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[pre-commit.ci] auto fixes from pre-commit.com hooks
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pre-commit-ci[bot] committed Dec 8, 2024
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Expand Up @@ -7,8 +7,8 @@ author: Justin Ji

<Spoiler title="Hint 1">

The upper bound for the number of bridges we can have is $n - 1$ because
each bridge is present in any spanning tree of the graph. A
The upper bound for the number of bridges we can have is $n - 1$ because
each bridge is present in any spanning tree of the graph. A
spanning tree is a subgraph that connects every node without cycles.

</Spoiler>
Expand All @@ -22,8 +22,8 @@ How can we use the rest of these nodes to use as many edges as possible?

<Spoiler title="Explanation">

The most bridges we can have in a graph with $n$ nodes is $n - 1$ bridges.
As a result, our answer is in the range $[n - 1, 2n - 2]$.
The most bridges we can have in a graph with $n$ nodes is $n - 1$ bridges.
As a result, our answer is in the range $[n - 1, 2n - 2]$.

Let's consider binary
searching on our answer. If we have $x$ edges that we need to use, then
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