Quick sort
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Quicksort is a divide-and-conquer sorting algorithm that dynamically divides the array into subarrays rather than using static divisions like Mergesort. It has three steps - divide the array into subarrays separated by a pivot element, recursively sort the subarrays, and combine the sorted subarrays. The algorithm works by picking a pivot element and partitioning the array such that elements less than the pivot are moved before it and greater elements after it. It then recursively applies this process to the subarrays until the entire array is sorted. The performance depends on how evenly the array is divided during partitioning, with best case being a split in the middle and worst case being a skewed division.
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Quick sort
- 1. Quick Sort Dr. Himani Mittal
- 2. Quick Sort Quicksort is a divide-and-conquer sorting algorithm in which division is dynamically carried out (as opposed to static division in Mergesort).
- 3. The three steps of Quicksort are as follows: • Divide: Rearrange the elements and split the array into two subarrays and an element in between such that so that each element in the left subarray is less than or equal the middle element and each element in the right subarray is greater than the middle element. • Conquer: Recursively sort the two subarrays. • Combine: None. Quick Sort
- 6. 15 20 5 30 35 10 ∞ 20 < 15 false so stop ∞<= 1510 > 15 false so stop i =2 m =1 j =7 i< j, interchange a[i] with a[j] 15 10 5 30 35 20 ∞ i < j (3 <6), true so continue in loop with i=2 and j=6 15 10 5 30 35 20 ∞ 5 <15 true 30 <15 false so stop for I = 4 35 >15 true 30>15 i =3 m =1 j =5 i< j, false, so no interchange. Repeat condition becomes true, So stop looping. interchange a[m] with a[j] 5>15 false so stop for j=3 5 10 15 30 35 20 ∞ Return j=3 as new pivot element
- 7. 30 35 20 ∞ 35>=30 20 <=30i =4 m =4 j =7 i< j, interchange a[i] with a[j] => 5< 6 , so change a[5] with a[6] 30 20 35 ∞ i < j, (5 < 6) true so continue in loop With i=5 and j=6 30 20 35 ∞ 35 >3020 <30i =6 m =4 j =5 i< j, false,No interchange. While(i<j) becomes false , So stop looping .interchange a[m] with a[j] Return j=5 as new pivot element Two partitions: partition(a,1,2) and partition(a,4,7) 20 30 35 ∞
- 8. Quick Sort Call Tree p = 1, q = 6 j = 3 p = 4, q = 6 j = 5 p = 1, q = 2 j = 1 p = 2, q = 2 return p = 1, q = 0 return p = 6, q = 6 return p = 4, q = 4 return Though this tree seems balanced, in Quick Sort the tree is not always balanced because the partition position j will change according to its position in sorting order. This position will change according to input array. So best case is that array always splits in middle. Worst case is left or right skewed. Average case is array can split at any position s.