Optimal binary search tree - Cormen

Question

I am looking into optimal binary search tree in Introduction to Algorithms by Cormen etc. For reference I am attaching a text link .

Here on page 399 we have table which has contribution. I am not able to understand how author calculated this column. For example node k1 contribution is 0.30, k4 is 0.20. How has the author calculated this?

Answer 1

Look at the formula to get search cost in T => E[search cost in T]=.... (page 398 the bottom)

To get cost for k1:

k1=(depth(k1) + 1) * p1

Look at the table is given for value of depth(k1) and p1 (page 399) .

k1=(1+1)*0.15
  =2*0.15
  =0.3

k2=(0+1)*0.10
  =1*0.10
  =0.10

etc

I hope my explanation can help.