|
Data Structures and Algorithms
with Object-Oriented Design Patterns in Python |
Program 
defines the method typeset
which takes three arguments.
The first, l, is an array of n integers that
gives the lengths of the words in the sequence to be typeset.
The second, D, specifies the desired paragraph width
and the third, s, specifies the normal inter-word space.
Program: Dynamic programming example--typesetting a paragraph.
The method first computes the lengths, 
,
of all possible subsequences (lines 3-7).
This is done by using the dynamic programming paradigm
to evaluate the recursive definition of
given in Equation .
The running time for this computation is clearly 
.
The next step computes the one-line penalties 
as given by Equation (lines 8-14).
This calculation is a straightforward one
and its running time is also .
Finally, the minimum total costs, 
,
of typesetting each subsequence are determined
for all possible subsequences (lines 15-26).
Again we make use of the dynamic programming paradigm
to evaluate the recursive definition of
given in Equation .
The running time for this computation is 
.
As a result, the overall running time required to
determine the best way to typeset a paragraph of n words is .
Copyright © 2003, 2004 by Bruno R. Preiss, P.Eng. All rights reserved.