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

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.

思路：

无向图里找路径的问题，用邻接链或者邻接矩阵来建图，用邻接链的话注意两个方向，a/b的时候，既要把b加到a的邻接list里，也要把a加到b的邻接list里面。建好图之后就是查找了，图里面查找用bfs或者dfs都可以，dfs写起来简单点。复杂度没什么差别都是O(V+E)，这道题里面E = equations.length, V最多是2E，所以每次查找的复杂度是O(equations.length)，有queries.length次查找。注意防止重复路径，要用visited。

class Solution {
public double[] calcEquation(String[][] equations, double[] values, String[][] queries) {
// build graph, use adjacent list
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 Info(equation[1], values[i]));

if(!map.containsKey(equation[1])) map.put(equation[1], new ArrayList());
map.get(equation[1]).add(new Info(equation[0], 1 / values[i]));
}

double[] result = new double[queries.length];
for(int i = 0; i < result.length; i++) {
result[i] = find(queries[i][0], queries[i][1], 1, new HashSet());
}
return result;
}

HashMap<String, List<Info>> map;

private double find(String start, String end, double value, Set<String> visited) {
if(visited.contains(start)) return -1;
if(!map.containsKey(start)) return -1;

if(start.equals(end)) return value;
visited.add(start);
for(Info 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 Info {
String den;
double val;
Info(String den, double val) {
this.den = den;
this.val = val;
}
}
}