Problem 4. Determine the height of an n-element heap and prove its correctness.

Answered: Problem 4. Determine the height of an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. A student wants to know the effect of 2 parameter settings (Number of iterations and learning rate) on the computation time of an algorithm. Experiments were carried out by trying 3 different values for each parameter, then seeing the response to computation time. If we know the experimental results as shown in the following figure, what information can we get? Boxplot of Speed (sec) Boxplot of Speed (sec) 0,8 0,8- 0,7 0,7- 0,6 0.6 0,5 0,5- 0,4 0,4- 0,3 0,3- 0,2 0,2- 0,50 learning rate 500 1000 1500 0,05 0,95 Niteration Speed (sec)
a. Given the following algorithm, def Linear Search(a, x): for i in range(0, len(a)): if a[i] == x: return i return -1 What will be the result if a = [1,2,5,3] and x = = 2? b. What will be the result if a = [1,4,2,0] and x = 10?
DRAW A TREE OF THIS ARRAY IN DESECDING ORDER (HEAP SORTING)
If a = 270 and b = 46 then find the following: %3D 1) Find gcd(a, b) "use Euclidean algorithm" 2) Write the gcd(a, b) as a linear combination of a and b 3) Write a and b in standard form of prime factorization 4) Find l.c.m(a,b)
Solve the following Integer Programming problem using the graphical or branch and bound algorithm, where n=5, s=13.
Problem 10. Pigeonhole principle applications. Be sure to justify your answer. 10(d) There are 14 3-digit numbers in a list. Can you conclude that there are two distinct subsets of the 14 numbers that have the same sum?
Problem 12-27 (Algorithmic) Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here. Aynor: Cost = 80Q1 +5Q1² + 92 Spartanburg: Cost = 20Q2 +2.502² + 159 Where Q1 = number of chairs produced at Aynor Q2 = number of chairs produced at Spartanburg Andalus needs to manufacture a total of 30 kitchen chairs to meet an order just received. How many chairs should be made at Aynor and how many should be made at Spartanburg in order to minimize total production cost? When required, round your answers to the nearest dollar. The optimal solution is to produce and $ chairs at Aynor for a cost of $ chairs at Spartanburg for a cost of $ The total cost is
Which of the following is NOT normally considered in the complexity analysis of algorithms? A. Best case B. Worst case C. Null case D. Average case Justify your answer with explanations
Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…
2. "The Colored Cube Problem": We are given four cubes, the faces of which are colored with one of four colors. Since there are six faces, each cube would have more than one face colored with the same color. The coloring of the cubes is different so two cubes are not necessarily colored the same way. The problem is to stack the cubes vertically in such a way that we have a rectangular prism and each of the rectangles on a side of the prism has all four colors appearing in it, not necessarily in the same order. Structure the problem mathematically and analyze the possible solutions, if any.

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