Merge pull request #1199 from maiquang04/patch-1

jakobkogler · web-flow · commit 70177da781a9 · 2023-11-28T18:14:50.000+01:00
Update min_cost_flow.md
diff --git a/src/graph/min_cost_flow.md b/src/graph/min_cost_flow.md
@@ -42,7 +42,7 @@ the residual network contains only unsaturated edges (i.e. edges in which $F_{i
 
 Now we can talk about the **algorithms** to compute the minimum-cost flow.
 At each iteration of the algorithm we find the shortest path in the residual graph from $s$ to $t$.
-In contrary to Edmonds-Karp we look for the shortest path in terms of the cost of the path, instead of the number of edges.
+In contrast to Edmonds-Karp, we look for the shortest path in terms of the cost of the path instead of the number of edges.
 If there doesn't exists a path anymore, then the algorithm terminates, and the stream $F$ is the desired one.
 If a path was found, we increase the flow along it as much as possible (i.e. we find the minimal residual capacity $R$ of the path, and increase the flow by it, and reduce the back edges by the same amount).
 If at some point the flow reaches the value $K$, then we stop the algorithm (note that in the last iteration of the algorithm it is necessary to increase the flow by only such an amount so that the final flow value doesn't surpass $K$).
