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package leetcode;

import java.util.ArrayList;

import java.util.HashMap;

import java.util.HashSet;

import java.util.List;

/**

* Project Name : Leetcode

* Package Name : leetcode

* File Name : EvaluateDivision

* Creator : Edward

* Date : Dec, 2017

* Description : 399. Evaluate Division

*/

public class EvaluateDivision {

/**

* 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.

a / b * b / c = a / c

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"] ].

equation : "b", "c"

map : "a" 'b', 2.0

"b" 'a', 1/2.0

'c', 3.0

"c" 'b', 1/3.0

time : O(V+E)

space : O(n)

*/

HashMap<String, List<GraphNode>> map;

public double[] calcEquation(String[][] equations, double[] values, String[][] queries) {

map = new HashMap<>();

for (int i = 0; i < equations.length; i++) {

String[] equation = equations[i];

if (!map.containsKey(equation[0])) {

map.put(equation[0], new ArrayList<>());

}

map.get(equation[0]).add(new GraphNode(equation[1], values[i]));

if (!map.containsKey(equation[1])) {

map.put(equation[1], new ArrayList<>());

}

map.get(equation[1]).add(new GraphNode(equation[0], 1 / values[i]));

}

double[] res = new double[queries.length];

for (int i = 0; i < res.length; i++) {

res[i] = find(queries[i][0], queries[i][1], 1, new HashSet<>());

}

return res;

}

private double find(String start, String end, double value, HashSet<String> visited) {

if (visited.contains(start)) return -1;

if (!map.containsKey(start)) return -1;

if (start.equals(end)) return value;

visited.add(start);

for (GraphNode next : map.get(start)) {

double sub = find(next.den, end, value * next.val, visited);

if (sub != -1.0) return sub;

}

visited.remove(start);

return -1;

}

class GraphNode {

String den;

double val;

GraphNode(String den, double val) {

this.den = den;

this.val = val;

}

}

}