I'm implementing a select-kth algorithm using the Median of Medians pivot method. Specifically, I'm following the pseudocode listed here.. However, my code crashes (error discussed below), I see why it crashes, but I don't understand what I can do about it.
The Error
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 32017219
at Selection.partition(Selection.java:173)
The Reason
In the wiki link, the method select
will return a value if left == right
. However, when the mutual recursion is called from the return statement of pivot
, that means it will return a value (and not an index) back to the parent and the parent will set that value as the pivotIndex
.
The Code
public static int alg5(int[] a, int left, int right, int k) {
if (left == right) {
return a[left];
}
while (true) {
int pivotIndex = pivot(a, left, right);
pivotIndex = partition(a, left, right, pivotIndex);
if (k == pivotIndex) {
return a[k];
} else if (k < pivotIndex) {
right = pivotIndex - 1;
} else {
left = pivotIndex + 1;
}
}
}
public static int pivot(int[] a, int left, int right) {
for (int i = left; i <= right; i = i + 5) {
int subRight = i + 4;
if (subRight > right) {
subRight = right;
}
int median5 = partition5(a, i, subRight);
swap(a, median5, (int)(Math.floor(i / 5)));
}
return alg5(a, left, (int)(left + Math.ceil((right - left) / 5) - 1), ((right - left) / 10));
}
public static int partition5(int[] a, int left, int right) {
Arrays.sort(a);
return ((a.length - 1) / 2);
}
public static int partition(int[] a, int left, int right, int pivotIndex) {
int pivotValue = a[pivotIndex];
a = swap(a, pivotIndex, right);
int storeIndex = left;
for (int i = left; i <= right; i++) {
int aOfi = a[i];
if (a[i] < pivotValue) {
swap(a, storeIndex, i);
storeIndex++;
}
}
swap(a, right, storeIndex);
return storeIndex;
}
I completely understand why my code isn't working, I just don't understand how to fix it since it looks to be exactly what the algorithm specifies. Pointers are greatly appreciated!
There are quite a few mistakes:
The method pivot
should not modify the array a
. It should just find a pivot for the future partition
. A dirty fix is to call pivot(a.clone(), left, right);
. (You shouldn't do this, just to give you an idea.)
Math.ceil((right - left) / 5)
is an integer division. You should cast them to floats: Math.ceil(((float)(right - left)) / 5f)
.
In partition5
, you sort the whole array a
! You should just do comparisons to find the index of the median between a[left]
and a[right]
.
At some point you might have right < left
, so the first line of alg5
you should write if (left >= right)