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38 lines
1.6 KiB
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38 lines
1.6 KiB
HTML
<p>Given an array <code>arr</code> of positive integers, consider all binary trees such that:</p>
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<ul>
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<li>Each node has either <code>0</code> or <code>2</code> children;</li>
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<li>The values of <code>arr</code> correspond to the values of each <strong>leaf</strong> in an in-order traversal of the tree.</li>
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<li>The value of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree, respectively.</li>
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</ul>
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<p>Among all possible binary trees considered, return <em>the smallest possible sum of the values of each non-leaf node</em>. It is guaranteed this sum fits into a <strong>32-bit</strong> integer.</p>
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<p>A node is a <strong>leaf</strong> if and only if it has zero children.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree1.jpg" style="width: 500px; height: 169px;" />
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<pre>
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<strong>Input:</strong> arr = [6,2,4]
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<strong>Output:</strong> 32
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<strong>Explanation:</strong> There are two possible trees shown.
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The first has a non-leaf node sum 36, and the second has non-leaf node sum 32.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree2.jpg" style="width: 224px; height: 145px;" />
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<pre>
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<strong>Input:</strong> arr = [4,11]
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<strong>Output:</strong> 44
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>2 <= arr.length <= 40</code></li>
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<li><code>1 <= arr[i] <= 15</code></li>
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<li>It is guaranteed that the answer fits into a <strong>32-bit</strong> signed integer (i.e., it is less than 2<sup>31</sup>).</li>
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</ul>
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