algorithm: LCA by binary lifting (#1237)

* algorithm: LCA by binary lifting

* removed trailing spaces

* reduced code duplication by importing code from other file

* made requested changes

Graphs/test/LCABinaryLifting.test.js

@@ -0,0 +1,80 @@
+import lcaBinaryLifting from '../LCABinaryLifting'
+
+// The graph for Test Case 1 looks like this:
+//
+//         0
+//        /|\
+//       / | \
+//      1  3  5
+//     / \     \
+//    2   4     6
+//         \
+//          7
+//         / \
+//        11  8
+//             \
+//              9
+//               \
+//                10
+
+test('Test case 1', () => {
+  const root = 0
+  const graph = [
+    [0, 1],
+    [0, 3],
+    [0, 5],
+    [5, 6],
+    [1, 2],
+    [1, 4],
+    [4, 7],
+    [7, 11],
+    [7, 8],
+    [8, 9],
+    [9, 10]
+  ]
+  const queries = [
+    [1, 3],
+    [6, 5],
+    [3, 6],
+    [7, 10],
+    [8, 10],
+    [11, 2],
+    [11, 10]
+  ]
+  const lowestCommonAncestors = lcaBinaryLifting(root, graph, queries)
+  expect(lowestCommonAncestors).toEqual([0, 5, 0, 7, 8, 1, 7])
+})
+
+// The graph for Test Case 2 looks like this:
+//
+//         0
+//        / \
+//       1   2
+//      / \   \
+//     3   4   5
+//    /       / \
+//   6       7   8
+
+test('Test case 2', () => {
+  const root = 0
+  const graph = [
+    [0, 1],
+    [0, 2],
+    [1, 3],
+    [1, 4],
+    [2, 5],
+    [3, 6],
+    [5, 7],
+    [5, 8]
+  ]
+  const queries = [
+    [1, 2],
+    [3, 4],
+    [5, 4],
+    [6, 7],
+    [6, 8],
+    [7, 8]
+  ]
+  const lowestCommonAncestors = lcaBinaryLifting(root, graph, queries)
+  expect(lowestCommonAncestors).toEqual([0, 1, 0, 0, 0, 5])
+})