cp-algorithms · mhayter · Sep 11, 2025 · Sep 10, 2025
diff --git a/src/graph/01_bfs.md b/src/graph/01_bfs.md
@@ -42,7 +42,7 @@ while (!q.empty()) {
 We can notice that the difference between the distances between the source `s` and two other vertices in the queue differs by at most one.
 Especially, we know that $d[v] \le d[u] \le d[v] + 1$ for each $u \in Q$.
 The reason for this is, that we only add vertices with equal distance or with distance plus one to the queue during each iteration.
-Assuming there exists a $u$ in the queue with $d[u] - d[v] > 1$, then $u$ must have been insert in the queue via a different vertex $t$ with $d[t] \ge d[u] - 1 > d[v]$.
+Assuming there exists a $u$ in the queue with $d[u] - d[v] > 1$, then $u$ must have been inserted into the queue via a different vertex $t$ with $d[t] \ge d[u] - 1 > d[v]$.
 However this is impossible, since Dijkstra's algorithm iterates over the vertices in increasing order.
 
 This means, that the order of the queue looks like this: