Allowable Length

def find_stacks(rows: List[List[Piece]]) -> List[List[Piece]]:
    """
    Finds the stacks of the pieces.

    rows: List of row of pieces ordered from top to bottom.
    return: List of stacks of pieces ordered from top to bottom.
    """
    stacks = []
    for row in rows:
        for piece in row:
            added = False
            for stack in stacks:
                subpiece = stack[-1]
                if subpiece is subset piece:
                    stack.append(piece)
                    added = True
            if added == False:
                new_stack = [piece]
                stacks.append(new_stack)
    return stacks

len(1,1)	len(1,2)	len(1,3)	len(1,4)	…	len(1,n-1)	len(1,n)
	len(2,2)	len(2,3)	len(2,4)	…	len(2,n-1)	len(2,n)
		len(3,3)	len(3,4)	…	len(3,n-1)	len(3,n)
			len(4,4)	…	len(4,n-1)	len(4,n)
…	…	…	…	…	…	…
				…	len(n-1,n-1)	len(n-1,n)
				…	_	len(n,n)

\[\begin{split}\begin{align} & \text{len}(1,1) = \max\{L_d, L_1 + d\} = \max\{1.4, 1 + 0.3\} = 1.4 \\ & \text{len}(1,2) = 2 \times \max\{L_d, L_2 + d\} = \max\{1.4, 1.5 + 0.3\} = 2 \times 1.8 \\ & \text{len}(1,3) = 3 \times \max\{L_d, L_3 + d\} = \max\{1.4, 2 + 0.3\} = 3 \times 2.3 = 6.9 \\ & \text{len}(2,2) = \text{len}(1,1) + \max\{L_1+L_d , L_2 + d\} \\ & \quad = 1.4 + \max\{1+1.4, 1.5+0.3\} = 1.4 + 2.4 \\ & \text{len}(2,3) = \min\{\text{len}(1,1) + 2 \times \max\{L_1+L_d, L_3+d\} , \text{len}(1,2) + \max\{L_2+L_d, L_3+d\}\} \\ & \quad = \min\{1.4 + 2 \times \max\{1+1.4, 2+0.3\} ,2 \times 1.8 + \max\{1.5+1.4,2+0.3\}\} \\ & \quad = \min\{1.4 + 2 \times 2.4 ,2 \times 1.8 + 2.9\} = 6.2 \\ & \text{len}(3,3) = \text{len}(2,2)+\max\{L_2+L_d,L_3+d\} \\ & \quad = 1.4 + 2.4 + \max\{1.5+1.4, 2+0.3\} = 1.4 + 2.4 + 2.9 = 6.7 \end{align}\end{split}\]

My Table

(\(1.4, \varnothing\))	(\(3.6, \varnothing\))	(\(6.9, \varnothing\))
	(\(3.8, 1\))	(\(6.2, 1\))
		(\(6.7, 2\))