MergeSort

Merge sort is an O(n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945.

Conceptually, a merge sort works as follows

1. Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
2. Repeatedly merge sublists to produce new sublists until there is only 1 sublist remaining. This will be the sorted list

<Introduction to algorithm>

The merge sort algorithm closely follows the divide-and-conquer paradigm. Intuitively,
it operates as follows.
Divide: Divide the n-element sequence to be sorted into two subsequences of n=2
elements each.
Conquer: Sort the two subsequences recursively using merge sort.
Combine: Merge the two sorted subsequences to produce the sorted answer

/*
 * Best     Average    Worst     Memory   Stable
 * nlogn     nlogn     nlogn       n       Yes
*/
public class MergeSort {

    public static int[] sort(int[] a){
        if(a.length>1){
            int leftLength=a.length/2;
            int rightLength=a.length - leftLength;
            
            int[] left=new int[leftLength];
            int[] right=new int[rightLength];
            System.arraycopy(a, 0, left, 0, leftLength);
            System.arraycopy(a, leftLength, right, 0, rightLength);
            
            left=sort(left);
            right=sort(right);
            
            int i=0;
            int j=0;
            for(int k=0;k<a.length;k++){
                if(i<leftLength && j==rightLength){
                    a[k]=left[i];
                    i++;
                }
                else if(j<rightLength && i==leftLength){
                    a[k]=right[j];
                    j++;
                }
                else if(i<leftLength && j<rightLength){
                    if(left[i]<=right[j]){
                        a[k]=left[i];
                        i++;
                    }
                    else{
                        a[k]=right[j];
                        j++;
                    }
                }
            }
        }
        return a;
    }
    
    public static void printArray(int[] a){
        for(int i = 0;i < a.length;i++){
            System.out.print(a[i]+" ");
        }
    }
    
    public static void main(String[] args) {
        int[] a=new int[]{2, 1, 5, 4, 9, 8, 6, 7, 10, 3};
        sort(a);
        printArray(a);
        
    }

}