Pseudo-Palindromic Paths in a Binary Tree

Pseudo-Palindromic Paths in a Binary Tree is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Backtracking Patterns pattern, in the Palindrome Partitioning subpattern.

Problem statement

Given a binary tree where node values are digits from 1 to 9. A path in the binary tree is said to be pseudo-palindromic if at least one permutation of the node values in the path is a palindrome.

Return the number of pseudo-palindromic paths going from the root node to leaf nodes.

Example 1: Input: root = [2,3,1,3,1,null,1] Output: 2 Explanation: The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the red path [2,3,3], the green path [2,1,1], and the path [2,3,1]. Among these paths only red path and green path are pseudo-palindromic paths since the red path [2,3,3] can be rearranged in [3,2,3] (palindrome) and the green path [2,1,1] can be rearranged in [1,2,1] (palindrome).

Example 2: Input: root = [2,1,1,1,3,null,null,null,null,null,1] Output: 1 Explanation: The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the green path [2,1,1], the path [2,1,3,1], and the path [2,1]. Among these paths only the green path is pseudo-palindromic since [2,1,1] can be rearranged in [1,2,1] (palindrome).

Example 3: Input: root = [9] Output: 1

Constraints: The number of nodes in the tree is in the range [1, 105].

1 <= Node.val <= 9

Topics and companies

Topics: Bit Manipulation, Tree, Depth-first Search.

Reported in interviews at Amazon.

How to practise Pseudo-Palindromic Paths in a Binary Tree on Thita.ai

Starter code is provided in C, C#, C++, dart, elixir, erlang, Go, Java, JavaScript, Kotlin, PHP, Python, python3, racket, Ruby, Rust, Scala, Swift and TypeScript. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n) time and O(h) space.

Open Pseudo-Palindromic Paths in a Binary Tree in the code editor, or read the Pseudo-Palindromic Paths in a Binary Tree editorial for a worked solution with its approach and complexity analysis.

Where Pseudo-Palindromic Paths in a Binary Tree sits in the DSA pattern sheet

Problems related to Pseudo-Palindromic Paths in a Binary Tree

Other problems that use the same Palindrome Partitioning and Backtracking Patterns techniques:

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