EE113D Project: Heap Sort

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EE113D Project Heap Sort

• Shuofei Geng
• Michael Utanes
• Felix Lu

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Heap Sort - Motivation

• Concept of Sorting present in everyday life
• Sorting a list of grades
• MP3 Files on a computer
• Names on a phone Directory
• More advanced engineering problems
  rely on efficient
  sorting problems
• Heap Sort one of the best general-purpose
  sorting algorithms
• Applications
• Priority Queues,
• Interval Scheduling

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Heap Sort Project Goals

• Implement the Max Heap Sort Algorithm
• Utilize existing C code and convert to assembly
  language for use on using the DSK Plus Board
• Input data a random array of integer values
• Output data an array sorted in ascending order

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What is Heap Sort?

• Sorting Algorithm that first places objects into
  a heap
• Heap organized such that the largest value can
  easily be extracted while preserving heap
  structure
• Each time we delete (extract) the maximum, we
  place at next open position from the end of the
  sorted array
• Keep extracting largest value of heap until none
  remains, giving the elements in order
• Heap of remaining unsorted elements Sorted
  elements

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The Heap

• Heap can be represented as a balanced binary tree
• Each element is stored at a node.
• Max-Value at root of tree
• Heap Order A Parent node can
  have two Child Nodes
• The value of the Parent node always
  larger than the Child Nodes

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Heap Sort SiftDown Operation

• The siftDown() function is used to build and
  reconstruct the heap
• function sift(a, start, count)
  //Organize Heap
• var int root start, child //node
  in position i is parent of the nodes in positions
  2i and (2i1)
• while root 2 1 lt count
  //compare with two children,
  make swap
• child root 2 1
  //if chlidren larger than value if not keep
  traversing
• if child lt count - 1 and achild lt
  achild 1
• child child 1
• if aroot lt achild
• swap(aroot, achild)
• root child
• else
• return

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Heap Sort Pseudocode

• function heapSort(a, count)
• var int start count 2 - 1,
• end count - 1
• while start 0 //Build Heap
• sift(a, start, count)
• start start - 1
• while end gt 0
• swap(aend, a0)
  //Root Deletion
• sift(a, 0, end) //Heap
  Reorganized
• end end - 1
• function sift(a, start, count)
  //Organize Heap
• var int root start, child
  //node in position i is parent of the nodes in
  positions 2i and (2i 1)
• while root 2 1 lt count
  //compare with two children, make
  swap
• child root 2 1 //if chlidren
  larger than value if not keep traversing

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Heap Sort Pseudocode

• Heap Sort

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Comparison with Other Sorts

• Merge Sort Quick Sort
• Splits the items to be sorted into two groups,
  recursively sorts each group, and combines them
  into a final, sorted sequence
• Generally faster than heap sort, due to better
  data cache performance

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Comparison with Other Sorts
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Applications of Heap Sort

• Interval Scheduling
• List of tasks with various start/finish times
• Aim to perform tasks within specified time
  interval without overlapping
• Sort finish time of tasks then take earliest
  finish time until all tasks performed
• Priority Queue - Supports the following three
  operations
• Add an element to the queue with an associated
  priority
• Remove the element from the queue that has
  highest priority, and return it
• Peek at the element with highest priority without
  removing it
• Ex. Bandwidth Management

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Heap Sort Implementation

• Project Development
• First decide on topic for implementation
• Challenge No previous Heap Sort project exists
• Write Everything From Scratch
• Then Model Sorting algorithm with High Level
  Language (C or matlab)
• Internet contains many topics/code on Heap Sort
• Lastly, Program/Debug Max Heap Sorting Algorithm
• Utilize existing C code and convert to assembly
  language for use on using the DSK Plus Board
• Program consists of 2 files randomno.asm,
  heapsort.asm

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Heap Sort Implementation

• Program consists of two files
• randomno.asm - list, containing 100 random s
• To create list, we wrote a short C program
  RandomNoGenerator.c that outputs random s in
  assembly format i.e. .word 4
• Then we copied the input data to the correct file
  type to represent random array
• heapsort.asm Executable code
• Implements heap sort algorithm

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Heap Sort Implementation

• heapsort.asm Design Challenges
• Use of Pointers
• When to use
• Limited amount of Registers (AR0-AR7)
• Comparison Operations
• Flags TC NTC
• Function Usage
• Implementation
• Passing Parameters
• Returning from Function
• Adding nop instruction

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Heap Sort Implementation

• heapsort.asm Debugging Challenge
• Adding nop Instruction
• While executing program in whole program
  misbehaves
• Due to certain instructions taking longer than a
  cycle to complete, thus not properly registering
  values in time
• Solution Add nop instruction between lines
  where this is true
• Found by use of Breakpoints in code

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Heap Sort Discussion of Results

• Program correct in implementing Heap Sort
• Output a sorted array
• Also Concerned about Program Efficiency
• Does it meet the time requirement O(nlog2(n)),
  where n is the of elements in the array?

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Heap Sort Discussion of Results

• Does it meet the time requirement O(nlog2(n))?
• 1st- Check of times siftdown2() is called
• After function returns, the 1st and last element
  of array is swapped
• Process stops until function calls Max n times
• 2nd- See iterations performed inside function
• After every iteration, multiply the current index
  by 2 then use as current index
• Since only checking index which is in power of 2
  of the original root passed in as parameter, we
  can do at most log2(n) operations
• Therefore O(nlog2(n)) is satisfied

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Heap Sort - Summary

• Positives
• Does not require multiple arrays
• Does not include recursion
• Optimal for large data sets
• Runs well with computers with slow data caches
• Negatives
• Generally Slower than Merge Sort/Quick Sort
• Unstable