Quick Sort in Java

1. Time complexity : O(n*n) - Worst case , O(nlogn) - Best Case
2. Space complexity : O(logn) - height of recursion tree

Best case :

n/2^k = 1 
2^k = n 
k= log(n)
 Worst case :
Worst case occur when when the pivot partition the array in an extreme way e.g.
one array is empty and other array contains n-1 elements. 

So, for calculating quick sort time complexity in the worst case, 
we put i = n — 1 in the above equation of 
T(n) => T(n) = T(n — 1) + T(0) + cn = T(n — 1) + cn . 
In this method, we draw the recursion tree and sum the partitioning cost 
for each level => cn + c(n−1) + c(n−2) +⋯+ 2c + c ​= 
c (n + n−1 + n−2 + ⋯+ 2 + 1) = c(n(n+1)/2) = O(n²). 
So worst case time complexity of quick sort is O(n²).

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    static void swap(int arr[],int a,int b){
        int temp =arr[a];
        arr[a]=arr[b];
        arr[b] = temp;
    }
    
    static void quickSort(int arr[], int low, int high)
    {
        // code here
        
        if(high>low){
            int piv = partition(arr,low,high);
            quickSort(arr,low,piv-1);
            quickSort(arr,piv+1,high);
        }
    }
    static int partition(int arr[], int low, int high)
    {
        // your code here
        
        int piv = low;
        int i = low;
        int j = high;
        
        while(i<j){
            while(arr[i]<=arr[piv] && i<=high-1){i++;}
            while(arr[j]>arr[piv] && low+1<=j){j--;}
            
            if(i<j){
                swap(arr,i,j);
            }
        }
        
        swap(arr,piv,j);
        return j;
        
    }