minimum-height-trees

 

Intuition

The problem requires finding the minimum height trees in a graph. The intuition here is that for a tree to have minimum height, it should be centered around the middle of the graph. Trees with minimum height will have their roots as close to the center as possible.

Approach

Base Case Handling: If there's only one node in the graph, it's already the minimum height tree, so return a list containing that node.

Graph Representation: Create an adjacency list to represent the undirected graph. Also, keep track of the degree of each node, which represents the number of edges connected to it.

Initialization: Populate the adjacency list and degree array based on the edges provided.

Queue Initialization: Initialize a queue to perform a level-order traversal starting from the leaf nodes.

Leaf Node Identification: Identify leaf nodes (nodes with degree 1) and enqueue them.

Breadth-First Search (BFS): Perform a BFS traversal starting from the leaf nodes. At each level, enqueue the neighbors of the current nodes whose degrees become 1 after removing the current node from the graph.

Final Result: The last level of nodes visited in BFS will represent the potential centers of the minimum height trees. Return these nodes as the result.

Complexity

  • Time complexity:
    O(n + m)

  • Space complexity:
    O(n + m)

Code

Comments

Post a Comment

Popular posts from this blog

30. Substring with Concatenation of All Words

Problem Statement You are given a string s and an array of strings words. All the strings of words are of the same length. A concatenated substring in s is a substring that contains all the strings of any permutation of words concatenated. For example, if words = ["ab","cd","ef"], then "abcdef", "abefcd", "cdabef", "cdefab", "efabcd", and "efcdab" are all concatenated strings. "acdbef" is not a concatenated substring because it is not the concatenation of any permutation of words. Return the starting indices of all the concatenated substrings in s. You can return the answer in any order. Example 1: Input: s = "barfoothefoobarman", words = ["foo","bar"] Output: [0,9] Explanation: Since words.length == 2 and words[i].length == 3, the concatenated substring has to be of length 6. The substring starting at 0 is "barfoo". It is the concaten...
Read more

Lowest common ancestor in a binary Tree

Approach Define a recursive function rec that takes three parameters: root (the current node), p (first node to find the lowest common ancestor for), and q (second node to find the lowest common ancestor for). Check if the current node root is null or if it is either p or q . If any of these conditions is true, return the current node root as the lowest common ancestor. Recursively call the rec function for the left subtree of the current node and assign the result to a variable l . Recursively call the rec function for the right subtree of the current node and assign the result to a variable r . Check if both l and r are not null. If so, it means that p and q are found on different subtrees of the current node, and the current node root is their lowest common ancestor. Return the current node root . If l is null, it means that both p and q are on the right subtree (or not present in the tree). Return r . If none of the above conditions are met, it means ...
Read more

New start day 1 : 30/09/2020 (codeforces 71A) Way to long strings

 Question:  source (codeforces: https://codeforces.com/problemset/problem/71/A) Way too long strings   Sometimes some words like " localization " or " internationalization " are so long that writing them many times in one text is quite tiresome. Let's consider a word  too long if its length is  strictly more  than  10  characters. All too long words should be replaced with a special abbreviation. This abbreviation is made like this: we write down the first and the last letter of a word and between them, we write the number of letters between the first and the last letters. That number is in the decimal system and doesn't contain any leading zeroes. Thus, " localization " will be spelled as " l10n ", and " internationalization » will be spelled as " i18n ". You are suggested to automatize the process of changing the words with abbreviations. At that, all too long words should be replaced by the abbreviation and the words th...
Read more