Do a single allocation of the working/temp array and avoid copying of data during merge (unless moving a single remaining run from one array to the other).
Bottom up merge sort example.
package jsortbu;
import java.util.Random;
public class jsortbu {
static void MergeSort(int[] a) // entry function
{
if(a.length < 2) // if size < 2 return
return;
int[] b = new int[a.length];
BottomUpMergeSort(a, b);
}
static void BottomUpMergeSort(int[] a, int[] b)
{
int n = a.length;
int s = 1; // run size
if(1 == (GetPassCount(n)&1)){ // if odd number of passes
for(s = 1; s < n; s += 2) // swap in place for 1st pass
if(a[s] < a[s-1]){
int t = a[s];
a[s] = a[s-1];
a[s-1] = t;
}
s = 2;
}
while(s < n){ // while not done
int ee = 0; // reset end index
while(ee < n){ // merge pairs of runs
int ll = ee; // ll = start of left run
int rr = ll+s; // rr = start of right run
if(rr >= n){ // if only left run
do{ // copy it
b[ll] = a[ll];
ll++;
}while(ll < n);
break; // end of pass
}
ee = rr+s; // ee = end of right run
if(ee > n)
ee = n;
Merge(a, b, ll, rr, ee);
}
{ // swap references
int[] t = a;
a = b;
b = t;
}
s <<= 1; // double the run size
}
}
static void Merge(int[] a, int[] b, int ll, int rr, int ee) {
int o = ll; // b[] index
int l = ll; // a[] left index
int r = rr; // a[] right index
while(true){ // merge data
if(a[l] <= a[r]){ // if a[l] <= a[r]
b[o++] = a[l++]; // copy a[l]
if(l < rr) // if not end of left run
continue; // continue (back to while)
while(r < ee){ // else copy rest of right run
b[o++] = a[r++];
}
break; // and return
} else { // else a[l] > a[r]
b[o++] = a[r++]; // copy a[r]
if(r < ee) // if not end of right run
continue; // continue (back to while)
while(l < rr){ // else copy rest of left run
b[o++] = a[l++];
}
break; // and return
}
}
}
static int GetPassCount(int n) // return # passes
{
int i = 0;
for(int s = 1; s < n; s <<= 1)
i += 1;
return(i);
}
public static void main(String[] args) {
int[] a = new int[10000000];
Random r = new Random();
for(int i = 0; i < a.length; i++)
a[i] = r.nextInt();
long bgn, end;
bgn = System.currentTimeMillis();
MergeSort(a);
end = System.currentTimeMillis();
for(int i = 1; i < a.length; i++){
if(a[i-1] > a[i]){
System.out.println("failed");
break;
}
}
System.out.println("milliseconds " + (end-bgn));
}
}
Top down merge sort example. A pair of mutually recursive functions are used to avoid copy back operations. The direction of merge is based on the level of recursion. Merge() is the same for both bottom up and top down.
package jsorttd;
import java.util.Random;
public class jsorttd {
static void MergeSort(int[] a) // entry function
{
if(a.length < 2) // if size < 2 return
return;
int[] b = new int[a.length];
MergeSortAtoA(a, b, 0, a.length);
}
static void MergeSortAtoA(int[] a, int[] b, int ll, int ee)
{
if(ee - ll > 1) {
int rr = (ll + ee)>>1; // midpoint, start of right half
MergeSortAtoB(a, b, ll, rr);
MergeSortAtoB(a, b, rr, ee);
Merge(b, a, ll, rr, ee); // merge b to a
}
}
static void MergeSortAtoB(int[] a, int[] b, int ll, int ee)
{
if(ee - ll > 1) {
int rr = (ll + ee)>>1; //midpoint, start of right half
MergeSortAtoA(a, b, ll, rr);
MergeSortAtoA(a, b, rr, ee);
Merge(a, b, ll, rr, ee); // merge a to b
} else if((ee - ll) == 1) { // if just one element
b[ll] = a[ll]; // copy a to b
}
}
static void Merge(int[] a, int[] b, int ll, int rr, int ee) {
int o = ll; // b[] index
int l = ll; // a[] left index
int r = rr; // a[] right index
while(true){ // merge data
if(a[l] <= a[r]){ // if a[l] <= a[r]
b[o++] = a[l++]; // copy a[l]
if(l < rr) // if not end of left run
continue; // continue (back to while)
while(r < ee){ // else copy rest of right run
b[o++] = a[r++];
}
break; // and return
} else { // else a[l] > a[r]
b[o++] = a[r++]; // copy a[r]
if(r < ee) // if not end of right run
continue; // continue (back to while)
while(l < rr){ // else copy rest of left run
b[o++] = a[l++];
}
break; // and return
}
}
}
public static void main(String[] args) {
int[] a = new int[10000000];
Random r = new Random();
for(int i = 0; i < a.length; i++)
a[i] = r.nextInt();
long bgn, end;
bgn = System.currentTimeMillis();
MergeSort(a);
end = System.currentTimeMillis();
for(int i = 1; i < a.length; i++){
if(a[i-1] > a[i]){
System.out.println("failed");
break;
}
}
System.out.println("milliseconds " + (end-bgn));
}
}
Both methods take about 1 second to sort 10 million integers on my system (Win 7, Intel 3770K 3.5 ghz, NetBeans 8.1, Java 1.8.0_65-b17).