Largest BST(JAVA).md

Largest BST(JAVA).md

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+# Finding the Size of the Largest BST in Java
+
+This Java code demonstrates how to find the size of the largest Binary Search Tree (BST) within a given binary tree using a recursive approach.
+
+## Important Points
+
+- Define a `TreeNode` class to represent individual nodes in the binary tree.
+
+- Create a `BSTInfo` class to store information about each subtree, including size, minimum value, maximum value, and whether it's a valid BST.
+
+- Define a `BinaryTree` class to represent the binary tree, with methods to find the size of the largest BST.
+
+- The `largestBSTSize` method in the `BinaryTree` class initiates the process of finding the largest BST.
+
+- The `largestBSTHelper` method is a recursive function that determines whether a subtree is a valid BST and calculates its size.
+
+- The `main` method demonstrates how to use the `BinaryTree` class to find the size of the largest BST within a binary tree.
+
+```java
+class TreeNode {
+    int val;
+    TreeNode left;
+    TreeNode right;
+
+    public TreeNode(int val) {
+        this.val = val;
+        left = null;
+        right = null;
+    }
+}
+
+class BSTInfo {
+    int size;
+    int min;
+    int max;
+    boolean isBST;
+
+    public BSTInfo(int size, int min, int max, boolean isBST) {
+        this.size = size;
+        this.min = min;
+        this.max = max;
+        this.isBST = isBST;
+    }
+}
+
+class BinaryTree {
+    TreeNode root;
+
+    public BinaryTree() {
+        root = null;
+    }
+
+    // Function to find the size of the largest BST within a binary tree
+    public int largestBSTSize() {
+        BSTInfo info = largestBSTHelper(root);
+        return info.size;
+    }
+
+    private BSTInfo largestBSTHelper(TreeNode node) {
+        if (node == null) {
+            return new BSTInfo(0, Integer.MAX_VALUE, Integer.MIN_VALUE, true);
+        }
+
+        BSTInfo leftInfo = largestBSTHelper(node.left);
+        BSTInfo rightInfo = largestBSTHelper(node.right);
+
+        if (leftInfo.isBST && rightInfo.isBST && node.val > leftInfo.max && node.val < rightInfo.min) {
+            int size = 1 + leftInfo.size + rightInfo.size;
+            int min = Math.min(node.val, leftInfo.min);
+            int max = Math.max(node.val, rightInfo.max);
+            return new BSTInfo(size, min, max, true);
+        } else {
+            // If the current subtree is not a BST, return the maximum size from its children
+            return new BSTInfo(Math.max(leftInfo.size, rightInfo.size), 0, 0, false);
+        }
+    }
+}
+
+public class Main {
+    public static void main(String[] args) {
+        BinaryTree tree = new BinaryTree();
+        tree.root = new TreeNode(10);
+        tree.root.left = new TreeNode(5);
+        tree.root.right = new TreeNode(15);
+        tree.root.left.left = new TreeNode(1);
+        tree.root.left.right = new TreeNode(8);
+        tree.root.right.right = new TreeNode(7);
+
+        int largestBSTSize = tree.largestBSTSize();
+        System.out.println("Size of the largest BST: " + largestBSTSize);
+    }
+}
+```
+In this code, the `BinaryTree` class represents the binary tree, and the `largestBSTSize` method finds the size of the largest BST within the binary tree. The `largestBSTHelper` method is a recursive helper function that returns information about the BST rooted at the current node. The `BSTInfo` class is used to store information about each subtree, including its size, minimum, maximum, and whether it is a valid BST.