Merge pull request cp-algorithms#1162 from joaomarcosth9/patch-1

jakobkogler · web-flow · commit 7c8dbc1c88f4 · 2023-10-13T19:49:52.000+02:00
Update bellman_ford.md
diff --git a/src/graph/bellman_ford.md b/src/graph/bellman_ford.md
@@ -20,7 +20,7 @@ Let us assume that the graph contains no negative weight cycle. The case of pres
 
 We will create an array of distances $d[0 \ldots n-1]$, which after execution of the algorithm will contain the answer to the problem. In the beginning we fill it as follows: $d[v] = 0$, and all other elements $d[ ]$ equal to infinity $\infty$.
 
-The algorithm consists of several phases. Each phase scans through all edges of the graph, and the algorithm tries to produce **relaxation** along each edge $(a,b)$ having weight $c$. Relaxation along the edges is an attempt to improve the value $d[b]$ using value $d[a] + c$. In fact, it means that we are trying to improve the answer for this vertex using edge $(a,b)$ and current response for vertex $a$.
+The algorithm consists of several phases. Each phase scans through all edges of the graph, and the algorithm tries to produce **relaxation** along each edge $(a,b)$ having weight $c$. Relaxation along the edges is an attempt to improve the value $d[b]$ using value $d[a] + c$. In fact, it means that we are trying to improve the answer for this vertex using edge $(a,b)$ and current answer for vertex $a$.
 
 It is claimed that $n-1$ phases of the algorithm are sufficient to correctly calculate the lengths of all shortest paths in the graph (again, we believe that the cycles of negative weight do not exist). For unreachable vertices the distance $d[ ]$ will remain equal to infinity $\infty$.
 
