Question

I am trying hard to understand how the table is computed in this ‘Assembly line scheduling’ problem in Chapter 15 ‘Dynamic Programming’ on Intorduction to Algorithms book by Cormen.

Can anyone give me a hint on what are the two tables about & how they get calculated ? Been searching on google for past 2 hours.

Answer 1

The 1st table contains the fastest way to pass station Si,j:

• f1[j] is the fastest way to pass station j of assembly line 1
• f2[j] is the fastest way to pass station j of assembly line 2

For example, f2(3)=22, since 2+7+2+5+6=22, and this is the fastest way to pass station 3 of assembly line 2.

In the 2nd table, li(j) shows the assembly line number (1 or 2) that is used in step j-1 as part of the fastest way to reach li(j).

For example, l1(2)=1 since the fastest way to reach station 2 in assembly line 1 is through station 1 on assembly line 1. (2+7 < 4+8+2)

l2(2)=1 since the fastest way to reach station 2 in assembly line 2 is through station 1 on assembly line 1. (2+7+2 < 4+8).