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D3128: Update Prim's algorithm to match current implementation
- Consolidate two prim() overloads into a single signature with defaulted WF and CompareOp template parameters (seed moved to second parameter) - Remove init_dist parameter; add explicit requires clause for basic_edge_weight_function with plus<> combine - Update mst.hpp and prim.hpp signatures accordingly - algorithms.tex: resolve \phil note by documenting delegation to dijkstra_shortest_paths; fix lstinputlisting line range (24-39); correct Mandates type (vertex_property_map_value_t<Weight>); add init_shortest_paths precondition; update Effects; add Throws section; add Remarks for disconnected-graph usage"
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Lines changed: 47 additions & 43 deletions

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‎D3128_Algorithms/src/mst.hpp‎

Lines changed: 12 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -21,23 +21,19 @@ auto inplace_kruskal(IELR&& e, OELR&& t, CompareOp compare);
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/*
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* Prim's Algorithm
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*/
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template <adjacency_list G, class Predecessor, class Weight>
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auto prim(G&& g, Predecessor& predecessor, Weight& weight, const vertex_id_t<G>& seed = 0);
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template <adjacency_list G,
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class Predecessor,
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class Weight,
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class CompareOp,
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class WF>
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requires basic_edge_weight_function<G,
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WF,
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vertex_property_map_value_t<Weight>,
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CompareOp,
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class WF = function<vertex_property_map_value_t<Weight>(const remove_reference_t<G>&,
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const edge_t<G>&)>,
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class CompareOp = less<vertex_property_map_value_t<Weight>>>
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requires vertex_property_map_for<Predecessor, G> &&
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vertex_property_map_for<Weight, G> &&
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basic_edge_weight_function<G, WF, vertex_property_map_value_t<Weight>, CompareOp,
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plus<vertex_property_map_value_t<Weight>>>
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auto prim(G&& g,
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Predecessor& predecessor,
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Weight& weight,
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CompareOp compare,
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vertex_property_map_value_t<Weight> init_dist,
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WF&& weight_fn,
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vertex_id_t<G> seed = 0);
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auto prim(G&& g,
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const vertex_id_t<G>& seed,
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Predecessor& predecessor,
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Weight& weight,
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WF&& weight_fn = [](const auto&, const edge_t<G>& uv) { return edge_value(g, uv); },
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CompareOp compare = less<vertex_property_map_value_t<Weight>>());

‎D3128_Algorithms/src/prim.hpp‎

Lines changed: 11 additions & 17 deletions
Original file line numberDiff line numberDiff line change
@@ -1,22 +1,16 @@
1-
template <adjacency_list G,
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class Predecessor,
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class Weight>
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requires vertex_property_map_for<Predecessor, G> &&
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vertex_property_map_for<Weight, G>
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void prim(G&& g, Predecessor& predecessor, Weight& weight, const vertex_id_t<G>& source = 0);
7-
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template <adjacency_list G,
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class Predecessor,
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class Weight,
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class CompareOp,
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class WF>
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class WF = function<vertex_property_map_value_t<Weight>(const remove_reference_t<G>&,
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const edge_t<G>&)>,
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class CompareOp = less<vertex_property_map_value_t<Weight>>>
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requires vertex_property_map_for<Predecessor, G> &&
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vertex_property_map_for<Weight, G> &&
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basic_edge_weight_function<G, WF, vertex_property_map_value_t<Weight>, CompareOp, plus<vertex_property_map_value_t<Weight>>>
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void prim(G&& g,
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Predecessor& predecessor,
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Weight& weight,
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CompareOp compare,
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vertex_property_map_value_t<Weight> init_dist,
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WF&& weight_fn,
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vertex_id_t<G> source = 0);
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basic_edge_weight_function<G, WF, vertex_property_map_value_t<Weight>, CompareOp,
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plus<vertex_property_map_value_t<Weight>>>
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auto prim(G&& g,
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const vertex_id_t<G>& seed,
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Predecessor& predecessor,
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Weight& weight,
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WF&& weight_fn = [](const auto&, const edge_t<G>& uv) { return edge_value(g, uv); },
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CompareOp compare = less<vertex_property_map_value_t<Weight>>());

‎D3128_Algorithms/tex/algorithms.tex‎

Lines changed: 24 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -1691,8 +1691,7 @@ \subsection{Inplace Kruskal Minimum Spanning Tree}
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\subsection{Prim Minimum Spanning Tree}
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Find the minimum weight spanning tree of a graph using Prim's algorithm.
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\phil{Use general form of dijkstra's shortest path?}
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Delegates to \lstinline{dijkstra_shortest_paths} with a projecting combine function that uses the edge weight directly rather than accumulating path distance.
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\begin{table}[ht]
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\setcellgapes{3pt}
@@ -1712,14 +1711,14 @@ \subsection{Prim Minimum Spanning Tree}
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\end{table}
17131712

