diff --git a/src/data_structures/segment_tree.md b/src/data_structures/segment_tree.md index 92ce2595c..e49f56b45 100644 --- a/src/data_structures/segment_tree.md +++ b/src/data_structures/segment_tree.md @@ -44,7 +44,7 @@ Here is a visual representation of such a Segment Tree over the array $a = [1, 3 From this short description of the data structure, we can already conclude that a Segment Tree only requires a linear number of vertices. The first level of the tree contains a single node (the root), the second level will contain two vertices, in the third it will contain four vertices, until the number of vertices reaches $n$. -Thus the number of vertices in the worst case can be estimated by the sum $1 + 2 + 4 + \dots + 2^{\lceil\log_2 n\rceil} = 2^{\lceil\log_2 n\rceil + 1} \lt 4n$. +Thus the number of vertices in the worst case can be estimated by the sum $1 + 2 + 4 + \dots + 2^{\lceil\log_2 n\rceil} \lt 2^{\lceil\log_2 n\rceil + 1} \lt 4n$. It is worth noting that whenever $n$ is not a power of two, not all levels of the Segment Tree will be completely filled. We can see that behavior in the image. pFad - Phonifier reborn

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