COMP 171 Data Structures and Algorithms

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COMP 171Data Structures and Algorithms

• Tutorial 3
• Merge Sort Quick Sort

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Merge Sort

• mergesort(A, left, right)
• if left lt right then
• middle ? ?(left right) / 2?
• mergesort(A, left, middle)
• mergesort(A, middle1, right)
• merge(A, left, middle1, right)
• end if
• end mergesort

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• merge(A, p, q, r)
• n1 ? q p
• n2 ? r q 1
• create array L1..n11, R1..n21
• for i ? 1 to n1 do Li ? Api-1
• for j ? 1 to n2 do Rj ? Aqj-1
• Ln11 ? Rn21 ? 8
• I ? j ? 1
• for k ? p to r
• if LI lt Rj then
• Ak ? Li
• i ? i 1
• else
• Ak ? Rj
• j ? j 1
• end if
• end for k
• end merge

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• Assume mergesort(A, left, right) takes T(n) to
  run where n right left 1 no. of elements
  in array Aleft..right
• T(1) O(1)
• If array size 1, nothing need to be done
• T(n) divide conquer combine
• O(1) 2T(n/2) O(n)
• T(1) O(1)
• T(n) 2T(n/2) O(n)

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• Best Case O(n ? n)
• Worst Case ?(n ? n)
• Running Time T(n ? n)
• Advantage
• Stable running time
• Fast running time
• Disadvantage
• Need extra memory space for merge step

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Quick Sort

• quicksort(A, left, right)
• if left lt right then
• middle ? partition(A, left, right)
• quicksort(A, left, middle1 )
• quicksort(A, middle1, right)
• end if
• end quicksort

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• partition(A, left, right)
• x ? Aright
• i ? left 1
• for j ? left to right 1
• if Aj lt x then
• i ? i 1
• swap(Ai, Aj)
• end if
• end for j
• swap(Ai1, Aright)
• return i 1
• end partition

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• Advantage
• No extra memory is needed
• Fast running time (in average)
• Disadvantage
• Unstable in running time
• Finding pivot element is a big issue!