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Find median of BST in O(n) time and O(1) space in Python
Suppose we have Binary Search Tree(BST), we have to find median of it. We know for even number of nodes, median = ((n/2th node + (n+1)/2th node) /2 For odd number of nodes, median = (n+1)/2th node.
So, if the input is like
then the output will be 7
To solve this, we will follow these steps −
if root is same as None, then
return 0
node_count := number of nodes in the tree
count_curr := 0
current := root
while current is not null, do
if current.left null, then
count_curr := count_curr + 1
if node_count mod 2 is not 0 and count_curr is same as(node_count + 1) /2, then
return previous.data
otherwise when node_count mod 2 is 0 and count_curr is same as(node_count/2) +1, then
return(previous.data + current.data) /2
previous := current
current := current.right
otherwise,
previous := current.left
while previous.right is not null and previous.right is not same as current, do
previous := previous.right
if previous.right is null, then
previous.right := current
current := current.left
otherwise,
previous.right := None
previous := previous
count_curr := count_curr + 1
if node_count mod 2 is not 0 and count_curr is same as(node_count + 1) / 2, then
return current.data
otherwise when node_count mod 2 is 0 and count_curr is same as(node_count / 2) + 1, then
return(previous.data+current.data) /2
previous := current
current := current.right
Example
Let us see the following implementation to get better understanding −
class TreeNode: def __init__(self, data): self.data = data self.left = None self.right = None def number_of_nodes(root): node_count = 0 if (root == None): return node_count current = root while (current != None): if (current.left == None): node_count+=1 current = current.right else: previous = current.left while (previous.right != None and previous.right != current): previous = previous.right if(previous.right == None): previous.right = current current = current.left else: previous.right = None node_count += 1 current = current.right return node_count def calculate_median(root): if (root == None): return 0 node_count = number_of_nodes(root) count_curr = 0 current = root while (current != None): if (current.left == None): count_curr += 1 if (node_count % 2 != 0 and count_curr == (node_count + 1)//2): return previous.data elif (node_count % 2 == 0 and count_curr == (node_count//2)+1): return (previous.data + current.data)//2 previous = current current = current.right else: previous = current.left while (previous.right != None and previous.right != current): previous = previous.right if (previous.right == None): previous.right = current current = current.left else: previous.right = None previous = previous count_curr+= 1 if (node_count % 2 != 0 and count_curr == (node_count + 1) // 2 ): return current.data elif (node_count%2 == 0 and count_curr == (node_count // 2) + 1): return (previous.data+current.data)//2 previous = current current = current.right root = TreeNode(7) root.left = TreeNode(4) root.right = TreeNode(9) root.left.left = TreeNode(2) root.left.right = TreeNode(5) root.right.left = TreeNode(8) root.right.right = TreeNode(10) print(calculate_median(root))
Input
root = TreeNode(7) root.left = TreeNode(4) root.right = TreeNode(9) root.left.left = TreeNode(2) root.left.right = TreeNode(5) root.right.left = TreeNode(8) root.right.right = TreeNode(10)
Output
7
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