public SpecialBST(int value)
{
this.value = value;
leftSubtreeSize = 0;
left = null;
right = null;
}
// Average case: when the created BST is balanced
// O(nlog(n)) time | O(n) space - where n is the length of the array
// ---
// Worst case: when the the created BST is like a linked list
// O(n^2) time | O(n) space
public static List <int> RightSmallerThan(List <int> array)
{
if (array.Count == 0)
{
return(new List <int>());
}
List <int> rightSmallerCounts = new List <int>(array);
int lastIdx = array.Count - 1;
SpecialBST bst = new SpecialBST(array[lastIdx]);
rightSmallerCounts[lastIdx] = 0;
for (int i = array.Count - 2; i >= 0; i--)
{
bst.insert(array[i], i, rightSmallerCounts);
}
return(rightSmallerCounts);
}
public void insertHelper(int value, int idx, List <int> rightSmallerCounts,
int numSmallerAtInsertTime)
{
if (value < this.value)
{
leftSubtreeSize++;
if (left == null)
{
left = new SpecialBST(value);
rightSmallerCounts[idx] = numSmallerAtInsertTime;
}
else
{
left.insertHelper(value, idx, rightSmallerCounts,
numSmallerAtInsertTime);
}
}
else
{
numSmallerAtInsertTime += leftSubtreeSize;
if (value > this.value)
{
numSmallerAtInsertTime++;
}
if (right == null)
{
right = new SpecialBST(value);
rightSmallerCounts[idx] = numSmallerAtInsertTime;
}
else
{
right.insertHelper(value, idx, rightSmallerCounts,
numSmallerAtInsertTime);
}
}
}