draw a circle first with the maximum radius as far as possible.

draw a circle inside each rectangle

1. there must be four corner spaces where you can continue to draw circles
2. there may also be length-width remaining space of a rectangle to continue to draw a circle (if it is a square, this bar does not exist)

the idea is that after each circle is drawn, according to the current length and width , calculate the above two possible length, width, radius , put into priority queue , and then take out the maximum radius value to continue to draw the circle until count is 0

use the following picture to illustrate the idea of the solution to this problem

Picture from: http://mathworld.wolfram.com/.

it is obvious that every time you fill a circle, the radius should be as strong > as possible and directly take the maximum value that can be filled .
the subject considers two circles, make one of them smaller, and then leave space for the other to achieve a larger total area . In fact, does not exist
of course it is quite complicated to write code. All kinds of irrational number operations.
if the precision requirement is not high, using the method of translation, constantly offsetting the center point of the circle should be a more scientific idea

Update 2018.12.29:
look at figure 1 and figure 2 below. It's so obvious. (aheb) 2 = (A) 2 + (B) 2 + 2AB.
(Abib) 2 > (A) 2 + (B) 2, it must be that the larger the radius, the bigger the , that's all.

think backwards:
Let one large circle reduce the radius of X, it is impossible to increase the radius of another small circle > X .
therefore, there is no question of how the two circles are arranged and positioned.
is always filled in with the largest circle, which is the optimal solution .