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# 399.Evaluate-Division

## 题目描述

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.

## 代码

### Approach #1 DFS

Binary relationship is represented as a graph usually. Does the direction of an edge matters? -- Yes. Take a / b = 2 for example, it indicates `a --2--> b` as well as `b --1/2--> a`. Thus, it is a directed weighted graph.
class Solution {
public double[] calcEquation(List<List<String>> equations, double[] values, List<List<String>> queries) {
Map<String, Map<String, Double>> graph = buildGraph(equations, values);
double[] result = new double[queries.length];
for (int i = 0; i < queries.length; i++) {
result[i] = getPathWeight(queries[i], queries[i], new HashSet<>(), graph);
}
return result;
}
private double getPathWeight(String start, String end, Set<String> visited, Map<String, Map<String, Double>> graph) {
if (!graph.containsKey(start)) return -1.0;
if (graph.get(start).containsKey(end))
return graph.get(start).get(end);
for (Map.Entry<String, Double> neighbor: graph.get(start).entrySet()) {
if (!visited.contains(neighbour.getKey())) {
double productWeight = getPathWeight(neighbour.getKey(), end, visited, graph);
if (productWeight != -1.0) {
return neighbour.getValue() * productWeight;
}
}
}
return -1.0;
}
private Map<String, Map<String, Double>> buildGraph(String[][] equations, double[] values) {
Map<String, Map<String, Double>> graph = new HashMap<>();
String u, v;
for (int i = 0; i < equations.length; i++) {
u = equations[i];
v = equations[i];
graph.putIfAbsent(u, new HashMap<>());
graph.get(u).put(v, values[i]);
graph.putIfAbsent(v, new HashMap<>());
graph.get(v).put(u, 1 / values[i]);
}
return graph;
}
}