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Insights from Leetcode problems.
Finding a cycle in a linked-list
Use two runners. \(\displaystyle O(n)\)
Runner 1 goes two steps per iteration.
Runner 2 goes one step per iteration.
If there is a cycle, runner 2 will lap runner 1 within 2 cycles.
Finding duplicates in an array
If you have an array of ints where each number appears \(\displaystyle n\) times and one number appears \(\displaystyle m\gt n\) times where \(\displaystyle gcd(n,m)==1\),
then you count the number of times each bit appears and take it mod \(\displaystyle n\).
The remaining bits will remain \(\displaystyle m \mod n\) times.
