written 6.7 years ago by | modified 2.5 years ago by |

Sort the following numbers using Quick sort algorithm. Show all passes of execution also state the following state the time complexity.

65, 70, 75, 80, 60, 55, 50, 45

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Sort the following numbers using Quick sort algorithm. Show all passes of execution also state the following state the time complexity.

written 6.7 years ago by | modified 2.5 years ago by |

Sort the following numbers using Quick sort algorithm. Show all passes of execution also state the following state the time complexity.

65, 70, 75, 80, 60, 55, 50, 45

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written 2.5 years ago by |

*Step 1 −** Choose the high-index Pivot.*

*Step 2 −** Take two variables to point Left and Right of the list excluding Pivot.*

*Step 3 −** Left points to the low index.*

*Step 4 −** Right points to the high index.*

*Step 5 −** If the value at the Left is less than the pivot move in the right direction.*

*Step 6 −** If the value at the Right is greater than the pivot move in the left direction.*

*Step 7 −** If both step 5 and step 6 do not match SWAP Left and Right.*

*Step 8 −** If left ≥ right, the point where they met is a new pivot. Checks the value of old and new Pivots whether there is a need for Swapping or not.*

**The given example using Quick Sort -**

- Quick Sort is sensitive to the order of input data.
- It gives the worst performance when elements are already in ascending or descending order.

**Best Case Time Complexity -**

- In Quicksort, the best-case occurs when the pivot element is the middle element or near to the middle element. The best-case time complexity of quicksort is

$$O(n^*log\ n)$$

**Average Case Complexity -**

- If array elements are not in properly ascending and not properly descending order. The average case time complexity of quicksort is

$$O(n^*log\ n)$$

**Worst-Case Complexity -**

- In quick sort, the worst case occurs when the pivot element is either the greatest or smallest element.
- It divides the array into sections of 1 and (n-1) elements in each call.
- Then, there are (n-1) divisions in all.
- Therefore, here total comparisons required are

$$f(n) = n \times (n-1) = O(n^2)$$

** Space Complexity of Quick Sort -** $O(n^*log\ n)$

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