitmask \verb|m|, the following iterates through all submasks of \verb|m|.
+                \lstinputlisting[language=C++]{snippets/subset_enumeration.cpp}
+                \lstinputlisting[language=Python]{snippets/subset_enumeration.py}
         \section{Strings}
             \subsection{Knuth Morris Pratt: String Matching} \label{kmp}
             \subsection{Levinshtein Distance: Edit Distance}

diff --git a/acm_uci_handbook/snippets/subset_enumeration.cpp b/acm_uci_handbook/snippets/subset_enumeration.cpp
@@ -0,0 +1,3 @@
+for (int s=m; s; s=(s-1)&m) {
+    // ...
+}
diff --git a/acm_uci_handbook/snippets/subset_enumeration.py b/acm_uci_handbook/snippets/subset_enumeration.py
@@ -0,0 +1,4 @@
+s = m
+while s:
+    # ...
+    s = (s-1) & m
diff --git a/acm_uci_handbook/snippets/sum_over_subsets.cpp b/acm_uci_handbook/snippets/sum_over_subsets.cpp
@@ -0,0 +1,7 @@
+// Initialize S array
+for (int i = 0; i < (1<<N); ++i)
+    S[i] = A[i];
+
+for (int i = 0; i < N; ++i) for (int mask = 0; mask < (1<<N); ++mask)
+    if (mask & (1<<i))
+        S[mask] += S[mask^(1<<i)];
diff --git a/acm_uci_handbook/snippets/sum_over_subsets.py b/acm_uci_handbook/snippets/sum_over_subsets.py
@@ -0,0 +1,8 @@
+from copy import copy
+
+S = copy(A)
+for i in range(N):
+    for mask in range(1<<N):
+        if mask & (1<<i):
+            S[mask] += S[mask^(1<<i)]
+