Heap Sort in Design and Analysis of algorithmssamairaakram
Brief description of Heap Sort and its types.it includes Binary Tree and its types. analysis and algorithm of Heap Sort. comparison b/w Heap,Qucik and Merge Sort.
Heap Sort in Design and Analysis of algorithmssamairaakram
Brief description of Heap Sort and its types.it includes Binary Tree and its types. analysis and algorithm of Heap Sort. comparison b/w Heap,Qucik and Merge Sort.
Algorithm Design and Complexity - Course 4 - Heaps and Dynamic ProgammingTraian Rebedea
Course 4 for the Algorithm Design and Complexity course at the Faculty of Engineering in Foreign Languages - Politehnica University of Bucharest, Romania
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
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Similar to Heaps & its operation -Max Heap, Min Heap
Algorithm Design and Complexity - Course 4 - Heaps and Dynamic ProgammingTraian Rebedea
Course 4 for the Algorithm Design and Complexity course at the Faculty of Engineering in Foreign Languages - Politehnica University of Bucharest, Romania
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
2. Heap is a complete binary tree data
structure that satisfies the heap
property: for every node, the value
of its children is less than or equal
to its own value. Heaps are usually
used to implement priority queues,
where the smallest (or largest)
element is always at the root of the
tree
3. MAX HEAP
In a max heap, the parent
node's value is always
greater than or equal to the
values of its children. This
arrangement ensures that
the maximum element is at
the root of the heap
4. MIN HEAP
A min heap is a binary tree-based
data structure where the value of
each node is less than or equal to
the values of its children. In other
words, the smallest element is
always at the root. This satisfies
the min-heap property.
• The root node contains the
minimum value: 3.
• Each parent node has a
smaller value than its children.
• It satisfies the property of a min
heap.
5.
6.
7. A Priority queue is a BIFO container: The best one in
comes out first. That means that each element is
assigned a priority number, and the element with the
highest priority comes out first. Heaps are commonly
used to implement priority queues, where elements are
removed based on their priority. The highest (max heap)
or lowest (min heap) priority element is always at the
root.
9. MAX-HEAPIFY OPERATION
Find location of largest value of A[i], A[left(i)], A[right(i)]
If not A[i], max-heap property does not hold.
Exchange A[i] with the larger of the two children to
preserve max-heap property.
Continue this process of compare/exchange down the
heap until sub-tree rooted at I is a max-heap.
At a leaf, the sub-tree rooted at the leaf is trivially a max-
heap.
Algorithm
MAX-HEAPIFY(A, I ,n)
{
l-=left(i)
R=right(i)
Largest=I
If l <=n and A[i] > A[largest]
Largest=I
If r <= n and A[r] > A[largest]
largest-=r
If largest!=I
Exchange(A[i] ,A[largest])
MAX-HEAPIFY(A, largest, n)
}
If any node violets the heap property then swap
this node with its larger children to maintain the
heap property, this is called heapify.
10.
11. BUILD-MAX-HEAP
To build a max-heap from any tree, we can
thus start heapifying each sub-tree from the
bottom up and end up with a max-heap after
the function is applied on all elements
including the root element . In this case of
complete tree, the first index of non-leaf node
is given by n/2-1.
Algorithm
Build-max-Heap(A)
{
n=length[A]
For(i=floor(n/2);i>=1; i__)
{
MAX_HEAPIFY(A, I, n);
}
}
12. Heap sort is a comparison based
sorting technique based on Binary
Heap data structure. It is similar
to selection sort where we first find
the maximum element and place
the maximum elements at the end.
Build a max-heap from any array
Swap the root with the last element in the array
Discard this last node by decreasing the heap size
Perform Max-Heapify operation on the new root
node
Repeat this process until only one node remains.
13. g
Program for
implementation of Heap
sort
#include<stdio.h>
Void heapify(int arr[], int n, int i)
Int largest =I;
Int 1=2*i+1;
Int r=2*i+2;
If(l<n && arr[1] > arr[largest])
Largest=1;
If(r< && arr[r] >arr[largest])
Largest=r;
If (largest !=i)
[
Swap(arr[i], arr[largest]);
Heapify(arr, n, largest);
}}
Void heapsort(int arr[], int n)
{
For(int i=n/2-1; i>=0; i--)
Heapify(arr, n, i);
For(int i=n-1;i>=0; i--)
{
Swap(arr[0], arr[i]);
Heapify(arr, I, 0);
}}
Void printArray(int arr[], int n){
For(int i=0; i<n; ++i)
Cout <<arr[i] << “”;
Cout<< “/n”;
}
Int main()
{
Int arr[]={ 12, 11, 13, 5, 6, 7}
Int n=6;
Heapsort(arr n);
Printf(“Sorted array is n”);
printArray(arr,n);
}
OUTPUT
5 6 7 11 12 13