hwk-challenge - 2 You are given a tree T having n...

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TA: Catalin-Stefan Tiseanu Challenge Problem Set Clyde Kruskal Here are a couple of challenge homework problems, not to be turned in. You can discuss the answers with Catalin-Stefan Tiseanu during office hours. Problem 1 An inversion in an array is defined as a pair of indices ( i,j ) with i < j and A [ i ] > A [ j ] . For example, the array [ 3,2,4,1 ] has 4 inversions (1 with all three other elements and 3 with 2). Give an efficient algorithm to compute the number of inversions in an array A of n integers. Hint : Your algorithm should take O ( n lg n ) time. Hint : Think about adapting a sorting algorithm you studied in class. Problem
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Unformatted text preview: 2 You are given a tree T , having n vertices (rooted at vertex r for convenience). You are also given k pairs ( x i , y i ) , 1 ≤ i ≤ k . The task is to output for each pair ( x i , y i ) whether x i is an ancestor of y i in tree T (that is, output yes if x i is an ancestor of y i , and no if it is not). Note that x i is an ancestor of y i can be reframed as y i is in the subtree rooted at x i for convenience. Your algorithm should take O ( n + k ) time. Hint : Think about the graph traversal methods you learned in class. 1...
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