Lessons from Perfect Squares (Summary)

$1.$ Square roots and logarithms are connected: $\log(\sqrt{n}) = \frac{1}{2} \log(n)$.

$2.$ Dynamic programming builds solutions from smaller subproblems, and logarithms help analyze how many subproblems you have.

$3.$ Time complexity depends on both the number of states ($n$) and the transitions per state ($\sqrt{n}$), giving $O(n \sqrt{n})$ total.