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Algorithms-Lecture,Section-2-Spring 2025

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Consider a double hashing scheme in which the primary hash function is h1(k) = k mod 23, and the secondary hash function is h2(k) = 1 + (k mod 19). Assume that the table size is 23.

Find the address returned by probe 1 in the probe sequence for the key value k = 90. Assume that the probe sequence begins at probe 0.
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Which one of the following assumptions is necessary for solving TSP using dynamic programming?

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Which of the following statements correctly describes the process of reducing a general CNF (Conjunctive Normal Form) to 3-CNF (3-literal CNF) as covered in lectures?

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You are given an empty min-heap. Insert the following integers one by one into the heap in the given order (e.g., first insert 35, and then 40, and then 15, etc. ), maintaining the min-heap property after each insertion:

35, 40, 15, 30, 10, 45

Which of the following represents the final min-heap as an array?

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You are given the following list of integers and are asked to sort them in increasing order:

[386, 250, 720, 412, 718]

You are to apply Radix Sort, using Counting Sort as a stable sorting algorithm at each digit level, starting from the least significant digit.

After sorting the array by the second digit (tens place), what will the list look like?

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Consider the following functions. 

f(n) = 2n

g(n) = n!

h(n) = nlog n

Which of the following statements is true? 

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Based on the discussion from our lectures, if we use the string matching algorithm with a finite automaton for the text T= “CDABADBAAA” and the pattern P= “ABAD”, how many states will the finite automaton have?
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Suppose you inserted the keys 12, 13, 7, 10, 22, 11, 20, 1, 5, 7, 25  into an open addressing hash table of size 13 using the hash function h(x) = (3 x + 7) mod 13 with linear probing. What is the load factor?

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What is the lps[ ] array for the pattern “AAACAAAAAC” used by the Knuth-Mosrris-Pratt algorithm

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What is the minimum total weight of unscheduled tasks when there is one processor, no preemption is allowed, and there are 8 tasks with equal lengths (li) of 2, with given weights and deadlines as follows: 

t1: (w1 = 2, d1 = 10), t2: (w2 = 3, d2 = 12), t3: (w3 = 8, d3 = 6), t4: (w4 = 6, d4 = 4), t5: (w5 = 5, d5 = 2), t6: (w6 = 4, d6 = 4), t7: (w7 = 10, d7 = 8), t8: (w7 = 12, d7 = 6)?

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