399. Evaluate Division

Equations are given in the format A / B = k, where A and B are variables represented as strings, and k is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return -1.0.

Example:

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 ].

The input is: vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries, where equations.size() == values.size(), and the values are positive. This represents the equations. Return vector<double>.

According to the example above:

equations = [["a", "b"], ["b", "c"]],
values = [2.0, 3.0],
queries = [["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"]].

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

Solution: Graph & DFS

import collections


class Solution(object):
    def calcEquation(self, equations, values, queries):
        """
        :type equations: List[List[str]]
        :type values: List[float]
        :type queries: List[List[str]]
        :rtype: List[float]
        """
        graph = collections.defaultdict(dict)
        for [u, v], val in zip(equations, values):
            graph[u][v] = val
            graph[v][u] = 1.0 / val

        result = []
        for u, v in queries:
            result.append(self.dfs(graph, u, v, set()))
        return result

    def dfs(self, graph, start, end, visited):
        if start not in graph or end not in graph:
            return -1.0
        if start == end:
            return 1.0
        visited.add(start)
        for neighbor in graph[start]:
            if neighbor not in visited:
                val = self.dfs(graph, neighbor, end, visited)
                if val != -1.0:
                    return graph[start][neighbor] * val
        visited.remove(start)
        return -1.0

Lessons:

• Map all the equations into weighted graph.