Prim with adjacency list

Author: xaero7

graph_theory.tex

@@ -4,7 +4,8 @@
 \chapter{图论}
 \label{graph_theory}
 
-
+\newcommand{\prefixgrapthy}[1]{graph\_theory/#1}
+\newcommand{\xprefixgrapthy}[1]{graph_theory/#1}
 
 \section{最短路}
 
@@ -44,12 +45,21 @@ \subsection{Floyd，邻接矩阵存储}
 
 
 \section{最小生成树 / 森林}
-\subsection{Prim}
-例：\href{https://xoj.red/problems/show/1240}{XOJ 1240 Agri-Net 最短网络}
-\lstinputlisting{graph_theory/mst_prim_matrix.cpp}
 
-\subsection{Prim + priority\_queue优化}
-\lstinputlisting{graph_theory/mst_prim_priority_queue.cpp}
+\begin{example}[最小生成树]
+\href{https://xoj.red/problems/show/1240}{XOJ 1240 Agri-Net 最短网络}
+\end{example}
+
+\xsubsection{Prim + 邻接矩阵}{\prefixgrapthy{mst\_prim\_matrix.cpp}}
+
+\lstinputlisting{\xprefixgrapthy{mst_prim_matrix.cpp}}
+
+\xsubsection{Prim + 邻接表}{\prefixgrapthy{mst\_prim\_vector.cpp}}
+
+\lstinputlisting{\xprefixgrapthy{mst_prim_vector.cpp}}
+
+\xsubsection{Prim + priority\_queue优化}{\prefixgrapthy{mst\_prim\_priority\_queue.cpp}}
+\lstinputlisting{\xprefixgrapthy{mst_prim_priority_queue.cpp}}
 
 \subsection{Kruskal}
 \lstinputlisting{graph_theory/mst_kruskal.cpp}

graph_theory/mst_prim_vector.cpp

@@ -0,0 +1,60 @@
+#include<bits/stdc++.h>
+using namespace std;
+const int maxn = 110, INF = 0x3fffffff;
+struct Edge {
+	int from, to, dist;
+	Edge(int u, int v, int w):from(u),to(v),dist(w){}
+};
+struct Prim {
+	int n, m;
+	vector<Edge> edges;
+	vector<int> G[maxn]; //G[i]表示从顶点i出发的所有边的编号 
+	bool vis[maxn];
+	
+	void init(int n) {
+		this->n = n;
+		for (int i=0; i<n; i++) G[i].clear();
+		edges.clear();
+	}
+	
+	void add_edge(int from, int to, int dist) {
+		edges.push_back(Edge(from, to, dist));
+		m = edges.size();
+		G[from].push_back(m-1);
+	}
+	
+	int prim(int u) {
+		int ans = 0;
+		vis[u] = true;
+		for (int i=0; i<n-1; i++) {
+			int min = INF, sel_e;
+			for (int j=0; j<n; j++) {
+				if (!vis[j]) continue;
+				for (int k=0; k<G[j].size(); k++) {
+					Edge &e = edges[G[j][k]];
+					if (!vis[e.to] && e.dist<min) {
+						min = e.dist;
+						sel_e = G[j][k];
+					}
+				}
+			}
+			Edge &e = edges[sel_e];
+			vis[e.to] = true;
+			ans += e.dist;
+		}
+		return ans;
+	}
+} mst;
+
+int main() {
+	int n, w;
+	scanf("%d", &n);
+	mst.init(n);
+	for (int i=0; i<n; i++)
+		for (int j=0; j<n; j++) {
+			scanf("%d", &w);
+			if (i != j)
+				mst.add_edge(i, j, w); //邻接矩阵自动会加反向边 
+		}
+	printf("%d\n", mst.prim(0));
+}