Analysis of Algorithm (Bubblesort and Quicksort)

Analysis of Algorithm (Bubblesort and Quicksort)

• 1.
  Quick Sort Jimenez, Jake Rojas,Davis Jacob Miguel, Flynce
• 2.
  Quick Sort  Quicksortuses divide-and-conquer, and so it's a recursive algorithm. The way that quicksort uses divide-and-conquer is a little different from how merge sort does. In merge sort, the divide step does hardly anything, and all the real work happens in the combine step.  Quicksort is the opposite: all the real work happens in the divide step. In fact, the combine step in quicksort does absolutely nothing.
• 3.
  Quick Sort  Hereis how quicksort uses divide-and-conquer: think of sorting a sub array[p…r], Where initially the sub array is array[0…n-1]. We take this set of array as an example: 40 20 10 80 60 50 7 30 100 0 1 2 3 4 5 6 7 8
• 4.
  Quick Sort  Divide 1.Choose any element in the sub array [p…r] call this element Pivot. We now have our Pivot which is 40 at array 0 40 20 10 80 60 50 7 30 100 0 1 2 3 4 5 6 7 8
• 5.
  Quick Sort  Givena pivot, re-arrange the elements of the array such that the resulting array consists of:  One sub-array that contains elements >= pivot  Another sub-array that contains elements < pivot We call this procedure Partitioning.
• 6.
  Quick Sort  Givenagain the array 40 20 10 80 60 50 7 30 100 0 1 2 3 4 5 6 7 8 7 20 10 30 40 50 80 60 100 <= Data [pivot] > Data [pivot]
• 7.
  Quick Sort  Conquer Afterdividing recursively sort each sub array <= Data [pivot] 7 20 10 30 7 20 10 30 7 20 10 30 7 10 20 30 7 20 10 30 7 10 20 30 7 10 20 30
• 8.
  Quick Sort  Conquer Afterdividing recursively sort each sub array  > Data [pivot] 50 60 80 100 50 80 60 100 50 80 60 100 50 80 60 100 50 60 80 100 50 80 60 100 50 60 80 100 50 60 80 100
• 9.
  Quick Sort  Combine Once the conquer step recursively sorts, we are done. Why? All elements to the left of the pivot, in array are less than or equal to the pivot and are sorted, and all elements to the right of the pivot, in are greater than the pivot and are sorted.  The elements can't help but be sorted! So we combine the Left sub array + Pivot + Right sub array.  Output of the sorted array: 7 10 20 30 40 50 60 80 100
• 10.
  Quick Sort  Quicksort Analysis Scenarios Sorting Algorithm Worst-Case O(n2) Best-Case O(n log n)/O(n) Average-CaseA O(n log n)
• 11.
  Quick Sort Advantage ofQuicksort:  Efficient average case compared to any sort algorithm  The elegant recursive definition  The popularity due to its high efficiency
• 12.
  Quick Sort Disadvantage ofQuicksort  The difficulty of implementing the partitioning algorithm  The average efficiency for the worst case scenario, which is not offset by the difficult implementation
• 13.
  Bubble Sort Jimenez, Jake Rojas,Davis Jacob Miguel, Flynce
• 14.
  Bubble Sort  Thebubble sort makes multiple passes through a list. It compares adjacent items and exchanges those that are out of order. Each pass through the list places the next largest value in its proper place. In essence, each item “bubbles” up to the location where it belongs.
• 15.
  Bubble Sort  BubbleSort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order. First Pass: ( 5 1 4 2 8 ) –> ( 1 5 4 2 8 )  Here, algorithm compares the first two elements, and swaps since 5 > 1. ( 1 5 4 2 8 ) –> ( 1 4 5 2 8 )  Swap since 5 > 4
• 16.
  Bubble Sort ( 14 5 2 8 ) –> ( 1 4 2 5 8 )  Swap since 5 > 2 ( 1 4 2 5 8 ) –> ( 1 4 2 5 8 )  Now, since these elements are already in order (8 > 5), algorithm does not swap them.
• 17.
  Bubble Sort  SecondPass: ( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ) ( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
• 18.
  Bubble Sort  Now,the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted. Third Pass: ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
• 19.
  Bubble Sort  Now,the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted. Third Pass: ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
• 20.
  Bubble Sort Advantages ofBubble sort:  Easy to understand.  Easy to implement.  In-place, no external memory is needed.  Performs greatly when the array is almost sorted.
• 21.
  Bubble Sort Disadvantages Bubblesort:  Very expensive, O(n2)O(n2)in worst case and average case.  It does more element assignments than its counterpart, insertion sort.