Algorithm 3_Quick_Sort

  Choose an index named middleIndex between fist Index and last index of an array which is to be sort.We can get a rearranged array that has the following jfeatures: all elements from first index to middle index is smaller than array[middleindex];all elements from middle index to last index is larger than array[middleindex].The Partition method return the middle index so we can rearrange the two subarray by the same way.

  Let’s show it.

        //swap two items of the arr
        private void Swap(Int32[] arr, Int32 firstIndex, Int32 secondIndex)
        ...{
            if (firstIndex < arr.Length && secondIndex < arr.Length)
            ...{
                Int32 temp = arr[firstIndex];
                arr[firstIndex] = arr[secondIndex];
                arr[secondIndex] = temp;
            }
        }

        //In this method,we use arr[lastIndex] as the middleValue
        private Int32 Partition(Int32[] arr, Int32 firstIndex, Int32 lastIndex)
        ...{
            if (firstIndex < arr.Length && lastIndex < arr.Length)
            ...{
                Int32 middleValue = arr[lastIndex];
                Int32 i = firstIndex - 1;
                for (Int32 j = firstIndex; j < lastIndex; j++)
                ...{
                    if (arr[j] <= middleValue)
                        Swap(arr, ++i, j);
                }
                Swap(arr, i + 1, lastIndex);
                return i + 1;
            }
            else
            ...{
                return -1;
            }
        }

        public void Sort(Int32[] arr, Int32 firstIndex, Int32 lastIndex)
        ...{
            if (firstIndex < lastIndex)
            ...{
                Int32 middleIndex = Partition(arr, firstIndex, lastIndex);
                Sort(arr, firstIndex, middleIndex - 1);
                Sort(arr, middleIndex + 1, lastIndex);
            }
        }

 

       Ok,it fine.

       Let's make a random index between firstIndex and lastIndex,Choose arr[randomIndex] as the middleValue

       

private Int32 RandomizedPartition(Int32[] arr, Int32 firstIndex, Int32 lastIndex)
        ...{
            Random randomer = new Random();
            Int32 index = randomer.Next(firstIndex, lastIndex);
            Swap(arr, index, lastIndex);
            return Partition(arr, firstIndex, lastIndex);
        }

        public void RandomizedSort(Int32[] arr, Int32 firstIndex, Int32 lastIndex)
        ...{
            if (firstIndex < lastIndex)
            ...{
                Int32 middleIndex = RandomizedPartition(arr, firstIndex, lastIndex);
                RandomizedSort(arr, firstIndex, middleIndex - 1);
                RandomizedSort(arr, middleIndex + 1, lastIndex);
            }
        }

the worst-case running time of  QuickSort is big theta n*n on an input array of n numbers.

But the quicksort is often the best practical choice for sorting because it is efficient in the average:its expected running time is big theta n*lgn.