LintCode 1106: Maximum Binary Tree

原创已于 2023-09-26 00:14:27 修改 · 237 阅读

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于 2018-11-24 09:08:15 首次发布

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本文详细介绍了如何使用分治法和遍历法构建最大二叉树的两种算法实现。通过实例输入输出展示了构建过程，并提供了完整的C++代码实现。

题目为：
1106. Maximum Binary Tree
Given an integer array with no duplicates. A maximum tree building on this array is defined as follow:

The root is the maximum number in the array.
The left subtree is the maximum tree constructed from left part subarray divided by the maximum number.
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
Input: [3,2,1,6,0,5]
Output: return the tree root node representing the following tree:

  6
/   \

3 5
\ /
2 0

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

Solution:
用分治法，每次找到最大值，然后分两半，递归。

/**
 * Definition of TreeNode:
 * class TreeNode {
 * public:
 *     int val;
 *     TreeNode *left, *right;
 *     TreeNode(int val) {
 *         this->val = val;
 *         this->left = this->right = NULL;
 *     }
 * }
 */

class Solution {
public:
    /**
     * @param nums: an array
     * @return: the maximum tree
     */
    TreeNode * constructMaximumBinaryTree(vector<int> &nums) {
        return helper(nums, 0, nums.size() - 1); 
    }
    
private:
    TreeNode * helper(vector<int> &nums, int start, int end) {
        if (start > end) return NULL;
        
        int max = nums[start];
        int max_index = start;
        
        for (int i = start; i <= end; ++i) {

            if (nums[i] > max) {
                max = nums[i];
                max_index = i;
            }
        }
        
        TreeNode *node = new TreeNode(nums[max_index]);
        node->left = helper(nums, start, max_index - 1);
        node->right = helper(nums, max_index + 1, end);
        return node;
    }
};

解法2：用遍历。注意max_element()和distance()的用法。

class Solution {
public:
    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {
        auto maxIter = max_element(nums.begin(), nums.end());
        int maxId = distance(nums.begin(), maxIter);
        TreeNode *root = new TreeNode(*maxIter);
        if (maxId > 0) {
            vector<int> nums_left(nums.begin(), nums.begin() + maxId); 
            root->left = constructMaximumBinaryTree(nums_left);
        }
        if (maxId < nums.size() - 1) {
            vector<int> nums_right(nums.begin() + maxId + 1, nums.end());
            root->right = constructMaximumBinaryTree(nums_right);
        }
        return root;
    } 
};