Construct Binary Tree from Inorder and Postorder Traversal

Category: Algorithms January 17, 2013

Given inorder and postorder traversal of a tree, construct the binary tree.

Analysis

This problem can be illustrated by using a simple example.

in-order:   4 2 5  (1)  6 7 3 8
post-order: 4 5 2  6 7 8 3  (1)

From the post-order array, we know that last element is the root. We can find the root in in-order array. Then we can identify the left and right sub-trees of the root from in-order array.

Using the length of left sub-tree, we can identify left and right sub-trees in post-order array. Recursively, we can build up the tree.

For this example, the constructed tree is:

Java Solution

public TreeNode buildTree(int[] inorder, int[] postorder) {
	int inStart = 0;
	int inEnd = inorder.length - 1;
	int postStart = 0;
	int postEnd = postorder.length - 1;
 
	return buildTree(inorder, inStart, inEnd, postorder, postStart, postEnd);
}
 
public TreeNode buildTree(int[] inorder, int inStart, int inEnd,
		int[] postorder, int postStart, int postEnd) {
	if (inStart > inEnd || postStart > postEnd)
		return null;
 
	int rootValue = postorder[postEnd];
	TreeNode root = new TreeNode(rootValue);
 
	int k = 0;
	for (int i = 0; i < inorder.length; i++) {
		if (inorder[i] == rootValue) {
			k = i;
			break;
		}
	}
 
	root.left = buildTree(inorder, inStart, k - 1, postorder, postStart,
			postStart + k - (inStart + 1));
	// Becuase k is not the length, it it need to -(inStart+1) to get the length
	root.right = buildTree(inorder, k + 1, inEnd, postorder, postStart + k- inStart, postEnd - 1);
	// postStart+k-inStart = postStart+k-(inStart+1) +1
 
	return root;
}

Category >> Algorithms

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raviteja varma

why are we using two functions with varying parameters,what would be the output if only first function is used.
Darewreck

int k = 0;
for (int i = 0; i < inorder.length; i++) {
if (inorder[i] == rootValue) {
k = i;
break;
}
}

i should be = to instart and not 0.
Matias SM

A solution for the case where duplicated values are admitted.
Note: I used sub list for clarity may/should be changed to indexed “sublists” for efficiency.

TreeNode reconstruct(List inOrder, List postOrder) { int rootValue = postOrder.get(postOrder.size() - 1); TreeNode root = new TreeNode(rootValue); for (int i = 0; i 0) { TreeNode left = reconstruct(inOrder.subList(0, i), postOrder.subList(0, postOrder.size() - rightSize - 1)); if (left == null) continue; //wasn't the root what we found root.left = left; } if (rightSize > 0) { TreeNode right = reconstruct( inOrder.subList(i + 1, inOrder.size()), postOrder.subList(postOrder.size() - rightSize - 1, postOrder.size() - 1)); if (right == null) continue; //wasn't the root what we found root.right = right; } return root; //both subtrees succeeded } } return null; }
Mohamed Yakout

This code is working only if all elements are unique, But I tried this method on the following:

int[] inorder = {4,1,5,1,6,7,3,8};
int[] postorder = {4,5,1,6,7,8,3,1};

I got this error Exception in thread “main” java.lang.ArrayIndexOutOfBoundsException: -1
DivyaJyoti Rajdev

Arrays.asList does not work as expected for primitives, only Objects. that change would give you the wrong answer
Zheyu Jin

Nice.
Just some suggestions for more readable code:

1. use inclusive start index and exclusive end index. [start, end) so that you don’t need hairy +1 and -1.
2.give these expressions a name: postStart+k-(inStart+1); postStart+k-inStart.
Burhan COKCA

int k=0;

for(int i=0; i< inorder.length; i++){
if(inorder[i]==rootValue){
k = i;
break;
}

}

can be simplified as

int k = java.util.Arrays.asList(inorder).indexOf(rootValue)
blah

what if the binary tree has duplicates?
F

Isnt
postStart+k-(inStart+1) will always be k-1?
Taras

this is BT, but not necessarily BST
Amritesh

in-order: 4 2 5 (1) 6 7 3 8

is this correct inorder as left subtree element of 1 are greater than 1. Left Subtree should be lesser
Guest

The for loop “for(int i=0; i< inorder.length; i++){" can be simplified to "for(int i = inStart; i <= inEnd; ++i){" in case duplicated

Construct Binary Tree from Inorder and Postorder Traversal

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