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For anyone with a similar question who reads this in the future, I found this very helpful series of YouTube videos concerning algorithms. I liked it because the series covers topics in a similar order to the book. There is no assumption of what you do or don't know, material is covered from the ground up. Each video provides multiple examples of problems.

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The key to learning this, or much of anything, is reinforcement and feedback. Reinforcement comes from doing exercises and solving problems in a course like this and the book has plenty of mid chapter and end chapter exercises and problems. You can do a lot of these. All of them may be asking too much, but you want to be able to answer any of them. Getting ...

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MergeSort is fairly easy to implement in Python and it's a straightforward divide-and-conquer algorithm. You keep splitting the collection in half until it is in trivial-to-sort pieces. This splitting reduces sorting from O(n^2) to O(nlog(n)). Second example: computing integer powers. if the power is even, square base and integer divide exponent by 2. ...

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Another one is the following job scheduling problem: N jobs are arriving with priorities: priority_1 arrival_time_1 execution_time_1 priority_2 arrival_time_2 execution_time_2 ... priority_N arrival_time_N execution_time_N The arriving jobs are queued. When the CPU can process the next job, he will pick the one that has already arrived and has the ...

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How about Huffman encodings? Given a text that uses an alphabet of $n$ unique characters, how can we uniquely encode the alphabet so that the text uses the smallest amount of bits? More formally for Huffman encodings (as formulated by Tardos & Kleinberg in their book Algorithm Design): Given an alphabet and a set of frequencies for letters, we ...

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One nice problem that I found is: Given n segments in 2D Euclidean space, find two segments that intersect. Seek for $O(n \cdot log(n))$ solution. https://cp-algorithms.com/geometry/intersecting_segments.html

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