问题
The implementation below is stable as it used <=
instead of <
at line marked XXX. This also makes it more efficient. Is there any reason to use <
and not <=
at this line?
/**
class for In place MergeSort
**/
class MergeSortAlgorithm extends SortAlgorithm {
void sort(int a[], int lo0, int hi0) throws Exception {
int lo = lo0;
int hi = hi0;
pause(lo, hi);
if (lo >= hi) {
return;
}
int mid = (lo + hi) / 2;
/*
* Partition the list into two lists and sort them recursively
*/
sort(a, lo, mid);
sort(a, mid + 1, hi);
/*
* Merge the two sorted lists
*/
int end_lo = mid;
int start_hi = mid + 1;
while ((lo <= end_lo) && (start_hi <= hi)) {
pause(lo);
if (stopRequested) {
return;
}
if (a[lo] <= a[start_hi]) { // LINE XXX
lo++;
} else {
/*
* a[lo] >= a[start_hi]
* The next element comes from the second list,
* move the a[start_hi] element into the next
* position and shuffle all the other elements up.
*/
int T = a[start_hi];
for (int k = start_hi - 1; k >= lo; k--) {
a[k+1] = a[k];
pause(lo);
}
a[lo] = T;
lo++;
end_lo++;
start_hi++;
}
}
}
void sort(int a[]) throws Exception {
sort(a, 0, a.length-1);
}
}
回答1:
Because the <=
in your code assures that same-valued elements (in left- and right-half of sorting array) won't be exchanged.
And also, it avoids useless exchanges.
if (a[lo] <= a[start_hi]) {
/* The left value is smaller than or equal to the right one, leave them as is. */
/* Especially, if the values are same, they won't be exchanged. */
lo++;
} else {
/*
* If the value in right-half is greater than that in left-half,
* insert the right one into just before the left one, i.e., they're exchanged.
*/
...
}
Assume that same-valued element (e.g., ‘5’) in both-halves and the operator above is <
.
As comments above shows, the right ‘5’ will be inserted before the left ‘5’, in other words, same-valued elements will be exchanged.
This means the sort is not stable.
And also, it's inefficient to exchange same-valued elements.
I guess the cause of inefficiency comes from the algorithm itself. Your merging stage is implemented using insertion sort (as you know, it's O(n^2)).
You may have to re-implement when you sort huge arrays.
回答2:
Fastest known in place stable sort:
http://thomas.baudel.name/Visualisation/VisuTri/inplacestablesort.html
来源:https://stackoverflow.com/questions/1933822/why-is-in-place-merge-sort-not-stable