Leetcode #399: Evaluate Division
In this guide, we solve Leetcode #399 Evaluate Division in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [Ai, Bi] and values[i] represent the equation Ai / Bi = values[i]. Each Ai or Bi is a string that represents a single variable.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Depth-First Search, Breadth-First Search, Union Find, Graph, Array, String, Shortest Path
Intuition
The data forms a graph, so we should explore nodes and edges systematically.
A traversal ensures we visit each node once while maintaining the needed state.
Approach
Build an adjacency list and traverse with BFS or DFS.
Aggregate results as you visit nodes.
Steps:
- Build the graph.
- Traverse with BFS/DFS.
- Accumulate the required output.
Example
Input: equations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
Output: [6.00000,0.50000,-1.00000,1.00000,-1.00000]
Explanation:
Given: a / b = 2.0, b / c = 3.0
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ?
return: [6.0, 0.5, -1.0, 1.0, -1.0 ]
note: x is undefined => -1.0
Python Solution
class Solution:
def calcEquation(
self, equations: List[List[str]], values: List[float], queries: List[List[str]]
) -> List[float]:
def find(x):
if p[x] != x:
origin = p[x]
p[x] = find(p[x])
w[x] *= w[origin]
return p[x]
w = defaultdict(lambda: 1)
p = defaultdict()
for a, b in equations:
p[a], p[b] = a, b
for i, v in enumerate(values):
a, b = equations[i]
pa, pb = find(a), find(b)
if pa == pb:
continue
p[pa] = pb
w[pa] = w[b] * v / w[a]
return [
-1 if c not in p or d not in p or find(c) != find(d) else w[c] / w[d]
for c, d in queries
]
Complexity
The time complexity is O(V+E). The space complexity is O(V).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.