Define as the minimum number of perfect squares that sum to . You want .
For each , try subtracting all perfect squares . Then for all valid . The base case is .
How many perfect squares are there? About . So for each , you do work. Total time: .
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
$ curl repovive.com/roadmaps/math-fundamentals/logarithms/perfect-squares-the-insight-dp-with-square-roots
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████████████████████████████████████████████████████████████████████