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{\small
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\lstinputlisting[firstline=24,lastline=43]{D3128_Algorithms/src/mst.hpp}
1714+
\lstinputlisting[firstline=24,lastline=39]{D3128_Algorithms/src/mst.hpp}
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}
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\begin{itemdescr}
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\pnum\mandates
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\begin{itemize}
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\item
1722-
\lstinline{compare} operator is a valid comparison operation on two edge values of type \lstinline{edge_value_t<G>} which returns a bool.
1721+
\lstinline{compare} is a valid strict weak ordering on values of type \lstinline{vertex_property_map_value_t<Weight>}.
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\end{itemize}
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\pnum\hardprecond
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\begin{itemize}
@@ -1729,30 +1728,45 @@ \subsection{Prim Minimum Spanning Tree}
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\lstinline{weight} contains an entry for each vertex of \lstinline{g}.
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\item
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\lstinline{predecessor} contains an entry for each vertex of \lstinline{g}.
1731+
\item
1732+
\lstinline{weight} and \lstinline{predecessor} have been initialized before calling
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(e.g.\ via \lstinline{init_shortest_paths(g, weight, predecessor)}).
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\end{itemize}
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\pnum\preconditions
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\begin{itemize}
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\item
1736-
\lstinline{weight_fn}, when provided, must satisfy
1737-
\lstinline{basic_edge_weight_function<G, WF, vertex_property_map_value_t<Weight>, CompareOp>}.
1738+
\lstinline{weight_fn} must satisfy
1739+
\lstinline{basic_edge_weight_function<G, WF, vertex_property_map_value_t<Weight>, CompareOp,}
1740+
\lstinline{plus<vertex_property_map_value_t<Weight>>>}.
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When omitted, the default is \lstinline{edge_value(g, uv)}.
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\end{itemize}
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\pnum\effects
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\begin{itemize}
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\item
1743-
\lstinline{predecessor[v]} is the parent vertex of \lstinline{v} in a tree rooted at \lstinline{seed} and \lstinline{weight[v]} is the value of the edge between \lstinline{v} and \lstinline{predecessor[v]} in the tree. When \lstinline{compare} is \lstinline{<} and \lstinline{init_dist==+inf}, \lstinline{predecessor} represents a minimum weight spanning tree.
1746+
\lstinline{predecessor[v]} is the parent vertex of \lstinline{v} in a tree rooted at \lstinline{seed}
1747+
and \lstinline{weight[v]} is the value of the edge between \lstinline{v} and \lstinline{predecessor[v]}
1748+
in the tree. \lstinline{predecessor[seed] == seed}.
1749+
When \lstinline{compare} is \lstinline{<}, \lstinline{predecessor} represents a minimum weight spanning tree.
17441750
\item
1745-
If \lstinline{predecessor} and \lstinline{weight} are not initialized by the user, and the graph is not fully connected, \lstinline{predecessor[v]} and \lstinline{weight[v]} will be undefined for vertices not in the same connected component as \lstinline{seed}.
1751+
For vertices not reachable from \lstinline{seed}, \lstinline{predecessor[v]} and \lstinline{weight[v]}
1752+
retain their initialized values (as set by \lstinline{init_shortest_paths}).
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\end{itemize}
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%\pnum\result
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\pnum\returns The total weight of the minimum spanning tree rooted at \lstinline{seed}.
1749-
%\pnum\throws
1756+
\pnum\throws
1757+
\begin{itemize}
1758+
\item \lstinline{std::out_of_range} if \lstinline{seed} is not a valid vertex ID in \lstinline{g}.
1759+
\item \lstinline{std::out_of_range} if \lstinline{predecessor} or \lstinline{weight} are undersized for the graph.
1760+
\item \lstinline{std::out_of_range} if a negative edge weight is encountered (for signed weight types).
1761+
\item \lstinline{std::logic_error} if an internal invariant violation is detected.
1762+
\end{itemize}
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\pnum\complexity
17511764
\begin{itemize}
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\item \textbf{Time:} $\mathcal{O}(|E|\log{|V|})$.
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\item \textbf{Space:} $\mathcal{O}(|V|)$ auxiliary --- priority queue and bookkeeping arrays.
17541767
\end{itemize}
1755-
%\pnum\remarks
1768+
\pnum\remarks Only produces a spanning tree for the connected component containing \lstinline{seed}.
1769+
For disconnected graphs, call \lstinline{prim} once per component with a seed vertex from each component.
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%\pnum\errors
17571771
\end{itemdescr}
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