Fixes example in breadth-first-search.md

danilopereira10 · web-flow · commit 73dc9f28b911 · 2024-10-12T23:03:26.000-04:00
The current code can't find a path of even length from a source vertex s to a target vertex t. But, it can find a walk of even length
diff --git a/src/graph/breadth-first-search.md b/src/graph/breadth-first-search.md
@@ -152,10 +152,10 @@ Let $d_a []$ be the array containing shortest distances obtained from the first
 Now for each vertex it is easy to check whether it lies on any shortest path between $a$ and $b$:
 the criterion is the condition $d_a [v] + d_b [v] = d_a [b]$.
 
-* Find the shortest path of even length from a source vertex $s$ to a target vertex $t$ in an unweighted graph:
+* Find the shortest walk of even length from a source vertex $s$ to a target vertex $t$ in an unweighted graph:
 For this, we must construct an auxiliary graph, whose vertices are the state $(v, c)$, where $v$ - the current node, $c = 0$ or $c = 1$ - the current parity.
 Any edge $(u, v)$ of the original graph in this new column will turn into two edges $((u, 0), (v, 1))$ and $((u, 1), (v, 0))$.
-After that we run a BFS to find the shortest path from the starting vertex $(s, 0)$ to the end vertex $(t, 0)$.
+After that we run a BFS to find the shortest walk from the starting vertex $(s, 0)$ to the end vertex $(t, 0)$.
 
 ## Practice Problems
 
