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.

解法：

这个题a/b, b/c, so we know a/c 因此是一个graph问题

edge case：

a/b thus we also know b/a 因此是一个undirected graph

a/b, a/c 所以图结构为：

Map<String,Map<String,Double>>

<a,<b,v1>,<c,v2>>, <b,<a, v1>>,<c,<a, v2>>

  Map<String,Map<String,Double>> dividendToDivisor = new HashMap<>();  
   public boolean notFound = true;  
   public double[] calcEquation(String[][] equations, double[] values, String[][] queries) {  
     for(int i = 0; i < equations.length; i++){  
       String[] eq = equations[i];  
       dividendToDivisor.putIfAbsent(eq[0],new HashMap<>());  
       dividendToDivisor.get(eq[0]).put(eq[1],values[i]);  
       dividendToDivisor.putIfAbsent(eq[1],new HashMap<>());  
       dividendToDivisor.get(eq[1]).put(eq[0],1/values[i]);  
     }  
     double[] ans = new double[queries.length];  
     for(int i = 0; i < queries.length; i++){  
       String[] q = queries[i];  
       notFound = true;  
       ans[i] = find(q[0],q[1],new HashSet<>());  
     }  
     return ans;    
   }  
   public double find(String x, String y,Set<String> visited){  
     // System.out.println(x+" "+y+(visited.contains(x)||!dividendToDivisor.containsKey(x)));  
     if(visited.contains(x) || !dividendToDivisor.containsKey(x)) return -1;  
     if(x.equals(y)) {notFound = false; return 1.0;}  
     visited.add(x);  
     for(Map.Entry<String, Double> entry: dividendToDivisor.get(x).entrySet()) {  
       String next = entry.getKey();  
       double ans = find(next,y,visited);  
       if(!notFound)   
         return dividendToDivisor.get(x).get(next)*ans;  
     }  
     visited.remove(x);  
     return -1;  
   }