Radix Sort ---------- - 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 ---------- > 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: $O(n^3 \log n)$