I've been subscribed to Interview Cake for years, and today they had a really interesting question: Given a list of n + 1 integers in the range 1...n, find one of the duplicates (there is guaranteed to be at least one) in O(n) time and O(1) additional space. The answer is really interesting1, and I recommend trying it, but I don't think it makes sense to care about additional space rather than total space, and I still think using a set to keep track of numbers (the most obvious solution) is the best solution in practice.
It's worth it to use more memory
There's a common programming interview question that asks you to find the single non-duplicated value in a list of duplicated integers. This can be done in O(n) time and O(1) space by XOR'ing the values, and doing so is almost always the wrong answer. A better solution when you can afford to do it1 is to use a hash table to count occurrences.
Indexing and sorting to find data quickly
To make your data faster to lookup, you can either store it in an order that makes it easier to search, or add one or more indexes. For practical work, you can let your file system do this for you, or use a pre-built database (either relational or not). I'll describe from the lowest-level to highest level so you can understand what I'm suggesting, but my real-world answer is that I would store most kinds of data in a relational database like PostgreSQL and put indexes on any column that I want to do lookups by.
How to find palindromes in Python
In school this week, the idea of finding palindromes in Python came up, as a homework assignment in a class I took last semester. A friend asked me for some guidance in how to do this in Python, so I showed him my "simple" solution:
#!/usr/bin/env python3
from …