[LeetCode] 654. Maximum Binary Tree

Problem:

Given an integer array with no duplicates. A maximum tree building on this array is defined as follow:

1. The root is the maximum number in the array.
2. The left subtree is the maximum tree constructed from left part subarray divided by the maximum number.
3. The right subtree is the maximum tree constructed from right part subarray divided by the maximum number.

Construct the maximum tree by the given array and output the root node of this tree.

Example 1:

Input: [3,2,1,6,0,5]Output: return the tree root node representing the following tree:      6    /   \   3     5    \    /      2  0          \        1

Note:

1. The size of the given array will be in the range [1,1000].

解题思路：典型的分治问题，每个子问题先找出最大的元素构造root，再以该数组元素为分界构造左节点，

最后是右节点，可以通过递归简单求得解。

Solution:

/** * Definition for a binary tree node. * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */class Solution {public:    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {        return constructTreeNode(nums, 0, nums.size()-1);    }        TreeNode* constructTreeNode(vector<int>& nums, int left, int right) {        if (left > right) return NULL;        int maxIndex = left;        for (int i = left; i <= right; i++) {            if (nums[i] > nums[maxIndex]) maxIndex = i;        }        TreeNode* root = new TreeNode(nums[maxIndex]);        root->left = constructTreeNode(nums, left, maxIndex-1);        root->right = constructTreeNode(nums, maxIndex+1, right);        return root;    }};