By Ageev A.A.
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Additional info for A 3/2-approximation algorithm for the jump number of interval orders
1 Write an algorithm that, given a list of n numbers, returns the largest and smallest numbers in the list. Estimate the running time of the algorithm. Can you design an algorithm that performs only 3n/2 comparisons to ﬁnd the smallest and largest numbers in the list? 2 Write two algorithms that iterate over every index from (0, 0, . . , 0) to (n1 , n2 , . . , nd ). Make one algorithm recursive, and the other iterative. 3 Is log n = O(n)? Is log n = Ω(n)? Is log n = Θ(n)? 4 You are given an unsorted list of n − 1 distinct integers from the range 1 to n.
You could estimate the running time of the algorithm simply by taking the product of the number of operations and the time per operation. However, computing devices are constantly improving, leading to a decreasing time per operation, so your notion of the running time would soon be outdated. 5 The recursion tree for R ECURSIVE F IBONACCI(n). Vertices enclosed in dashed circles represent duplicated effort—the same value had been calculated in another vertex in the tree at a higher level. As the tree grows larger, the number of dashed vertices increases exponentially (2i − 2 at level i), while the number of regular vertices increases linearly (2 per level).
This ﬁt well with the work of the Augustinian monk Gregor Mendel in the 1860s, whose experiments with garden peas suggested the existence of genes that were responsible for inheritance. Evidence that traits (more precisely, genes) are located on chromosomes came in the 1920s through the work of Thomas Morgan. Unlike Mendel, Morgan worked in New York City and lacked the garden space to cultivate peas, so he instead used fruit ﬂies for his experiments: they have a short life span and produce numerous offspring.