Suppose we are provided a binary tree. We have to find out if there exist binary search trees (BST) in the subtrees of it and find out the sum of the largest BST. To find out the sum, we add the values of each node in that BST. We return the sum value as output.
So, if the input is like
then the output will be 12.
The BST in the given binary tree is −
sum of the nodes = 12.
To solve this, we will follow these steps −
Let us see the following implementation to get better understanding −
class TreeNode: def __init__(self, val, left = None, right = None): self.val = val self.left = left self.right = right def insert(temp,data): que = [] que.append(temp) while (len(que)): temp = que[0] que.pop(0) if (not temp.left): if data is not None: temp.left = TreeNode(data) else: temp.left = TreeNode(0) break else: que.append(temp.left) if (not temp.right): if data is not None: temp.right = TreeNode(data) else: temp.right = TreeNode(0) break else: que.append(temp.right) def make_tree(elements): Tree= TreeNode(elements[0]) for element in elements[1:]: insert(Tree, element) return Tree def solve(root): c, m, value = 0, None, 0 def recurse(node): if node: nonlocal c, m left_val = recurse(node.left) right_val = recurse(node.right) count = -float("inf") if (node.left == None or node.left.val <= node.val) and (node.right == None or node.val <= node.right.val): count = left_val + right_val + 1 if count > c: c = count m = node return count return 0 def calculate_sum(root): nonlocal value if root is not None: calculate_sum(root.left) value += root.val calculate_sum(root.right) recurse(root) calculate_sum(m) return value tree = make_tree([1, 4, 6, 3, 5]) print(solve(tree))
tree = make_tree([1, 4, 6, 3, 5]) print(solve(tree))
12