Convert Sorted Array to Binary Search Tree

本文介绍了一种使用二分法从有序数组构建平衡二叉搜索树的方法,并提供了详细的C++实现代码。通过递归地选取中间元素作为根节点,确保了树的高度平衡。

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思想:二分法建立平衡二叉树,和用链表建立的思想一样,处理过程大致相同

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode *BalanceBst(vector<int> &num, int beg, int end){
              if(beg > end)
              return NULL;
              int mid = (beg+end)>>1;
              TreeNode *root = new TreeNode(num[mid]);
              root->left = BalanceBst(num, beg, mid-1);
              root->right = BalanceBst(num, mid+1, end);
              return root;
    }
   
    TreeNode *sortedArrayToBST(vector<int> &num) {
         // IMPORTANT: Please reset any member data you declared, as
         // the same Solution instance will be reused for each test case.
              return BalanceBst(num, 0, num.size()-1);
    }
};

To convert the given array to a complete BST, we need to perform the following steps: 1. Sort the array in ascending order 2. Construct a complete binary tree using the sorted array 3. Perform inorder traversal of the binary tree and store the elements in the original array in the same order as the traversal Here's the implementation of the to_bst(lst) function in Python: ```python def to_bst(lst): # Sort the input list lst.sort() # Construct a complete binary tree using the sorted list n = len(lst) if n == 0: return lst root = lst[n // 2] left_subtree = to_bst(lst[:n // 2]) right_subtree = to_bst(lst[n // 2 + 1:]) binary_tree = [root] + left_subtree + right_subtree # Perform inorder traversal of the binary tree and store the elements in the original array inorder_traversal(binary_tree, lst, 0) return lst def inorder_traversal(binary_tree, lst, i): # Perform inorder traversal of the binary tree and store the elements in the original array n = len(binary_tree) if i >= n: return inorder_traversal(binary_tree, lst, 2 * i + 1) lst[i] = binary_tree[i] inorder_traversal(binary_tree, lst, 2 * i + 2) ``` The to_bst(lst) function takes in the input list and returns the same list after converting it to a complete BST. The function first sorts the input list in ascending order. It then constructs a complete binary tree using the sorted list by recursively dividing the list into two halves and setting the middle element as the root of the binary tree. Finally, the function performs an inorder traversal of the binary tree and stores the elements in the original list in the same order as the traversal.
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