### Python program to find largest binary search tree in a Binary Tree.

Description:
To find the largest BST in BT we need to write a function to find the largest subtree which is also a Binary Search Tree (BST).
A Tree is BST if following is true for every node x.
1. The largest value in left subtree (of x) is smaller than value of x.
2. The smallest value in right subtree (of x) is greater than value of x.

Example :
Here the maximum size  BST subtree is :

Program :

# Python program to find largest BST in a Binary Tree.
minVal= -2147483648 maxVal = 2147483647 # Helper function that allocates a new node with the given data and None left and right pointers. class newNode: def __init__(self, data): self.data = data self.left = None self.right = None # Returns Information about subtree which includes size of largest subtree which is a BST def largestBSTBT(root): # Base cases : When tree is empty or it has # one child. if (root == None): return 0, minVal, maxVal, 0, True if (root.left == None and root.right == None) : return 1, root.data, root.data, 1, True # Recur for left subtree and right subtrees l = largestBSTBT(root.left) r = largestBSTBT(root.right) # Create a return variable and initialize its size. ret = [0, 0, 0, 0, 0] ret[0] = (1 + l[0] + r[0]) # If whole tree rooted under current root is BST. if (l[4] and r[4] and l[1] < root.data and r[2] > root.data) : ret[2] = min(l[2], min(r[2], root.data)) ret[1] = max(r[1], max(l[1], root.data)) # Update answer for tree rooted under # current 'root' ret[3] = ret[0] ret[4] = True return ret # If whole tree is not BST, return maximum # of left and right subtrees ret[3] = max(l[3], r[3]) ret[4] = False return ret # Driver Code if __name__ == '__main__': """Let us construct the following Tree 20 / \ 25 30 / 10 """ root = newNode(20) root.left = newNode(25) root.right = newNode(30) root.left.left = newNode(10) print("Size of the largest BST is",largestBSTBT(root)[3])
Output:

Size of the largest BST is 2 >>>

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