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
queries are:
return
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.
Build a map from all the equations. The variables are indices and equations are edges. Map the string variable with certain index using hash map. Then build a matrix to represent all values that can be represented by the given equations. For example, a/b means a and b are neighbors, b/c means b and c are neighbors, thus we know a and c are connected and we can calculate the value of a/c by a/b * b/c, as well as c / a by 1.0 / (a/c).
After that, for each query, if we cannot find the index in the map, we cannot get the result.
public double[] calcEquation(String[][] equations, double[] values, String[][] queries) { int len = equations.length; Mapindices = new HashMap<>(); int index = 0; for (String[] eq : equations) { if (!indices.containsKey(eq[0])) { indices.put(eq[0], index++); } if (!indices.containsKey(eq[1])) { indices.put(eq[1], index++); } } double[][] relations = new double[index][index]; for (int i = 0; i < index; i++) { Arrays.fill(relations[i], -1.0); } for (int i = 0; i < len; i++) { String[] eq = equations[i]; double v = values[i]; int first = indices.get(eq[0]); int second = indices.get(eq[1]); relations[first][second] = v; relations[second][first] = 1.0 / v; } for (int i = 0; i < index; i++) { for (int j = 0; j < index; j++) { for(int k = 0; k < index; k++) { if (relations[i][j] != -1.0) { continue; } if (relations[i][k] != -1.0 && relations[k][j] != -1.0) { relations[i][j] = relations[i][k] * relations[k][j]; if (relations[i][j] != 0.0) { relations[j][i] = 1.0 / relations[i][j]; } } } } } double[] rst = new double[queries.length]; for (int i = 0; i < queries.length; i++) { if (!indices.containsKey(queries[i][0]) || !indices.containsKey(queries[i][1])) { rst[i] = -1.0; } else { int first = indices.get(queries[i][0]); int second = indices.get(queries[i][1]); rst[i] = relations[first][second]; } } return rst; }
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