Give an example of a set of n line segments with an order on them that...
Give an example of a set of n line segments with an order
on
them that makes the algorithm create a search structure of
size Θ(n2) and worst-case query time Θ(n).
Homework Answers
Add Answer to:
Give an example of a set of n line segments with an order
on
them that...
The intersection detection problem for a set S of n line segments is to determine whether...
The intersection detection problem for a set S of n line segments is to determine whether there exists a pair of segments in S that intersect. Give a plane sweep algorithm that solves the intersection detection problem in O(nlogn) time. Prove it only requires O(nlogn) time.
Give an algorithm with the following properties. • Worst case running time of O(n 2 log(n))....
Give an algorithm with the following properties. • Worst case running time of O(n 2 log(n)). • Average running time of Θ(n). • Best case running time of Ω(1).
Questions 1a–d are about developing an efficient implementation of a Set that combines the advantages of...
Questions 1a–d are about developing an efficient implementation of a Set that combines the advantages of a hash table and a balanced binary search tree. In particular, the search function for your data structure should have O (lg n ) worst case complexity and Θ(1) expected case complexity, and it should not be limited to values in a small range (as a bit vector would). (a) Describe how you would store data values in memory. (b) Give pseudocode for how...
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the...
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the input. Explain the difference between the two statements below, and give an explicit example of an algorithm for which one statement is true but the other is false. 1. The worst case time complexity of A is n2. 2. A is O(n). (e) Give an example of an algorithm (with a clear input type) which has a Big-Oh (0) and Big-Omega (12) bound on...
Consider the following problem: given n positive integers, separate them into two groups such that adding...
Consider the following problem: given n positive integers, separate them into two groups such that adding all the numbers in one group gives the same result as adding all the numbers in the other group. For example, if the numbers are 1, 2, 3, 4, then the two groups could be {1, 4} and {2, 3}, which both sum to 5. For another example, if the numbers are 5, 6, 11, then the two groups could be {5, 6} and...
Computer Algorithm question 8) Give an algorithm for building a heap in O(n) 9) Prove the...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
Here is a recursive algorithm that answers the same question as posed on Group HW3, finding...
Here is a recursive algorithm that answers the same question as posed on Group HW3, finding the number of people who are taller than everyone before them in line. NumCanSeeRec(a1,... , an : list of n 2 1 distinct heights) (a) ifn -1 then (b return 1 (c) c= ŅumCanSeeRee(a1, , an-1) d) for i:- 1 ton- 1 (e) if a, an then return c (g) return c+1 Answer the following questions about this algorithm. Please show your work. (a)...
Insertion sort on small arrays in merge sort Although merge-sort runs in Θ(n log n) worst-case...
Insertion sort on small arrays in merge sort Although merge-sort runs in Θ(n log n) worst-case time and insertion sort runs in Θ(n 2 ) worst-case time, the constant factors in insertion sort can make it faster in practice for small problem sizes on many machines. Thus, it makes sense to coarsen the leaves of the recursion by using insertion sort within merge sort when subproblems become sufficiently small. Consider a modification to merge sort in which n/k sublists of...
Example 1.9: 1.23 "The median of an ordered set is an element such that the number...
Example 1.9:
1.23 "The median of an ordered set is an element such that the number of elements less than the median is within one of the number that are greater, assuming no ties. a. Write an algorithm to find the median of three distinct integers a, b, and c. b. Describe D. the set of inputs for your algorithm. in light of the discussion in Sec- tion 1.4.3 following Example 1.9. c. How many comparisons does your algorithm do...
What is the worst-case asymptotic time complexity of the following divide-andconquer algorithm (give a Θ-bound). The...
What is the worst-case asymptotic time complexity of the following divide-andconquer algorithm (give a Θ-bound). The input is an array A of size n. You may assume that n is a power of 2. (NOTE: It doesn’t matter what the algorithm does, just analyze its complexity). Assume that the non-recursive function call, bar(A1,A2,A3,n) has cost 3n. Show your work! Next to each statement show its cost when the algorithm is executed on an imput of size n abd give the...
(d) Consider an algorithm A, whose runtime is dependent on some "size" variable n of the input. Explain the difference between the two statements below, and give an explicit example of an algorithm for which one statement is true but the other is false. 1. The worst case time complexity of A is n2. 2. A is O(n). (e) Give an example of an algorithm (with a clear input type) which has a Big-Oh (0) and Big-Omega (12) bound on...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
Here is a recursive algorithm that answers the same question as posed on Group HW3, finding the number of people who are taller than everyone before them in line. NumCanSeeRec(a1,... , an : list of n 2 1 distinct heights) (a) ifn -1 then (b return 1 (c) c= ŅumCanSeeRee(a1, , an-1) d) for i:- 1 ton- 1 (e) if a, an then return c (g) return c+1 Answer the following questions about this algorithm. Please show your work. (a)...
Example 1.9:
1.23 "The median of an ordered set is an element such that the number of elements less than the median is within one of the number that are greater, assuming no ties. a. Write an algorithm to find the median of three distinct integers a, b, and c. b. Describe D. the set of inputs for your algorithm. in light of the discussion in Sec- tion 1.4.3 following Example 1.9. c. How many comparisons does your algorithm do...
Most questions answered within 3 hours.
-
What is meant by a “term premium”?
What can explain such a premium? Is it a...
asked 47 minutes ago -
23. Which molecule has only covalent bonds? A. CO2 B. Al2O3 C.
Mg3N2
24. The octet...
asked 1 hour ago -
the
total pressure for a mixture of N2O4 and NO2 is 2.20 atm. If Kp=
7.10...
asked 1 hour ago -
Delaware Corp. prepared a master budget that included $22,385
for direct materials, $28,600 for direct labor,...
asked 1 hour ago -
For pesticide HCB (hexachlorobenzene), its logarithmic partition
coefficient log Kow is 5.6. What would be the...
asked 1 hour ago -
A chemist requires 0.422 mil Na2CO3 for a reaction. How many
grams does this correspond to?
asked 1 hour ago -
If the vapor pressure of carvone is approximately 9.4 torr at 99
°C, approximately how much...
asked 1 hour ago -
A juice bottling company is carrying out a test at 10%
significance that the mean population...
asked 1 hour ago -
What is the reflectivity (in percent) needed to keep water at a
temperature near its freezing...
asked 1 hour ago -
Suppose that the average surface temperature of Earth is 300K.
Assume this is uniform over its...
asked 1 hour ago -
Draw the condensed structural formula for alkenes and alkynes or
the line-angle structural formula for cycloalkenes...
asked 1 hour ago -
M. Laing has suggested a new arrangement of the periodic table
(J.Chem.Ed.1989, 66,
746). Answer the following...
asked 2 hours ago