![• Array is a data structure where all elements are arranged sequentially.
Array
• It is a collection of elements of same data type.
• The base value is index 0
• To access elemnts :
variable_name[ index of element ]](https://image.slidesharecdn.com/quick-sortalgorithm-250416071440-5366b009/85/Quick-Sort-Algorithm-and-pivot-selection-3-320.jpg)
![ALGORITHM
QuickSort ( arr, low, high )
{
If ( low < high )
{
pivotindex = Partition ( arr, low, high )
QuickSort ( arr, low, pivotindex-1 )
QuickSort ( arr, pivotindex+1, high)
}
}
Partition ( arr, low, high )
{
pivot = arr[0];
i = low;
j = high;
while ( i < j )
{
while (arr[ i ] <= pivot && i <= high-1)
{
i++;
}
while (arr[ j ] > pivot && i >= low+1)
{
j--;
}
If (i<j)
swap (arr[ i ], arr[ j ] );
}
swap (arr[ low ], arr[ j ]);
return(j);
}](https://image.slidesharecdn.com/quick-sortalgorithm-250416071440-5366b009/85/Quick-Sort-Algorithm-and-pivot-selection-10-320.jpg)
Quick-Sort Algorithm and pivot selection
- 1. QUICK-SORT ALGORITHM By Subhranjali Behera (MCA, Utkal University)
- 2. • Basic Fundamentals • Introduction to Quick Sort • Steps to perform Quick Sort • Algorithm and pseudocode for Quick Sort • Analysis of Quick Sort COURSE OUTLINE
- 3. • Array is a data structure where all elements are arranged sequentially. Array • It is a collection of elements of same data type. • The base value is index 0 • To access elemnts : variable_name[ index of element ]
- 4. Recursio n • The process in which a function calls itself is called recursion. • Through Recursion, we can reduce the length of our code and make it easier to rea and write. • For example factorial of a number. Suppose 5! = 5*4*3*2*1 which is same as 5*4! int fact(int n) { if (n < = 1) // base case(solution to base case is provided) return 1; else return n*fact(n-1); }
- 5. INTRODUCTION TO SORTING • Sorting is the process of arranging elements of an array in non increasing or non decreasing order. • Example of Sorting: Consider an array of numbers: A={5, 2, 8, 1, 3} After sorting in non increasing order: A={1, 2, 3, 5, 8} After sorting in non decreasing order: A={8, 5, 3, 2, 1}
- 6. INTRODUCTION TO QUICK SORT ALGORITHM • QuickSort is fastest sorting algorithm • It is a divide-and-conquer algorithm that makes it easier to solve problems. • It is efficient on large data sets.
- 7. DIVIDE AND CONQUER Consists of the Following 3 Steps: • Divide: Dividing the Problem Into Smaller Sub-Problems. • Conquer: Solve Sub-Problems by Calling Recursively. • Combine: Combine the Sub-Problems to Get the Final Solution of the Whole Problem.
- 8. Steps To perform Quicksort: Choose a Pivot • There are no such rules for choosing a pivot. Place the pivot in its correct position. Partition the elements into two sections • Elements <= pivot in left side • Elements > pivot in right side Recursively Quicksort the two halves until down to one element STEPS OF QUICK SORT ALGORITHM
- 9. ALGORITHM QuickSort ( arr, low, high ) { If ( low < high ) { pivotindex = Partition ( arr, low, high ) QuickSort ( arr, low, pivotindex-1 ) QuickSort ( arr, pivotindex+1, high) } }
- 10. ALGORITHM QuickSort ( arr, low, high ) { If ( low < high ) { pivotindex = Partition ( arr, low, high ) QuickSort ( arr, low, pivotindex-1 ) QuickSort ( arr, pivotindex+1, high) } } Partition ( arr, low, high ) { pivot = arr[0]; i = low; j = high; while ( i < j ) { while (arr[ i ] <= pivot && i <= high-1) { i++; } while (arr[ j ] > pivot && i >= low+1) { j--; } If (i<j) swap (arr[ i ], arr[ j ] ); } swap (arr[ low ], arr[ j ]); return(j); }
- 11. Case Time Complexity Space Complexity Best Case O(n log n) O(log n) Average Case O(n log n) O(log n) Worst Case O(n²) O(n) ANALYSIS OF QUICK SORT ALGORITHM
- 12. Thank You