Presentation on binary search, quick sort, merge sort and problems
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The document discusses four sorting algorithms: binary search, quicksort, merge sort, and their working principles. It provides: 1) Binary search works by repeatedly dividing a sorted list in half and evaluating the target value against the midpoint. 2) Quicksort uses a pivot element to partition an array into subarrays of smaller size, sorting them recursively. 3) Merge sort divides an array into halves, recursively sorts them, and then merges the sorted halves back together. 4) Examples are given of how each algorithm would sort sample arrays through their divide and conquer approaches.
![Algorithm:
Low= 1; High = n;
while Low < High {
m = floor( (Low+High)/2 );
if k <= A[m]
then High = m - 1
else Low = m + 1
}
if A[Low] = k then j = Low else j = 0
Created by Sumita Das](https://image.slidesharecdn.com/presentationonbinarysearchquicksortmergesortandproblems-160914042706/85/Presentation-on-binary-search-quick-sort-merge-sort-and-problems-5-320.jpg)
![Algorithm:
• Input: Array E and indices first, and last, s.t. elements
E[i] are defined for first ≤ i ≤ last
• Ouput: E[first], …, E[last] is a sorted rearrangement of
the array
• Void quickSort(Element[] E, int first, int last)
if (first < last)
Element pivotElement = E[first];
int splitPoint = partition(E, pivotElement, first,
last);
quickSort (E, first, splitPoint –1 );
quickSort (E, splitPoint +1, last );
return;
Created by Sumita Das](https://image.slidesharecdn.com/presentationonbinarysearchquicksortmergesortandproblems-160914042706/85/Presentation-on-binary-search-quick-sort-merge-sort-and-problems-9-320.jpg)
![Algorithm:
• Split array A[1..n] in two and make copies of each half in
arrays B[1.. n/2 ] and C[1.. n/2 ]
• sort arrays B and C
• Merge sorted arrays B and C into array A
Created by Sumita Das](https://image.slidesharecdn.com/presentationonbinarysearchquicksortmergesortandproblems-160914042706/85/Presentation-on-binary-search-quick-sort-merge-sort-and-problems-11-320.jpg)
![References
[1]Introduction to Algorithms 2nd ,Cormen, Leiserson, Rivest and
Stein, The MIT Press, 2001.](https://image.slidesharecdn.com/presentationonbinarysearchquicksortmergesortandproblems-160914042706/85/Presentation-on-binary-search-quick-sort-merge-sort-and-problems-20-320.jpg)
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Presentation on binary search, quick sort, merge sort and problems
- 1. By- Sumita Das Presentation On Binary Search, Quick Sort, Merge Sort And Problems Created by Sumita Das
- 2. Binary Search • If we have an ordered list and we know how many things are in the list (i.e., number of records in a file), we can use a different strategy. • The binary search gets its name because the algorithm continually divides the list into two parts. Created by Sumita Das
- 3. How a Binary Search Works Always look at the center value. Each time you get to discard half of the remaining list. Created by Sumita Das
- 4. Initialize FailureGet Midpoint High < Low < >Compare Adjust High Adjust Low Success= Created by Sumita Das
- 5. Algorithm: Low= 1; High = n; while Low < High { m = floor( (Low+High)/2 ); if k <= A[m] then High = m - 1 else Low = m + 1 } if A[Low] = k then j = Low else j = 0 Created by Sumita Das
- 6. •Similar to merge sort - divide-and- conquer recursive algorithm •One of the fastest sorting algorithms •Average running time O(NlogN) •Worst-case running time O(N2 ) Quick sort Created by Sumita Das
- 7. Basic idea 1.Pick one element in the array, which will be the pivot. 2.Make one pass through the array, called a partition step, re-arranging the entries so that: •the pivot is in its proper place. •entries smaller than the pivot are to the left of the pivot. •entries larger than the pivot are to its right. Created by Sumita Das
- 8. 3.Recursively apply quick sort to the part of the array that is to the left of the pivot, and to the right part of the array. Note: Here we don't have the merge step, at the end all the elements are in the proper order. Created by Sumita Das
- 9. Algorithm: • Input: Array E and indices first, and last, s.t. elements E[i] are defined for first ≤ i ≤ last • Ouput: E[first], …, E[last] is a sorted rearrangement of the array • Void quickSort(Element[] E, int first, int last) if (first < last) Element pivotElement = E[first]; int splitPoint = partition(E, pivotElement, first, last); quickSort (E, first, splitPoint –1 ); quickSort (E, splitPoint +1, last ); return; Created by Sumita Das
- 10. Merge Sort • Uses recursion. Slightly faster than heap, but uses twice as much memory from the 2nd array. • Sometimes called “divide and conquer” sort. • Works by recursively splitting an array into two equal halves, sorting the items, then re-merging them back into a new array. Created by Sumita Das
- 11. Algorithm: • Split array A[1..n] in two and make copies of each half in arrays B[1.. n/2 ] and C[1.. n/2 ] • sort arrays B and C • Merge sorted arrays B and C into array A Created by Sumita Das
- 12. Using Divide and Conquer: Merge Sort • Merge Sort Strategy Sorted Merge Sorted Sorted Sort recursively by Mergesort Sort recursively by Mergesort first last (first + last)/2 Created by Sumita Das
- 13. Example : Binary Searching 14? 14? Created by Sumita Das
- 14. Binary Searching 14 Created by Sumita Das
- 15. Example : Quick sort Created by Sumita Das
- 16. Example : Merge Sort – n Power of 2 1 2 3 4 5 6 7 8 q = 462317425 1 2 3 4 7425 5 6 7 8 6231 1 2 25 3 4 74 5 6 31 7 8 62 1 5 2 2 3 4 4 7 1 6 3 7 2 8 6 5 Divide
- 17. Example – n Power of 2 1 5 2 2 3 4 4 7 1 6 3 7 2 8 6 5 1 2 3 4 5 6 7 8 76543221 1 2 3 4 7542 5 6 7 8 6321 1 2 52 3 4 74 5 6 31 7 8 62 Conquer and Merge
- 18. Example – n Not a Power of 2 62537416274 1 2 3 4 5 6 7 8 9 10 11 q = 6 416274 1 2 3 4 5 6 62537 7 8 9 10 11 q = 9q = 3 274 1 2 3 416 4 5 6 537 7 8 9 62 10 11 74 1 2 2 3 16 4 5 4 6 37 7 8 5 9 2 10 6 11 4 1 7 2 6 4 1 5 7 7 3 8 Divide
- 19. Example – n Not a Power of 2 77665443221 1 2 3 4 5 6 7 8 9 10 11 764421 1 2 3 4 5 6 76532 7 8 9 10 11 742 1 2 3 641 4 5 6 753 7 8 9 62 10 11 2 3 4 6 5 9 2 10 6 11 4 1 7 2 6 4 1 5 7 7 3 8 74 1 2 61 4 5 73 7 8 Conquer and Merge
- 20. References [1]Introduction to Algorithms 2nd ,Cormen, Leiserson, Rivest and Stein, The MIT Press, 2001.
- 21. Thank you…. Created by Sumita Das