add Bellman-Ford

code/BellmanFord.cpp

@@ -0,0 +1,31 @@
+// Bellman-Ford algorithm
+// compute shortest path in a directed graphdefaults
+// even with negative coststypede
+// find negative cycles
+// COMPLEXITY: O(nm)
+typedef struct Edge{
+  int u, v, w;
+  Edge(int u, int v, int w) : u(u), v(v), w(w) {}
+}Edge;
+vector<Edge> edges;
+int  dist[10000];
+int nodenum, edgenum;
+const int INF = 1000000000;
+// set dest[*] = INF, dist[src] = 0
+// fill edges, nodenum, edgenum
+void relax(int u, int v, int w) {
+  if(dist[v] > dist[u] + w) {
+    dist[v] = dist[u] + w;
+	// predecessor[v] = u
+  }
+}
+// return false if there is a negative cycle
+bool BellmanFord() {
+	for(int i = 0; i < nodenum-1; i++)
+		for(int j = 0; j < edgenum; j++) // (if there is no changes we can break)
+			relax(edges[j].u, edges[j].v, edges[j].w);
+	for(int i = 0; i < edgenum; i++)
+		if(dist[edges[i].u] + edges[i].w < dist[edges[i].v])
+      return false;
+  return true;
+}

main.tex

@@ -132,6 +132,9 @@ Temps de cuisson : $O(n)$
 \subsection{DFS/BFS}
 {\scriptsize\lstinputlisting{code/BFS_DFS.cpp}} % OK
 
+\subsection{Bellman-Ford}
+{\scriptsize\lstinputlisting{code/BellmanFord.cpp}} % OK
+
 \section{Structures de données}
 
 \subsection{Suffix arrays}