Algorithms And Data Structures

# Get A 3/2-approximation algorithm for the jump number of PDF

By Ageev A.A.

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Some authors define big omega by saying f(n) is Ω(g(n)) if there is some n0 and c > 0 such that for all n ≥ n0 we have f(n) ≥ cg(n). 15 a. Is it true for this definition that f(n) is Ω(g(n)) if and only if g(n) is O(f(n))? b. 4? c. 14(a) or (b) hold for this definition of big omega? 16 Order the following functions by growth rate: (a) n, (b) √¯n, (c) logn, (d) loglogn, (e) log2n, (f) n/logn, (g) √¯nlog2n, (h) (1/3)n, (i) (3/2)n, (j) 17. , n = 2, 4, 8, 16 , . .. Give the formula that expresses the value of the variable count in terms of the value of n when the procedure terminates.

Front. The second statement puts nil into the next field of that cell. The third statement makes the header both the first and last cell of the queue. The procedure DEQUEUE(Q) deletes the first element of Q by disconnecting the old header from the queue. The first element on the list becomes the new dummy header cell. 20 shows the results created by the sequence of commands MAKENULL(Q), ENQUEUE(x, Q), ENQUEUE(y, Q), DEQUEUE(Q). Note that after dequeueing, the element x being in the element field of the header cell, is no longer considered part of the queue.

If p is END(L), then L becomes a1, a2, . . , an, x. If list L has no position p, the result is undefined. 2. LOCATE(x, L). This function returns the position of x on list L. If x appears more than once, then the position of the first occurrence is returned. If x does not appear at all, then END(L) is returned. 3. RETRIEVE(p, L). This function returns the element at position p on list L. The result is undefined if p = END(L) or if L has no position p. Note that the elements must be of a type that can be returned by a function if RETRIEVE is used.