Merge pull request #98 from jeantimex/evaluate-division

feat(graph): Added evaluate division.

README.md

@@ -79,6 +79,7 @@ A collection of JavaScript problems and solutions for studying algorithms.
 - [Graph Valid Tree](src/graph/graph-valid-tree.js)
 - [Number of Connected Components in an Undirected Graph](src/graph/number-of-connected-components-in-an-undirected-graph.js)
 - [Reconstruct Itinerary](src/graph/reconstruct-itinerary.js)
+- [Evaluate Division](src/graph/evaluate-division.js)
 
 ### Linked List
 

src/graph/__tests__/evaluate-division-test.js

@@ -0,0 +1,26 @@
+import { assert } from 'chai';
+import { serializeUndirectedGraph, deserializeUndirectedGraph } from 'utils/graph-util';
+import calcEquation from '../evaluate-division';
+
+describe('Evaluate Division', () => {
+  const testCases = [
+    [
+      [['a', 'b'], ['b', 'c']],
+      [2.0, 3.0],
+      [['a', 'c'], ['b', 'a'], ['a', 'e'], ['a', 'a'], ['x', 'x']],
+      [6.0, 0.5, -1.0, 1.0, -1.0],
+    ],
+    [[['a', 'b'], ['c', 'b']], [2.0, 4.0], [['a', 'c'], ['b', 'a']], [0.5, 0.5]],
+  ];
+
+  testCases.forEach((testCase, index) => {
+    it(`should evaluate the division ${index}`, () => {
+      const equations = testCase[0];
+      const values = testCase[1];
+      const queries = testCase[2];
+      const expected = testCase[3];
+      const actual = calcEquation(equations, values, queries);
+      assert.deepEqual(actual, expected);
+    });
+  });
+});

src/graph/evaluate-division.js

@@ -0,0 +1,118 @@
+/**
+ * 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<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.
+ */
+
+/**
+ * @param {string[][]} equations
+ * @param {number[]} values
+ * @param {string[][]} queries
+ * @return {number[]}
+ */
+const calcEquation = (equations, values, queries) => {
+  const result = [];
+
+  // Step 1. Build the undirected graph with adjacency list
+  const adjList = buildGraph(equations, values);
+
+  // Step 2. For each query, try to find a path in the graph
+  // that can link the nodes in the query
+  for (let i = 0; i < queries.length; i++) {
+    const [from, to] = queries[i];
+    const value = dfs(adjList, from, to, 1, new Set());
+
+    // If value is null, that means there's no such path
+    result.push(value ? value : -1.0);
+
+    if (value) {
+      // Update the graph to avoid duplicate computation
+      adjList.get(from).set(to, value);
+      adjList.get(to).set(from, 1 / value);
+    }
+  }
+
+  return result;
+};
+
+/**
+ * @param {Map<string, Map<string, number>>} adjList
+ * @param {string} node
+ * @param {string} to
+ * @param {number} product
+ * @param {Set} visited
+ */
+const dfs = (adjList, node, to, product, visited) => {
+  if (!adjList.has(node)) {
+    return null; // Dead end
+  }
+
+  visited.add(node); // Mark the current node as visited
+
+  const neighbors = [...adjList.get(node).keys()];
+
+  for (let i = 0; i < neighbors.length; i++) {
+    const v = neighbors[i];
+    const current = product * adjList.get(node).get(v);
+
+    if (v === to) {
+      // Found the path, return the product
+      return current;
+    }
+
+    if (!visited.has(v)) {
+      // Continue to search for the path
+      const value = dfs(adjList, v, to, current, visited);
+
+      if (value) {
+        return value;
+      }
+    }
+  }
+
+  return null;
+};
+
+const buildGraph = (equations, values) => {
+  const adjList = new Map();
+
+  for (let i = 0; i < equations.length; i++) {
+    const [from, to] = equations[i];
+    const value = values[i];
+
+    if (!adjList.has(from)) {
+      adjList.set(from, new Map());
+    }
+
+    if (!adjList.has(to)) {
+      adjList.set(to, new Map());
+    }
+
+    // Build the undirected graph
+    adjList.get(from).set(to, value);
+    adjList.get(to).set(from, 1 / value);
+  }
+
+  return adjList;
+};
+
+export default calcEquation;