algorithm: binary lifting (#1218)

* Algorithm: BinaryLifting

* Update BinaryLifting.js

* made the requested changes

* added more comments

Graphs/test/BinaryLifting.test.js

@@ -0,0 +1,82 @@
+import binaryLifting from '../BinaryLifting'
+
+// 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 = [
+    [2, 1],
+    [6, 1],
+    [7, 2],
+    [8, 2],
+    [10, 2],
+    [10, 3],
+    [10, 5],
+    [11, 3]
+  ]
+  const kthAncestors = binaryLifting(root, graph, queries)
+  expect(kthAncestors).toEqual([1, 5, 1, 4, 8, 7, 1, 1])
+})
+
+// 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 = [
+    [2, 1],
+    [3, 1],
+    [3, 2],
+    [6, 2],
+    [7, 3],
+    [8, 2],
+    [8, 3]
+  ]
+  const kthAncestors = binaryLifting(root, graph, queries)
+  expect(kthAncestors).toEqual([0, 1, 0, 1, 0, 2, 0])
+})