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?
Homework Answers
8ans)
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for best case comlexity is O(nlog n)
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Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the...
Inal Examination 17. Which of the sorting algorithms listed below has the time fastest best case...
Inal Examination 17. Which of the sorting algorithms listed below has the time fastest best case run (a) Heap sort (b) Merge sort (c) Quick sort (d) Insertion sort 18. Which statement below is false: (a) Quick uick sort and merge sort are divide and conquer algorithte (b) Counting sort is a linear time sorting algorithm. (e) Insertion sort and quicksort have similar best case (d) Generic minimum spanning tree algorithm is 19. Counting sort and radix sort are linked...
Professor Strongmind has developed a hardware priority queue device for his computer. This de- vice can...
Professor Strongmind has developed a hardware priority queue device for his computer. This de- vice can store up to p records, each containing a key and a small amount of satellite data (such as a pointer). With this device, INSERT and EXTRACT-MIN operations on the priority queue can be performed in O(1) worst-case time each, as long as the records are stored in the device. Your task is to develop a sorting algorithm using the device. Suppose there are n...
problem 2 can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to...
problem 2
can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to write its pseudo-code). To sort an array A, you will then call Det-QuickSort(A, 1, n). You also need to provide the worst case time complexity analysis of your algorithm. 2. (20 points) Given a set of n distinct numbers, we wish to find the k largest in sorted order using a comparison-based algorithm. Give an algorithm that implements each of the following methods, and...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n into 3 subproblems of sizes n/2 , n/4 , n/8 , respectively with O(n) time; Recursively call on these subproblems; and then combine the results in O(n) time. The recursive call returns when the problems become of size 1 and the time in this case is constant." (a) Let T(n) denote the worst-case running time of this approach on the problem of size n....
Please give me a divide and conquer algorithm that has runtime better than O(n^2) along with...
Please give me a divide and conquer algorithm that has
runtime better than O(n^2) along with justification. Also please do
a runtime analysis on this algorithm.
Please DONT copy and paste other's
solution.THANKS
3. Give the best algorithm you can to convert an n digit number base 10 into binary. Here, we are counting operations on single digits as single steps, not arithmetic operations. You can use any of the multiplication algorithms we described in class.)
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
Let T be a heap storing n keys. Give an efficient algorithm for reporting all the...
Let T be a heap storing n keys. Give an efficient algorithm for
reporting all
the keys in T that are smaller than or equal to a given query key x
(which is
not necessarily in T). For example, given the heap of Figure 5.6
and query key
x = 7, the algorithm should report 4, 5, 6, 7. Note that the keys
do not need to be
reported in sorted order. Ideally, your algorithm should run in
O(k) time,...
Using C++, data structures, C++ STL, inputs and expected outputs are shown below. Max Heap Heap...
Using C++, data structures, C++ STL, inputs and expected
outputs are shown below.
Max Heap Heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either > (in a max heap) or s (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node. In binary-tree based heap, it...
In the text box below, write down a divide and conquer algorithm for counting the number...
In the text box below, write down a divide and conquer algorithm for counting the number of entries in a sorted array of ints that are smaller than a given value. In other words, the function takes as input an array A and an int value and returns the number of ints in A that are less than value. To get any credit, your solution must use the divide and conquer technique. To get full credit, your solution should run in time in the...
C++ Question 5 5 pts In a min-heap of N elements, if we want to find...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
Inal Examination 17. Which of the sorting algorithms listed below has the time fastest best case run (a) Heap sort (b) Merge sort (c) Quick sort (d) Insertion sort 18. Which statement below is false: (a) Quick uick sort and merge sort are divide and conquer algorithte (b) Counting sort is a linear time sorting algorithm. (e) Insertion sort and quicksort have similar best case (d) Generic minimum spanning tree algorithm is 19. Counting sort and radix sort are linked...
Professor Strongmind has developed a hardware priority queue device for his computer. This de- vice can store up to p records, each containing a key and a small amount of satellite data (such as a pointer). With this device, INSERT and EXTRACT-MIN operations on the priority queue can be performed in O(1) worst-case time each, as long as the records are stored in the device. Your task is to develop a sorting algorithm using the device. Suppose there are n...
problem 2
can use Det-Selection(A, p, q, r) as a sub-routine (i.e, you don't need to write its pseudo-code). To sort an array A, you will then call Det-QuickSort(A, 1, n). You also need to provide the worst case time complexity analysis of your algorithm. 2. (20 points) Given a set of n distinct numbers, we wish to find the k largest in sorted order using a comparison-based algorithm. Give an algorithm that implements each of the following methods, and...
Please give me a divide and conquer algorithm that has
runtime better than O(n^2) along with justification. Also please do
a runtime analysis on this algorithm.
Please DONT copy and paste other's
solution.THANKS
3. Give the best algorithm you can to convert an n digit number base 10 into binary. Here, we are counting operations on single digits as single steps, not arithmetic operations. You can use any of the multiplication algorithms we described in class.)
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
Let T be a heap storing n keys. Give an efficient algorithm for
reporting all
the keys in T that are smaller than or equal to a given query key x
(which is
not necessarily in T). For example, given the heap of Figure 5.6
and query key
x = 7, the algorithm should report 4, 5, 6, 7. Note that the keys
do not need to be
reported in sorted order. Ideally, your algorithm should run in
O(k) time,...
Using C++, data structures, C++ STL, inputs and expected
outputs are shown below.
Max Heap Heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either > (in a max heap) or s (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node. In binary-tree based heap, it...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
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