国外版

算法题（国外版）/get-maximum-in-generated-array.html

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+<p>You are given an integer <code>n</code>. A <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n + 1</code> is generated in the following way:</p>
+
+<ul>
+	<li><code>nums[0] = 0</code></li>
+	<li><code>nums[1] = 1</code></li>
+	<li><code>nums[2 * i] = nums[i]</code> when <code>2 &lt;= 2 * i &lt;= n</code></li>
+	<li><code>nums[2 * i + 1] = nums[i] + nums[i + 1]</code> when <code>2 &lt;= 2 * i + 1 &lt;= n</code></li>
+</ul>
+
+<p>Return<strong> </strong><em>the <strong>maximum</strong> integer in the array </em><code>nums</code>​​​.</p>
+
+<p>&nbsp;</p>
+<p><strong>Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 7
+<strong>Output:</strong> 3
+<strong>Explanation:</strong> According to the given rules:
+  nums[0] = 0
+  nums[1] = 1
+  nums[(1 * 2) = 2] = nums[1] = 1
+  nums[(1 * 2) + 1 = 3] = nums[1] + nums[2] = 1 + 1 = 2
+  nums[(2 * 2) = 4] = nums[2] = 1
+  nums[(2 * 2) + 1 = 5] = nums[2] + nums[3] = 1 + 2 = 3
+  nums[(3 * 2) = 6] = nums[3] = 2
+  nums[(3 * 2) + 1 = 7] = nums[3] + nums[4] = 2 + 1 = 3
+Hence, nums = [0,1,1,2,1,3,2,3], and the maximum is max(0,1,1,2,1,3,2,3) = 3.
+</pre>
+
+<p><strong>Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 2
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> According to the given rules, nums = [0,1,1]. The maximum is max(0,1,1) = 1.
+</pre>
+
+<p><strong>Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> According to the given rules, nums = [0,1,1,2]. The maximum is max(0,1,1,2) = 2.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>0 &lt;= n &lt;= 100</code></li>
+</ul>