Find the lexicographically smallest palindrome path in a binary tree

Binary trees are a basic data structure in computer science and provide an efficient way to organize data hierarchically. When traversing these trees, we often find interesting computational problems. Among them, determining the lexicographically smallest palindromic path is a fascinating challenge. This article illustrates an efficient C algorithm for solving this problem and provides detailed examples for better understanding.

Problem Statement

In a binary tree in which each node represents a lowercase English letter, our goal is to find the palindrome path with the smallest lexicographic order. If multiple paths match the criteria, we can return any of them. If no palindrome path exists, we should return an empty string.

method

Our solution to this problem involves traversing a binary tree using a depth-first search (DFS) technique. The DFS method allows us to explore every path from the root node to the leaf nodes.

C Solution

This is the C code that implements the above method -

Example

#include<bits/stdc++.h>
using namespace std;

struct Node {
   char data;
   Node *left, *right;
   Node(char c) : data(c), left(NULL), right(NULL) {}
};

string smallestPalindrome(Node* node, string s) {
   if(node == NULL)
      return "";
   
   s += node->data;
   
   if(node->left == NULL && node->right == NULL)
      return string(s.rbegin(), s.rend()) == s ? s : "";
   
   string left = smallestPalindrome(node->left, s);
   string right = smallestPalindrome(node->right, s);
   
   if(left == "")
      return right;
   if(right == "")
      return left;
   
   return min(left, right);
}

string smallestPalindromicPath(Node* root) {
   return smallestPalindrome(root, "");
}

int main() {
   Node* root = new Node('a');
   root->left = new Node('b');
   root->right = new Node('a');
   root->left->left = new Node('a');
   root->left->right = new Node('a');
   root->right->left = new Node('b');
   root->right->right = new Node('a');
   
   cout << smallestPalindromicPath(root) << endl;
   
   return 0;
}

Output

aaa

Test cases and instructions

Let us check a binary tree with the following structure -

     a
   /   \
  b     a
 / \   / \
a   a b   a

In this binary tree, there are multiple paths from the root node to the leaf nodes. Among all these paths, the function returns the lexicographically smallest palindrome path. In this case, the possible palindrome paths are "aaa" and "aba". Therefore, the output will be "aaa", which is the lexicographically smallest palindrome path.

in conclusion

Determining the lexicographically minimal palindrome path in a binary tree is an interesting problem that combines tree traversal and string manipulation concepts. The C solution provided above uses a depth-first search approach to solve this problem efficiently. Understanding these problems can enhance your understanding of binary trees and enhance your ability to solve computer science problems.

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