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Union-find

Union-find merges disjoint sets.

Union-find

Union-find tracks a graph's nodes in sets. find(x) locates x's root; union(x, y) merges two sets.

This structure is used in Kruskal's cycle check. Each node points to a parent; the root points to itself.

Parent array

Each node has a parent. Initially each node is its own parent: parent[i] = i. When merged, the parent is updated.

Finding the root follows the parent chain: while parent[x] != x: x = parent[x]. This loop continues until the root is found.

Practice init_parent function

Write init_parent(n). Return a parent array where each node is its own parent. Print it with print(init_parent(4)).

Starter code

solution.py
def init_parent(n):
    # Return parent array

Sample solution

solution.py
def init_parent(n):
    # Return parent array
    return list(range(n))
print(init_parent(4))

Expected output

[0, 1, 2, 3]

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 What does find(x) return?

  • x's root Correct answer
  • Its own root
  • Its neighbors
  • Its weight

Explanation: find(x) returns x's root.

2 Initial parent

Question 
parent[i] = ____
Answer 
parent[i] = i

Explanation: i is right.

3 Union-find: match the terms

Term Meaning
find Find root
union Merge sets
parent Parent array
root Self

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4