Evaluate Division

这周是做Graph相关的问题

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"] ]. 

这个题的主要思想是将每个分数当做图中的一个节点，边权为乘数的权值。 基础节点共有2n个，分别是他本身和其倒数。 
可以通过基础节点*基础分数或者新增节点*基础分数得到一个新增节点。

代码如下

public:      vector<double> calcEquation(vector<pair<string, string>> equations, vector<double>& values, 

                                 vector<pair<string, string>> queries) {           unordered_map<string, Node*> map;          vector<double> res;          for (int i = 0; i < equations.size(); i++) {              string s1 = equations[i].first, s2 = equations[i].second;              if (map.count(s1) == 0 && map.count(s2) == 0) {                  map[s1] = new Node();                  map[s2] = new Node();                  map[s1] -> value = values[i];                  map[s2] -> value = 1;                  map[s1] -> parent = map[s2];              } else if (map.count(s1) == 0) {                  map[s1] = new Node();                  map[s1] -> value = map[s2] -> value * values[i];                  map[s1] -> parent = map[s2];              } else if (map.count(s2) == 0) {                  map[s2] = new Node();                  map[s2] -> value = map[s1] -> value / values[i];                  map[s2] -> parent = map[s1];              } else {                  unionNodes(map[s1], map[s2], values[i], map);              }          }            for (auto query : queries) {              if (map.count(query.first) == 0 || map.count(query.second) == 0 || findParent(map[query.first]) !=                  findParent(map[query.second]))                  res.push_back(-1);              else                  res.push_back(map[query.first] -> value / map[query.second] -> value);          }          return res;      }        private:      struct Node {          Node* parent;          double value = 0.0;          Node()  {parent = this;}      };  //用来遍历的节点          void unionNodes(Node* node1, Node* node2, double num, unordered_map<string, Node*>& map) {          Node* parent1 = findParent(node1), *parent2 = findParent(node2);          double ratio = node2 -> value * num / node1 -> value;          for (auto it = map.begin(); it != map.end(); it++) {             if (findParent(it -> second) == parent1) {                  it -> second -> value *= ratio;              }          }          parent1 -> parent = parent2;      }            Node* findParent(Node* node) {          if (node -> parent == node)              return node;          node -> parent = findParent(node -> parent);          return node -> parent;      }  };