/**
* Sort array ar[left,right] using Quicksort method.
*/
void do_qsort (void *const pbase, size_t n, size_t s,
int(*cmp)(const void *,const void *)) {
void *pp;
long ct, num;
if (n <= 1) { return; }
/* locate median (also placeds it in pbase[n-1]. */
selectPivotIndex(pbase,n,s,cmp);
pp = partition (pbase,n,s,cmp);
ct = (long)pp - (long)pbase;
num = ct / s;
if (ct > minSize*s && ct > s) {
do_qsort (pbase, num, s, cmp);
} else if (ct > 1) {
insertion (pbase, num, s, cmp);
}
ct = (long)pbase + (n-1)*s - (long)pp;
num = ct / s;
if (ct > minSize*s && ct > s) {
do_qsort (pp+s, num, s, cmp);
} else if (ct > 1) {
insertion (pp+s, num, s, cmp);
}
}
/**
* Average-case linear time recursive algorithm to find position of kth
* element in ar, which is modified as this computation proceeds. Note 1
* <= k <= right-left+1. The comparison function, cmp, is needed to
* properly compare elements. Worst-case is quadratic, O(n^2).
*/
int selectKth (void **ar, int(*cmp)(const void *,const void *),
int k, int left, int right) {
int idx = selectPivotIndex (ar, left, right);
int pivotIndex = partition (ar, cmp, left, right, idx);
if (left+k-1 == pivotIndex) { return pivotIndex; }
/* continue the loop, narrowing the range as appropriate. If we are within
* the left-hand side of the pivot then k can stay the same. */
if (left+k-1 < pivotIndex) {
return selectKth (ar, cmp, k, left, pivotIndex - 1);
} else {
return selectKth (ar, cmp, k - (pivotIndex-left+1), pivotIndex+1, right);
}
}
int Sort::findKthGreatestValue(std::vector<int> &vector, int k, int leftIndex, int rightIndex)
{
assert(leftIndex >= 0 && leftIndex <= rightIndex && "Invalid left index.");
assert(rightIndex < vector.size() && "Invalid right index.");
assert(k > 0 && k <= rightIndex - leftIndex + 1 && "Invalid kth value.");
int initialPivotIndex = selectPivotIndex(vector, leftIndex, rightIndex);
// Partition the vector V so that the range V[leftIndex, finalPivotIndex) contains
// only values <= the pivot value, and V(finalPivotIndex, rightIndex] contains only
// values >= the pivot value.
//
int finalPivotIndex = partition(vector, leftIndex, rightIndex, initialPivotIndex);
// Note that when the above completes, the value at the finalPivotIndex must be
// the [(finalIndex + 1) - leftIndex]-th greatest value in the *range.*
// (This is easiest to see in the case where leftIndex = 0).
int orderOfPivotValue = (finalPivotIndex + 1) - leftIndex;
// If we have found the kth greatest value in the range, then we are done.
if (orderOfPivotValue == k) {
return vector[finalPivotIndex];
}
// Otherwise, continue looking for the kth greatest value, narrowing the range
// either to what comes before the finalPivotIndex, or what comes after.
if (orderOfPivotValue > k)
{
// If we found the nth greatest value where n > k, then we can search to
// the left of the nth value and leave k the same.
return findKthGreatestValue(vector, k, leftIndex, finalPivotIndex - 1);
}
else
{
// If we found the nth greatest value where n < k, then we need to search
// to the right of k.
//
// Note that now, we want to find the [k - orderOfPivotValue]-th greatest
// value in the remaining range:
return findKthGreatestValue(vector, k - orderOfPivotValue, finalPivotIndex + 1, rightIndex);
}
}
/**
* Sort array ar[left,right] using Quicksort method.
* The comparison function, cmp, is needed to properly compare elements.
*/
void do_qsort (void **ar, int(*cmp)(const void *,const void *),
int left, int right) {
int pivotIndex;
if (right <= left) { return; }
/* partition */
pivotIndex = selectPivotIndex (ar, left, right);
pivotIndex = partition (ar, cmp, left, right, pivotIndex);
if (pivotIndex-1-left <= minSize) {
insertion (ar, cmp, left, pivotIndex-1);
} else {
do_qsort (ar, cmp, left, pivotIndex-1);
}
if (right-pivotIndex-1 <= minSize) {
insertion (ar, cmp, pivotIndex+1, right);
} else {
do_qsort (ar, cmp, pivotIndex+1, right);
}
}
/**
* Average-case linear time algorithm to find position of kth element in
* ar, which is modified as this computation proceeds. Note 1 <= k <=
* right-left+1. The comparison function, cmp, is needed to properly
* compare elements.
*
* @param ar array of elements to be sorted.
* @param cmp comparison function to order elements.
* @param k kth smallest element to select.
* @param left lower bound index position (inclusive)
* @param right upper bound index position (inclusive)
*/
int selectKth (void **ar, int(*cmp)(const void *,const void *),
int k, int left, int right) {
do {
int idx = selectPivotIndex (ar, left, right);
int pivotIndex = partition (ar, cmp, left, right, idx);
if (left+k-1 == pivotIndex) {
return pivotIndex;
}
/* continue the loop, narrowing the range as appropriate. If we are within
* the left-hand side of the pivot then k can stay the same. */
if (left+k-1 < pivotIndex) {
right = pivotIndex - 1;
} else {
/* otherwise k must decrease by the size being removed. */
k -= (pivotIndex-left+1);
left = pivotIndex + 1;
}
} while (1);
}
