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32 lines
2.7 KiB
HTML
Lowest Common Ancestor
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<div class="ques-view"><p>The lowest common ancestor (LCA) of two nodes U and V in a tree is the deepest node that has both U and V as descendants.</p>
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<p>A binary search tree (BST) is recursively defined as a binary tree which has the following properties:</p>
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<ul>
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<li>The left subtree of a node contains only nodes with keys less than the node's key.</li>
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<li>The right subtree of a node contains only nodes with keys greater than or equal to the node's key.</li>
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<li>Both the left and right subtrees must also be binary search trees.</li>
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</ul>
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<p>Given any two nodes in a BST, you are supposed to find their LCA.</p>
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<h3 id="input-specification-">Input Specification:</h3>
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<p>Each input file contains one test case. For each case, the first line gives two positive integers: M (<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo></mrow>\le</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.63597em;"></span><span class="strut bottom" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span></span></span></span> 1,000), the number of pairs of nodes to be tested; and N (<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo></mrow>\le</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.63597em;"></span><span class="strut bottom" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span></span></span></span> 10,000), the number of keys in the BST, respectively. In the second line, N distinct integers are given as the preorder traversal sequence of the BST. Then M lines follow, each contains a pair of integer keys U and V. All the keys are in the range of <strong>int</strong>.</p>
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<h3 id="output-specification-">Output Specification:</h3>
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<p>For each given pair of U and V, print in a line <code>LCA of U and V is A.</code> if the LCA is found and <code>A</code> is the key. But if <code>A</code> is one of U and V, print <code>X is an ancestor of Y.</code> where <code>X</code> is <code>A</code> and <code>Y</code> is the other node. If U or V is not found in the BST, print in a line <code>ERROR: U is not found.</code> or <code>ERROR: V is not found.</code> or <code>ERROR: U and V are not found.</code>.</p>
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<h3 id="sample-input-">Sample Input:</h3>
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<pre><code class="lang-in">6 8
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6 3 1 2 5 4 8 7
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2 5
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8 7
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1 9
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12 -3
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0 8
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99 99
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</code></pre>
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<h3 id="sample-output-">Sample Output:</h3>
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<pre><code class="lang-out">LCA of 2 and 5 is 3.
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8 is an ancestor of 7.
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ERROR: 9 is not found.
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ERROR: 12 and -3 are not found.
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ERROR: 0 is not found.
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ERROR: 99 and 99 are not found.
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</code></pre>
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</div> |