maximum-binary-tree

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Algorithms

You are given an integer array <code>nums</code> with no duplicates. A maximum binary tree can be built recursively from <code>nums</code> using the following algorithm:

<ol>
	<li>Create a root node whose value is the maximum value in <code>nums</code>.</li>
	<li>Recursively build the left subtree on the subarray prefix to the left of the maximum value.</li>
	<li>Recursively build the right subtree on the subarray suffix to the right of the maximum value.</li>
</ol>

Return the maximum binary tree built from <code>nums</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/tree1.jpg" style="width: 302px; height: 421px;" />
<pre>
Input: nums = [3,2,1,6,0,5]
Output: [6,3,5,null,2,0,null,null,1]
Explanation: The recursive calls are as follow:
- The largest value in [3,2,1,6,0,5] is 6. Left prefix is [3,2,1] and right suffix is [0,5].
 - The largest value in [3,2,1] is 3. Left prefix is [] and right suffix is [2,1].
 - Empty array, so no child.
 - The largest value in [2,1] is 2. Left prefix is [] and right suffix is [1].
 - Empty array, so no child.
 - Only one element, so child is a node with value 1.
 - The largest value in [0,5] is 5. Left prefix is [0] and right suffix is [].
 - Only one element, so child is a node with value 0.
 - Empty array, so no child.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/tree2.jpg" style="width: 182px; height: 301px;" />
<pre>
Input: nums = [3,2,1]
Output: [3,null,2,null,1]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li>All integers in <code>nums</code> are unique.</li>
</ul>

constructMaximumBinaryTree

Maximum Binary Tree

Maximum Binary Tree II

maximum-binary-tree-ii

最大二叉树 II

Stack

Tree

Array

Divide and Conquer

Binary Tree

Monotonic Stack

&#32473;&#23450;&#19968;&#20010;&#19981;&#37325;&#22797;&#30340;&#25972;&#25968;&#25968;&#32452;&nbsp;<code>nums</code> &#12290;&nbsp;&#26368;&#22823;&#20108;&#21449;&#26641;&nbsp;&#21487;&#20197;&#29992;&#19979;&#38754;&#30340;&#31639;&#27861;&#20174;&nbsp;<code>nums</code> &#36882;&#24402;&#22320;&#26500;&#24314;:

<ol>
	<li>&#21019;&#24314;&#19968;&#20010;&#26681;&#33410;&#28857;&#65292;&#20854;&#20540;&#20026;&nbsp;<code>nums</code> &#20013;&#30340;&#26368;&#22823;&#20540;&#12290;</li>
	<li>&#36882;&#24402;&#22320;&#22312;&#26368;&#22823;&#20540;&nbsp;&#24038;&#36793;&nbsp;&#30340;&nbsp;&#23376;&#25968;&#32452;&#21069;&#32512;&#19978;&nbsp;&#26500;&#24314;&#24038;&#23376;&#26641;&#12290;</li>
	<li>&#36882;&#24402;&#22320;&#22312;&#26368;&#22823;&#20540; &#21491;&#36793; &#30340;&nbsp;&#23376;&#25968;&#32452;&#21518;&#32512;&#19978;&nbsp;&#26500;&#24314;&#21491;&#23376;&#26641;&#12290;</li>
</ol>

&#36820;&#22238;&nbsp;<code>nums</code> &#26500;&#24314;&#30340; &#26368;&#22823;&#20108;&#21449;&#26641; &#12290;

&nbsp;

&#31034;&#20363; 1&#65306;
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/tree1.jpg" />
<pre>
&#36755;&#20837;&#65306;nums = [3,2,1,6,0,5]
&#36755;&#20986;&#65306;[6,3,5,null,2,0,null,null,1]
&#35299;&#37322;&#65306;&#36882;&#24402;&#35843;&#29992;&#22914;&#19979;&#25152;&#31034;&#65306;
- [3,2,1,6,0,5] &#20013;&#30340;&#26368;&#22823;&#20540;&#26159; 6 &#65292;&#24038;&#36793;&#37096;&#20998;&#26159; [3,2,1] &#65292;&#21491;&#36793;&#37096;&#20998;&#26159; [0,5] &#12290;
 - [3,2,1] &#20013;&#30340;&#26368;&#22823;&#20540;&#26159; 3 &#65292;&#24038;&#36793;&#37096;&#20998;&#26159; [] &#65292;&#21491;&#36793;&#37096;&#20998;&#26159; [2,1] &#12290;
 - &#31354;&#25968;&#32452;&#65292;&#26080;&#23376;&#33410;&#28857;&#12290;
 - [2,1] &#20013;&#30340;&#26368;&#22823;&#20540;&#26159; 2 &#65292;&#24038;&#36793;&#37096;&#20998;&#26159; [] &#65292;&#21491;&#36793;&#37096;&#20998;&#26159; [1] &#12290;
 - &#31354;&#25968;&#32452;&#65292;&#26080;&#23376;&#33410;&#28857;&#12290;
 - &#21482;&#26377;&#19968;&#20010;&#20803;&#32032;&#65292;&#25152;&#20197;&#23376;&#33410;&#28857;&#26159;&#19968;&#20010;&#20540;&#20026; 1 &#30340;&#33410;&#28857;&#12290;
 - [0,5] &#20013;&#30340;&#26368;&#22823;&#20540;&#26159; 5 &#65292;&#24038;&#36793;&#37096;&#20998;&#26159; [0] &#65292;&#21491;&#36793;&#37096;&#20998;&#26159; [] &#12290;
 - &#21482;&#26377;&#19968;&#20010;&#20803;&#32032;&#65292;&#25152;&#20197;&#23376;&#33410;&#28857;&#26159;&#19968;&#20010;&#20540;&#20026; 0 &#30340;&#33410;&#28857;&#12290;
 - &#31354;&#25968;&#32452;&#65292;&#26080;&#23376;&#33410;&#28857;&#12290;
</pre>

&#31034;&#20363; 2&#65306;
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/24/tree2.jpg" />
<pre>
&#36755;&#20837;&#65306;nums = [3,2,1]
&#36755;&#20986;&#65306;[3,null,2,null,1]
</pre>

&nbsp;

&#25552;&#31034;&#65306;

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>nums</code> &#20013;&#30340;&#25152;&#26377;&#25972;&#25968; &#20114;&#19981;&#30456;&#21516;</li>
</ul>

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PL/B Language Development and Support