Construct Special Binary Tree from given Inorder traversal

最新推荐文章于 2021-07-06 08:51:48 发布

dongqifan

最新推荐文章于 2021-07-06 08:51:48 发布

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分类专栏：面试算法文章标签：二叉树

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本文介绍了一种根据给定中序遍历构造特殊二叉树的方法。这种二叉树的特点是每个节点的键值大于其左右子节点的键值。通过寻找数组中的最大值作为根节点，并递归地构建左右子树，最终完成整个二叉树的构造。

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package tree;

public class ConstructSpecialBinary {

	/**
	 * Construct Special Binary Tree from given Inorder traversal
Given Inorder Traversal of a Special Binary Tree in which key of every node is greater 
than keys in left and right children, construct the Binary Tree and return root.

Examples:

Input: inorder[] = {5, 10, 40, 30, 28}
Output: root of following tree
         40
       /   \
      10     30
     /         \
    5          28 
The idea used in Construction of Tree from given Inorder and Preorder traversals can be used here. 
Let the given array is {1, 5, 10, 40, 30, 15, 28, 20}. The maximum element in given array must be root. 
The elements on left side of the maximum element are in left subtree and elements on right side are in 
right subtree.

         40
      /       \  
   {1,5,10}   {30,15,28,20}
We recursively follow above step for left and right subtrees, and finally get the following tree.

          40
        /   \
       10     30
      /         \
     5          28
    /          /  \
   1         15    20
	 * @param args
	 */
	public static TreeNode construct(int[] inorder,int left,int right){
		if(left>right) return null;
		if(left==right) return new TreeNode(inorder[left]);
		
			int i = getmax(inorder,left,right);
			TreeNode root = new TreeNode(inorder[i]);
			root.left = construct(inorder, left, i-1);
			root.right = construct(inorder, i+1, right);
			return root;
		
	}
	private static int getmax(int[] inorder, int left, int right) {
		int i=left;
		int k = left;
		int max = inorder[left];
		for(;i<=right;i++){
			if(inorder[i]>max){
				k = i;
				break;
			}
		}
		return k;
	}
	
	public static void printin(TreeNode root){
		if(root==null) return;
		printin(root.left);
		System.out.print(root.value+" ");
		printin(root.right);
	}
	public static void main(String[] args) {
		int[] inorder = {1, 5, 10, 40, 30, 15, 28, 20};
		TreeNode root = construct(inorder, 0, inorder.length-1);
		printin(root);
		

	}

}