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POLargest Subtree Which is a Binary Search Tree (BST)
 

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  1. POLargest Subtree Which is a Binary Search Tree (BST)
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    <blockquote> <p>Given a binary tree, I want to find out the largest subtree which is a BST in it.</p> </blockquote> <p>This question is duplicate of <a href="https://stackoverflow.com/questions/2336148/finding-the-largest-subtree-in-a-bst">Finding the largest subtree in a BST</a>, where 1337c0d3r gives a O(n) solution by traversing the tree bottom up. There are two lines code confusing me. Can anyone help me explain it?</p> <pre><code>// Find the largest BST subtree in a binary tree. // If the subtree is a BST, return total number of nodes. // If the subtree is not a BST, -1 is returned. int findLargestBSTSubtree(BinaryTree *p, int &amp;min, int &amp;max, int &amp;maxNodes, BinaryTree *&amp; largestBST) { if (!p) return 0; bool isBST = true; int leftNodes = findLargestBSTSubtree(p-&gt;left, min, max, maxNodes, largestBST); int currMin = (leftNodes == 0) ? p-&gt;data : min; if (leftNodes == -1 || (leftNodes != 0 &amp;&amp; p-&gt;data &lt;= max)) isBST = false; int rightNodes = findLargestBSTSubtree(p-&gt;right, min, max, maxNodes, largestBST); int currMax = (rightNodes == 0) ? p-&gt;data : max; if (rightNodes == -1 || (rightNodes != 0 &amp;&amp; p-&gt;data &gt;= min)) isBST = false; if (isBST) { min = currMin; max = currMax; int totalNodes = leftNodes + rightNodes + 1; if (totalNodes &gt; maxNodes) { maxNodes = totalNodes; largestBST = p; } return totalNodes; } else { return -1; // This subtree is not a BST } } BinaryTree* findLargestBSTSubtree(BinaryTree *root) { BinaryTree *largestBST = NULL; int min, max; int maxNodes = INT_MIN; // INT_MIN is defined in &lt;climits&gt; findLargestBSTSubtree(root, min, max, maxNodes, largestBST); return largestBST; } </code></pre> <p>I've confused by the following two lines code. According to my common sense, after recursive traversing left tree, the <code>max</code> variable should be updated, why putting <code>int currMin = (leftNodes == 0) ? p-&gt;data : min;</code> right after recursive traversing left tree?<br> The same question for <code>int currMax = (rightNodes == 0) ? p-&gt;data : max;</code></p> <pre><code>... int currMin = (leftNodes == 0) ? p-&gt;data : min; ... int currMax = (rightNodes == 0) ? p-&gt;data : max; </code></pre>
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    1. COThe algoritm you need is very close to alpha-beta searching. (except you need to visit *almost* the whole tree and cannot prune)
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      1. POLargest Subtree Which is a Binary Search Tree (BST)
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