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Is it possible to read the Introduction to #Algorithms book (CLRS Book) in one dayâť“âť“ Here's what Cormen himself thinks about it. The C in #CLRS. #Sarcasm at its best. @goclasses_cse #cormen #clrs #daa #GoClasses #computerscience #dsa #datastructures #algorithm #daa #computerscience #algo #gatecse #gatecs #gatecsit https://www.instagram.com/p/ChtD6DBPcrF/?igshid=NGJjMDIxMWI=
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@gmwlucayababes and I were talking about if Carmen and Corey got together and accidentally wrote a fanfiction
Heap Sort
Towards the end a C++ implementation of heap and heap sort is presented.
A heap is a nearly complete binary tree. The tree is complete at every level except possibly at the lowest.
There are two kinds of heaps, max-heap and min-heap. A max-heap shall satisfy the property that $A[parent(i)] \ge A[i]$ and vice-verse for min-heap.
One can implement heaps using Array data structure. Where the left child of an index $i$ is given by $2i$ and the right child is given by the index $2i+1$.
The Heap-Sort consists of three main procedures
Heapify Runs in $\mathcal{O}(\log(n))$ time.
Build-heap which runs in linear time
Heap-sort which runs in $\mathcal{O}(n\log(n)) time$.
Pro tip: While implementing heap-sort using arrays, avoid using the zeroth index of an array.
Solutions
(CLRS, Introduction to Algorithms, 3rd ed)
$6.1-1$ Minimum = $2^{h-1}$ and maximum = $ 2^{h}-1 $
$6.1-2$ From the above relation, see that $h-1 \le \lfloor \lg n \rfloor < h$
$6.1-3$ Use induction.
$6.1-4$ The last leaf.
$6.1-5$ Yes.
$6.1-6$ No, the max-heap property is violated at node with element $14$.
$6.1-7$ Observe that those elements's left and right nodes will not belong to the array, and therefore they are leafs. It is also easy to see that any other element cannot be the leaf.
$6.2-1$ Illustration.
$6.2-2$ Code.
$6.2-3$ No effect.
$6.2-4$ Code.
$6.2-5$ Consider the case of a max-heap for a array sorted in ascending order, the heapify procedure on the root is going to take excatly $\lg n$ steps!
$6.3-1$ Illustration
$6.3-2$ The Max-Heapify procedure is designed under the assumption that if max-heapfify(A,i) is called, then the left and the right sub-heap is well-sorted and the only violation (if any) shall happen at the node only. Given this information, starting from top to bottom makes sense!
$6.3-3$ Use induction.
(ir)Relevent information
How to determine the size of an array in C. Careful with the sizeof operator and avoid a mistake that I once did. The answers, especially the second one emphasizes an important idea.
Min-Max heaps and generalized priority queues is a paper on a generalization of Heap, namely min-max heap. The paper extends the ideas of min-heap and max-heap into (an ultimate heap) min-max heap.
This is Cormen....
Walking for quite sometime he doesn't even realize he is walking the streets in the middle of the day with a straight jacket.
Something isn't right. Where am I? I don't recognize this street... Huh that looks like a nice shop. No.. no... I can't be shopping. I have to get my arms free. Oh but the smell...Â
Stomach rumbles aching for nourishment. Closes his eyes and smells the air, sticking his head up and turns his head toward the direction of a hot dog stand. He stops and drools looking more like a crazed man.
"Antes de que hubieran computadoras, habĂan algoritmos. Pero ahora que hay computadoras, hay incluso más algoritmos, y los algoritmos descanzan en el corazĂłn de la computaciĂłn"
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein Introduction to ALGORITHMS
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TOOL: Introduction to Algorithms (MIT by iTunes - Video)
Introduction to Algorithms
by MIT
Course Description
This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.Â
The textbook for this course is: Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 2nd ed. Cambridge, MA: MIT Press. ISBN: 0262032937.
http://ocw.mit.edu/
This content is provided under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 license.
http://ocw.mit.edu/terms/
source: iTunes MIT
