Lintcode 1257. Evaluate Division

Description

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.

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

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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"] ]. 

Solution:

Graph + DFS

Code (Java):

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public class Solution {     /**      * @param equations:      * @param values:      * @param queries:      * @return: return a double type array      */     public double[] calcEquation(List<List<String>> equations, double[] values, List<List<String>> queries) {         // write your code here         double[] ans = new double[queries.size()];                   if (equations == null || equations.size() == 0 || values == null|| values.length == 0) {             return ans;         }                   // build the graph         Map<String, List<Node>> adjList = new HashMap<>();         for (int i = 0; i < equations.size(); i++) {             List<String> equation = equations.get(i);             double value = values[i];             String n1 = equation.get(0);             String n2 = equation.get(1);                           // n1->n2             List<Node> neighbors = adjList.getOrDefault(n1, new ArrayList<>());             neighbors.add(new Node(n2, value));             adjList.put(n1, neighbors);                           // n2->n1             List<Node> neighbors2 = adjList.getOrDefault(n2, new ArrayList<>());             neighbors2.add(new Node(n1, 1.0 / value));             adjList.put(n2, neighbors2);         }                   // dfs to find the answer         for (int i = 0; i < queries.size(); i++) {             List<String> query = queries.get(i);             String n1 = query.get(0);             String n2 = query.get(1);                           if (!adjList.containsKey(n1) || !adjList.containsKey(n2)) {                 ans[i] = -1.0;             } else if (n1.equals(n2)) {                 ans[i] = 1.0;             } else {                 Set<String> visited = new HashSet<>();                 RetVal retval = dfs(n1, n2, adjList, 1.0, visited);                 if (retval.found) {                     ans[i] = retval.val;                 } else {                     ans[i]= -1.0;                 }             }         }                   return ans;     }           private RetVal dfs(String start, String end, Map<String, List<Node>> adjList, double val, Set<String> visited) {         RetVal retval = new RetVal(false, -1.0);         visited.add(start);                   if (start.equals(end)) {             return new RetVal(true, val);         }                   List<Node> neighbors = adjList.get(start);                   for (Node neighbor: neighbors) {             if (visited.contains(neighbor.label)) {                 continue;             }                           retval = dfs(neighbor.label, end, adjList, val * neighbor.val, visited);                           if (retval.found) {                 return retval;             }         }                   visited.remove(start);         return retval;     } }   class Node {     String label;     double val;           public Node (String label, double val) {         this.label = label;         this.val = val;     } }   class RetVal {     boolean found;     double val;           public RetVal (boolean found, double val) {         this.found = found;         this.val = val;     } }