clrs

I'm trying to do this exercise in Introduction to Algorithms by Cormen et al that has to do with the Disjoin Set data structure: Suppose that we wish to add the operation PRINT-SET(x) , which is given a node x and prints all the members of x 's set, in any order. Show how we can add just a single attribute to each node in a disjoint-set forest so that PRINT-SET(x) takes time linear in the number of members of x 's set , and the asymptotic running times of the other operations are unchanged. Assume that we can print each member of the set in O(1) time. Now, I'm quite sure that the attribute

This was a problem of CLR (Introduction to Algorithms) The question goes as follow: Suppose that the splits at every level of quicksort are in the proportion 1 - α to α, where 0 < α ≤ 1/2 is a constant. Show that the minimum depth of a leaf in the recursion tree is approximately - lg n/ lg α and the maximum depth is approximately -lg n/ lg(1 - α). (Don't worry about integer round-off.) http://integrator-crimea.com/ddu0043.html I'm not getting how to reach this solution. as per the link they show that for a ratio of 1:9 the max depth is log n/log(10/9) and minimum log n/log(10). Then how can

I'm wondering what the consensus is on the definition of "ancestor" in a computer science context. I only ask because in Introduction to Algorithms , Second Edition, p. 259 there is a description of the algorithm Tree-Successor(x) that seems odd. In finding the successor of node x , [...] if the right subtree of node x is empty and x has a successor y , then y is the lowest ancestor of x whose left child is also an ancestor of x . In a binary search tree with a root having key 2 and children 1 and 3 , the successor of 1 is its parent 2 . In this case, x is the left child of x 's successor, y .

You have a biased random number generator that produces a 1 with a probability p and 0 with a probability (1-p). You do not know the value of p. Using this make an unbiased random number generator which produces 1 with a probability 0.5 and 0 with a probability 0.5. Note : this problem is an exercise problem from Introduction to Algorithms by Cormen, Leiserson, Rivest, Stein.(clrs) pau.estalella The events (p)(1-p) and (1-p)(p) are equiprobable. Taking them as 0 and 1 respectively and discarding the other two pairs of results you get an unbiased random generator. In code this is done as easy

In CLRS , third Edition, on page 155, it is given that in MAX-HEAPIFY, "the worst case occurs when the bottom level of the tree is exactly half full" I guess the reason is that in this case, Max-Heapify has to "float down" through the left subtree. But the thing I couldn't get is "why half full" ? Max-Heapify can also float down if left subtree has only one leaf. So why not consider this as the worst case ? Read the entire context: The children's subtrees each have size at most 2n/3 - the worst case occurs when the last row of the tree is exactly half full Since the running time T(n) is