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Java-based LeetCode algorithm problem solutions, regularly updated
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package g0601_0700.s0654_maximum_binary_tree;

// #Medium #Array #Tree #Binary_Tree #Stack #Monotonic_Stack #Divide_and_Conquer
// #2022_03_21_Time_3_ms_(84.36%)_Space_54.4_MB_(17.04%)

import com_github_leetcode.TreeNode;

/*
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
/**
 * 654 - Maximum Binary Tree\.
 *
 * Medium
 *
 * You are given an integer array `nums` with no duplicates. A **maximum binary tree** can be built recursively from `nums` using the following algorithm:
 *
 * 1.  Create a root node whose value is the maximum value in `nums`.
 * 2.  Recursively build the left subtree on the **subarray prefix** to the **left** of the maximum value.
 * 3.  Recursively build the right subtree on the **subarray suffix** to the **right** of the maximum value.
 *
 * Return _the **maximum binary tree** built from_ `nums`.
 *
 * **Example 1:**
 *
 * ![](https://assets.leetcode.com/uploads/2020/12/24/tree1.jpg)
 *
 * **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.
 *
 * **Example 2:**
 *
 * ![](https://assets.leetcode.com/uploads/2020/12/24/tree2.jpg)
 *
 * **Input:** nums = [3,2,1]
 *
 * **Output:** [3,null,2,null,1]
 *
 * **Constraints:**
 *
 * *   `1 <= nums.length <= 1000`
 * *   `0 <= nums[i] <= 1000`
 * *   All integers in `nums` are **unique**.
**/
public class Solution {
    public TreeNode constructMaximumBinaryTree(int[] nums) {
        return mbt(nums, 0, nums.length - 1);
    }

    private TreeNode mbt(int[] nums, int l, int r) {
        if (l > r || l >= nums.length || r < 0) {
            return null;
        }
        if (l == r) {
            return new TreeNode(nums[r]);
        }
        int max = Integer.MIN_VALUE;
        int maxidx = 0;
        for (int i = l; i <= r; i++) {
            if (nums[i] > max) {
                max = nums[i];
                maxidx = i;
            }
        }
        TreeNode root = new TreeNode(max);
        root.left = (mbt(nums, l, maxidx - 1));
        root.right = (mbt(nums, maxidx + 1, r));
        return root;
    }
}