COMPSCI 220 – Tutorial 4
Sorting
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Quicksort
Heapsort
Quicksort
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Four basic steps:
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If n=0 or 1, return
Otherwise, choose one of the items as a pivot
Partition the remaining items into two disjoint subarrays by placing
the items greater than the pivot to its right and all the others to its
left
Return the result of quicksort of the left subarray, followed by the
pivot, followed by result of quicksort of the right subarray
In-place, not stable
𝜃(𝑛2 ) in worst case. 𝜃(𝑛 log 𝑛) in best and average case.
Quicksort
Heapsort
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Heap is a complete binary tree
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Basic steps:
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Every parent node in a minimum heap have a node key smaller
or equal to all of its child nodes.
Similar condition apples to maximum heap with obvious
difference.
Build a heap from the unsorted input
Read and output the root and delete the root node.
In-place, not stable
Heapsort
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Heap is built using bubbling up method.
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Root deletion using percolating down method.
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Add the node to the next slot available
Keep swapping the new node with its parent if the heap
property is not satisfied.
Move the last leaf of the heap to the root
Keep swapping this node with the larger (smaller) of its
respective new children if the heap property is not satisfied.
θ(𝑛 log 𝑛) in all cases.
Quickselect
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Finding the kth smallest element in a given list
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Basic steps:
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Can be done faster than soring in general
Very similar to quicksort
Select an element in the list as the pivot and partition the list
into two sublists just like quicksort
Recursively search the sublist depending on k and the size of
Average case 𝜃(𝑛)
Question 1
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(a) Perform quicksort on the following array, showing
each step of working. Take the median value as the pivot,
starting with 17.
Question 1
Question 2
Consider a maximum heap formed by the array.
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(a) How would you insert the node with a value 25 in to
the above heap?
Question 2
Question 2
Question 2
(b) How would you delete the root from the original heap
while maintaining the heap order?
Question 2
Question 2
Question 3
Describe the process of heapsort, and what is the time
complexity of each step.
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Construct heap  θ(n log n)
Output root and delete root  θ(log n)
Repeat until heap is empty  n times
Question 4
Find the 7th smallest element in the list 7 12 8 5 4 15 9 17
using quickselect
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4 5 8 7 12 15 9 17
9 7 8 12 15 17
15 17
looking for 7th element-right list
5th element - right list