human
How to print maximum number of A 's using given four keys | this function returns the optimal length string for N keystrokes.
The optimal string length is N when N is smaller than 7.
An array to store result of subproblems.
Initializing the optimal lengths array for uptil 6 input strokes ..
Solve all subproblems in bottom manner.
for any keystroke n , we will need to choose between : - 1. pressing Ctrl - V once after copying the A ' s ▁ obtained ▁ by ▁ n - 3 ▁ keystrokes . ▁ ▁ 2 . ▁ pressing ▁ Ctrl - V ▁ twice ▁ after ▁ copying ▁ the ▁ A ' s obtained by n - 4 keystrokes . 3. pressing Ctrl - V thrice after copying the A 's  obtained by n-5 keystrokes..
Driver Code.
for the rest of the array we will rely on the previous entries to compute new ones"
Solution in Python:
assistant
#Here is code to how to print maximum number of A 's using given four keys and the other steps required.
 def findoptimal ( N ) :
	if ( N <= 6 ) :
		return N
	screen = [ 0 ] * N
	for n in range ( 1 , 7 ) :
		screen [ n - 1 ] = n
	for n in range ( 7 , N + 1 ) :
		screen [ n - 1 ] = max ( 2 * screen [ n - 4 ] , max ( 3 * screen [ n - 5 ] , 4 * screen [ n - 6 ] ) ) ;
	return screen [ N - 1 ]
if __name__ == " _ _ main _ _ " :
	for N in range ( 1 , 21 ) :
		print ( " Maximum ▁ Number ▁ of ▁ A ' s ▁ with ▁ " , N , " ▁ keystrokes ▁ is ▁ " , findoptimal ( N ) )