README.md

399. Evaluate Division

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.

You are also given some queries, where queries[j] = [Cj, Dj] represents the jth query where you must find the answer for Cj / Dj = ?.

Return the answers to all queries. If a single answer cannot be determined, return -1.0.

Note: The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.

Note: The variables that do not occur in the list of equations are undefined, so the answer cannot be determined for them.

Example 1:

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

Example 2:

Input: equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]
Output: [3.75000,0.40000,5.00000,0.20000]

Example 3:

Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
Output: [0.50000,2.00000,-1.00000,-1.00000]

Constraints:

• 1 <= equations.length <= 20
• equations[i].length == 2
• 1 <= Ai.length, Bi.length <= 5
• values.length == equations.length
• 0.0 < values[i] <= 20.0
• 1 <= queries.length <= 20
• queries[i].length == 2
• 1 <= Cj.length, Dj.length <= 5
• Ai, Bi, Cj, Dj consist of lower case English letters and digits.

Solutions (Python)

1. Solution

class Solution:
    def calcEquation(self, equations: List[List[str]], values: List[float], queries: List[List[str]]) -> List[float]:
        parent = {}
        variablevalue = {}
        ret = []

        for (a, b), v in zip(equations, values):
            if a not in parent:
                variablevalue[a] = 1.
                parent[a] = a
            if b not in parent:
                variablevalue[b] = 1.
                parent[b] = b

            while parent[a] != parent[parent[a]]:
                variablevalue[a] *= variablevalue[parent[a]]
                parent[a] = parent[parent[a]]
            while parent[b] != parent[parent[b]]:
                variablevalue[b] *= variablevalue[parent[b]]
                parent[b] = parent[parent[b]]

            if parent[a] < parent[b]:
                variablevalue[parent[b]] = variablevalue[a] / \
                    variablevalue[b] / v
                parent[parent[b]] = parent[a]
            else:
                variablevalue[parent[a]] = variablevalue[b] / \
                    variablevalue[a] * v
                parent[parent[a]] = parent[b]

        for a in parent:
            while parent[a] != parent[parent[a]]:
                variablevalue[a] *= variablevalue[parent[a]]
                parent[a] = parent[parent[a]]

        for c, d in queries:
            if c in parent and d in parent and parent[c] == parent[d]:
                ret.append(variablevalue[c] / variablevalue[d])
            else:
                ret.append(-1.)

        return ret