Binary TreesBinary Trees36
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Accounts Merge Using Graphs and DSU

Problem Statement

You're given a list of accounts. Each account is a list where the first element is a user name and the rest are email addresses belonging to that person. Your task is to merge the accounts if any two accounts share at least one common email.

Important: Two accounts with the same name are not necessarily the same person unless they share an email. After merging, return each account with the name followed by the sorted list of unique emails.

Examples

Input Accounts Merged Output Description
[ ["John", "johnsmith@mail.com", "john00@mail.com"], ["John", "johnnybravo@mail.com"], ["John", "johnsmith@mail.com", "john_newyork@mail.com"], ["Mary", "mary@mail.com"] ] [ ["John", "john00@mail.com", "john_newyork@mail.com", "johnsmith@mail.com"], ["John", "johnnybravo@mail.com"], ["Mary", "mary@mail.com"] ] First and third John accounts are merged via common email
[ ["Alex", "a@mail.com"], ["Alex", "b@mail.com"], ["Alex", "a@mail.com", "b@mail.com"] ] [ ["Alex", "a@mail.com", "b@mail.com"] ] All Alex accounts are connected through emails
[] [] No accounts to process
[ ["Bob", "bob@mail.com"] ] [ ["Bob", "bob@mail.com"] ] Single account, no merging needed

Solution

Understanding the Problem

We are given a list of accounts where each account belongs to a person and contains a list of emails. Some people may have multiple accounts, and emails may appear in more than one account. Our goal is to merge all the accounts that belong to the same person, meaning any accounts that share at least one common email should be merged into one.

For example, if "John" has one account with ["john@gmail.com", "john@yahoo.com"] and another with ["john@yahoo.com", "john@outlook.com"], these two should be merged into a single account with all three emails, since "john@yahoo.com" is common to both.

We will solve this using Disjoint Set Union (DSU), which is great for managing groups of connected elements efficiently.

Step-by-Step Solution with Example

Step 1: Visualize the Problem as a Graph

Think of each email as a node in a graph. If two emails are part of the same account, draw an edge between them. This way, all emails that are connected form a cluster that belongs to the same user.

Step 2: Initialize DSU

We create a DSU (also known as Union-Find) structure to manage which emails are connected. Each email will be a node in this structure, and we'll use union and find operations to group them.

Step 3: Build Connections Using Union Operation

Iterate through each account. For every account, pick the first email and union it with all other emails in that account. This connects all emails in that account together.

Step 4: Map Emails to User Names

As we process each email, we also maintain a mapping from email to user name so that we can retrieve the correct name when building the final result.

Step 5: Group Emails by Root

After all unions are done, go through every email and use the find operation to determine its representative (root parent). Group all emails with the same root together. These are emails that belong to the same person.

Step 6: Sort and Format the Result

For each group of emails, sort them alphabetically and prepend the user name (using our earlier mapping). This gives us the merged account in the correct format.

Example:


Input: 
[
  ["John", "john@gmail.com", "john@yahoo.com"],
  ["John", "john@yahoo.com", "john@outlook.com"],
  ["Mary", "mary@gmail.com"]
]

Process:
- Union "john@gmail.com" with "john@yahoo.com"
- Union "john@yahoo.com" with "john@outlook.com"
- Map all emails to "John"
- Map "mary@gmail.com" to "Mary"

Result:
[
  ["John", "john@gmail.com", "john@outlook.com", "john@yahoo.com"],
  ["Mary", "mary@gmail.com"]
]

Edge Cases

  • Multiple accounts with no overlapping emails: Each account will remain separate.
  • One email used by multiple accounts of the same name: All such accounts should be merged using that common email as the connector.
  • Emails that belong to different users but look similar: Be careful; merge only if the actual email strings match exactly.
  • Empty account list: Simply return an empty result.

Finally

This problem is a great example of applying DSU to a real-world scenario involving connected data. By modeling emails as a graph and using DSU to manage the components, we can efficiently merge related accounts. Always remember to handle mapping and sorting properly when preparing the final answer.

Algorithm Steps

  1. Initialize a parent map for DSU: parent[email] = email.
  2. Iterate through each account:
    1. For each email in the account, perform union(email, first_email).
    2. Record email_to_name[email] = account[0].
  3. For each email, find its root parent using find(email) and group emails by root.
  4. For each group, sort the emails and prepend the name.
  5. Return the list of merged accounts.

Code

JavaScript
function accountsMerge(accounts) {
  const parent = {};
  const emailToName = {};

  function find(x) {
    if (parent[x] !== x) {
      parent[x] = find(parent[x]);
    }
    return parent[x];
  }

  function union(x, y) {
    parent[find(x)] = find(y);
  }

  for (const account of accounts) {
    const [name, ...emails] = account;
    for (const email of emails) {
      if (!parent[email]) parent[email] = email;
      emailToName[email] = name;
      union(emails[0], email);
    }
  }

  const unions = {};
  for (const email of Object.keys(parent)) {
    const root = find(email);
    if (!unions[root]) unions[root] = [];
    unions[root].push(email);
  }

  const result = [];
  for (const emails of Object.values(unions)) {
    emails.sort();
    result.push([emailToName[emails[0]], ...emails]);
  }

  return result;
}

console.log(accountsMerge([
  ["John", "johnsmith@mail.com", "john00@mail.com"],
  ["John", "johnnybravo@mail.com"],
  ["John", "johnsmith@mail.com", "john_newyork@mail.com"],
  ["Mary", "mary@mail.com"]
]));

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