From 5dbf37a9f277e19636f1e740e8befc421c19aa25 Mon Sep 17 00:00:00 2001
From: Aleksandr Mishukhin <100044766+aleksmish@users.noreply.github.com>
Date: Wed, 10 Sep 2025 14:31:43 +0300
Subject: [PATCH] fix typo
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Changed from  "then  u  must have been insert in the queue" to
"then  u  must have been inserted into the queue"
---
 src/graph/01_bfs.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/graph/01_bfs.md b/src/graph/01_bfs.md
index 5d7aee6f4..68a4a01c9 100644
--- 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: