# Evaluate Division ### Weighted Directed Graph -> Find Path Weight **Medium** 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, `vector&` values, `vector>` queries , where `equations.size() == values.size()`, and the `values` are positive. This represents the equations. Return `vector`. 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. ``` ## Solution & Analysis 把问题转化为图 Weighted Directed Graph，然后因为不同的路径到达目标path value应该是一样的，因此只需要用DFS找到一个路径即可返回。 建Adjacency List的时候，因为这是带权重的有向图，要顺便添加反向的edge，也就是1.0/value。 #### Version 2 - DFS ```java class Solution { class Edge { String from; String to; double value; Edge(String from, String to, double value) { this.from = from; this.to = to; this.value = value; } } public double[] calcEquation(String[][] equations, double[] values, String[][] queries) { // Build graph HashMap> map = buildGraph(equations, values); double[] result = new double[queries.length]; // Calculate result for each query by searching in the graph int idx = 0; for (String[] query: queries) { if (!map.containsKey(query[0])) { result[idx] = -1.0; } else { String n = query[0]; String d = query[1]; HashSet visited = new HashSet < > (); double val = dfs(map, visited, 1.0, n, d); result[idx] = val; } idx++; } return result; } // Build graph with adjacency list private HashMap> buildGraph(String[][] equations, double[] values) { HashMap> map = new HashMap<>(); for (int i = 0; i < equations.length; i++) { // convert input equation to edge with value if (!map.containsKey(equations[i][0])) { map.put(equations[i][0], new ArrayList()); } map.get(equations[i][0]).add(new Edge(equations[i][0], equations[i][1], values[i])); // reverse order to store inverse value for edge if (!map.containsKey(equations[i][1])) { map.put(equations[i][1], new ArrayList()); } map.get(equations[i][1]).add(new Edge(equations[i][1], equations[i][0], 1.0 / values[i])); } return map; } // Recursively search a path from numerator (from) to denominator (to); return -1.0 if not found private double dfs(HashMap> map, HashSet visited, double pathVal, String from, String to) { if (from.equals(to)) { return pathVal; } visited.add(from); List < Edge > edges = map.get(from); if (edges != null) { for (Edge e: edges) { if (visited.contains(e.to)) { continue; } visited.add(e.to); double value = dfs(map, visited, pathVal * e.value, e.to, to); if (value != -1.0) { return value; } } } return -1.0; } } ``` #### Version 1 - DFS (2 ms, faster than 64.65%) ```java class Solution { class Edge { String numerator; String denominator; double value; Edge (String numerator, String denominator, double value) { this.numerator = numerator; this.denominator = denominator; this.value = value; } // For debugging String printString() { return numerator + " - " + denominator + ": " + value; } } public double[] calcEquation(String[][] equations, double[] values, String[][] queries) { // build adjacency list HashMap> map = new HashMap<>(); for (int i = 0; i < equations.length; i++) { // convert input equation to edge with value if (!map.containsKey(equations[i][0])) { map.put(equations[i][0], new ArrayList()); } map.get(equations[i][0]).add(new Edge(equations[i][0], equations[i][1], values[i])); // reverse order to store inverse value for edge if (!map.containsKey(equations[i][1])) { map.put(equations[i][1], new ArrayList()); } map.get(equations[i][1]).add(new Edge(equations[i][1], equations[i][0], 1.0 / values[i])); } double[] result = new double[queries.length]; int idx = 0; for (String[] query: queries) { if (!map.containsKey(query[0])) { result[idx] = -1.0; } else { String n = query[0]; String d = query[1]; HashSet visited = new HashSet<>(); double val = dfs(map, visited, 1.0, n, d); result[idx] = val; } idx++; } return result; } private double dfs(HashMap> map, HashSet visited, double val, String numerator, String denominator) { if (numerator.equals(denominator)) { return val; } visited.add(numerator); List edges = map.get(numerator); if (edges != null) { for (Edge e: edges) { if (visited.contains(e.denominator)) { continue; } visited.add(e.denominator); double value = dfs(map, visited, val * e.value, e.denominator, denominator); if (value != -1.0) { return value; } } } return - 1.0; } // For debugging private void printAdjacencyList (HashMap> map) { for (Map.Entry> entry: map.entrySet()) { List v = entry.getValue(); for (Edge e: v) { System.out.println(e.printString()); } } } } ``` ## Reference --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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