*Convert Sorted Array to Binary Search Tree
2015-09-01 07:09
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Given an array where elements are sorted in ascending order, convert it to a height balanced BST.
Solution:
If you would have to choose an array element to be the root of a balanced BST, which element would you pick? The root of a balanced BST should be the middle element from the sorted array.
You would pick the middle element from the sorted array in each iteration. You then create a node in the tree initialized with this element. After the element is chosen, what is left? Could you identify the sub-problems within the problem?
There are two arrays left — The one on its left and the one on its right. These two arrays are the sub-problems of the original problem, since both of them are sorted. Furthermore, they are subtrees of the current node’s left and right child.
The code below creates a balanced BST from the sorted array in O(N) time (N is the number of elements in the array). Compare how similar the code is to a binary search algorithm. Both are using the divide and conquer methodology
reference: http://www.programcreek.com/2013/01/leetcode-convert-sorted-array-to-binary-search-tree-java/ http://articles.leetcode.com/2010/11/convert-sorted-array-into-balanced.html
Solution:
If you would have to choose an array element to be the root of a balanced BST, which element would you pick? The root of a balanced BST should be the middle element from the sorted array.
You would pick the middle element from the sorted array in each iteration. You then create a node in the tree initialized with this element. After the element is chosen, what is left? Could you identify the sub-problems within the problem?
There are two arrays left — The one on its left and the one on its right. These two arrays are the sub-problems of the original problem, since both of them are sorted. Furthermore, they are subtrees of the current node’s left and right child.
The code below creates a balanced BST from the sorted array in O(N) time (N is the number of elements in the array). Compare how similar the code is to a binary search algorithm. Both are using the divide and conquer methodology
public TreeNode sortedArrayToBST(int[] num) { if (num.length == 0) return null; return sortedArrayToBST(num, 0, num.length - 1); } public TreeNode sortedArrayToBST(int[] num, int start, int end) { if (start > end) return null; int mid = (start + end) / 2; TreeNode root = new TreeNode(num[mid]); root.left = sortedArrayToBST(num, start, mid - 1); root.right = sortedArrayToBST(num, mid + 1, end); return root; }
reference: http://www.programcreek.com/2013/01/leetcode-convert-sorted-array-to-binary-search-tree-java/ http://articles.leetcode.com/2010/11/convert-sorted-array-into-balanced.html
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