How do you solve Satisfiability of Equality Equations on LeetCode?

Satisfiability of Equality Equations (LeetCode #990) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Union-Find is a powerful tool for managing connected components.

What is the brute force solution for Satisfiability of Equality Equations?

The brute force approach for Satisfiability of Equality Equations is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible assignment of values to the variables to see if all equations can be satisfied. This is straightforward but inefficient, as it can lead to many unnecessary checks. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Satisfiability of Equality Equations?

Satisfiability of Equality Equations uses the following concepts: Array, String, Union-Find, Graph Theory. The recommended patterns to study are: Union-Find, Graph Theory.

What are the interview tips for Satisfiability of Equality Equations?

Explain your thought process clearly while coding. Discuss the trade-offs of different approaches. Practice Union-Find problems to become familiar with the structure.

What are common mistakes when solving Satisfiability of Equality Equations?

Not handling both types of equations correctly. Forgetting to check for contradictions after processing '==' equations.

#990

Satisfiability of Equality Equations

Medium

ArrayStringUnion-FindGraph TheoryUnion-FindGraph Theory

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach uses the Union-Find data structure to group variables that are equal and then checks for contradictions with the '!=' equations. This is efficient and avoids the combinatorial explosion of the brute force method.

⚙️

Algorithm

4 steps

1Step 1: Initialize a Union-Find structure to manage the connected components of equal variables.
2Step 2: Process all '==' equations to union the variables.
3Step 3: For each '!=' equation, check if the two variables are in the same component; if they are, return false.
4Step 4: If no contradictions are found, return true.

solution.py25 lines

1# Full working Python code
2class UnionFind:
3    def __init__(self, size):
4        self.parent = list(range(size))
5
6    def find(self, x):
7        if self.parent[x] != x:
8            self.parent[x] = self.find(self.parent[x])
9        return self.parent[x]
10
11    def union(self, x, y):
12        rootX = self.find(x)
13        rootY = self.find(y)
14        if rootX != rootY:
15            self.parent[rootY] = rootX
16
17def equationsPossible(equations):
18    uf = UnionFind(26)
19    for eq in equations:
20        if eq[1] == '=':
21            uf.union(ord(eq[0]) - ord('a'), ord(eq[3]) - ord('a'))
22    for eq in equations:
23        if eq[1] == '!' and uf.find(ord(eq[0]) - ord('a')) == uf.find(ord(eq[3]) - ord('a')):
24            return False
25    return True

ℹ

Complexity note: The time complexity is O(n) because we make a constant number of operations for each equation, and the Union-Find operations are nearly constant time due to path compression.

1Union-Find is a powerful tool for managing connected components.
2Understanding the difference between equality and inequality is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.