Lecture_Notes/Sorting/2.md

Radix Sort 
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- sort elements from lowest significant to most significant values
- explain: basically counting sort on each bit / digit
- **Stability:** inherently stable - won't work if unstable
- **complexity:** $O(n \log\max a[i])$





Sex-Tuples
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> Given A[n], all distinct
> find the count of sex-tuples such that
> $$\frac{a b + c}{d} - e = f$$
> Note: numbers can repeat in the sextuple

- Naive: ${n \choose 6} = O(n^6)$
- Optimization. Rewrite the equation as $ab + c = d(e + f)$
    - Now, we only need ${n \choose 3} = O(n^3)$
    - Caution: $d \neq 0$
    - Once you have array of RHS, sort it in $O(\log n^3)$ time.
    - Then for each value of LHS, count using binary search in the sorted array in $\log n$ time.
    - Total: $O(n^3 \log n)$