Solve InterviewCake's find duplicate beast mode

Write a function to find a duplicate item in a list of numbers. The values are
in the range [1, n]; the length of the list is n + 1. The solution should run in
linear time and consume constant space.

The solution is to construct a graph from the list. Each graph will have a cycle
where the last element in the cycle is a duplicate value.

See the solution for specific techniques on how to compute the length the cycle
without infinitely looping.

2 files changed, 116 insertions, 2 deletions

diff --git a/scratch/deepmind/part_two/find-duplicate-optimize-for-space-beast-mode.py b/scratch/deepmind/part_two/find-duplicate-optimize-for-space-beast-mode.py
new file mode 100644
index 000000000000..c9edc32c8856
--- /dev/null
+++ b/scratch/deepmind/part_two/find-duplicate-optimize-for-space-beast-mode.py
@@ -0,0 +1,114 @@
+import unittest
+
+
+################################################################################
+# InterviewCake's solution
+################################################################################
+def cycle_len(xs, i):
+    """
+    Returns the length of a cycle that contains no duplicate items.
+    """
+    result = 1
+    checkpt = i
+    current = xs[checkpt - 1]
+
+    while current != checkpt:
+        current = xs[current - 1]
+        result += 1
+
+    return result
+
+
+def theirs(xs):
+    """
+    This is InterviewCake's solution.
+    """
+    i = xs[-1]
+    for _ in range(len(xs) - 1):
+        i = xs[i - 1]
+
+    cycle_length = cycle_len(xs, i)
+
+    p0 = xs[-1]
+    p1 = xs[-1]
+    for _ in range(cycle_length):
+        p1 = xs[p1 - 1]
+
+    while p0 != p1:
+        p0 = xs[p0 - 1]
+        p1 = xs[p1 - 1]
+
+    print(p0, p1)
+
+    return p0
+
+
+################################################################################
+# My solution
+################################################################################
+def mine(xs):
+    """
+    This is the solution that I came up with, which differs from InterviewCake's
+    solution.
+    """
+    i = xs[-1]
+    offset = 1 if len(xs) % 2 == 0 else 2
+
+    for _ in range(len(xs) - offset):
+        i = xs[i - 1]
+
+    return i
+
+
+use_mine = True
+find_duplicate = mine if use_mine else theirs
+
+
+# Tests
+class Test(unittest.TestCase):
+    def test_just_the_repeated_number(self):
+        # len(xs) even
+        actual = find_duplicate([1, 1])
+        expected = 1
+        self.assertEqual(actual, expected)
+
+    def test_short_list(self):
+        # len(xs) even
+        actual = find_duplicate([1, 2, 3, 2])
+        expected = 2
+        self.assertEqual(actual, expected)
+
+    def test_medium_list(self):
+        # len(xs) even
+        actual = find_duplicate([1, 2, 5, 5, 5, 5])
+        expected = 5
+        self.assertEqual(actual, expected)
+
+    def test_long_list(self):
+        # len(xs) odd
+        actual = find_duplicate([4, 1, 4, 8, 3, 2, 7, 6, 5])
+        expected = 4
+        self.assertEqual(actual, expected)
+
+    ############################################################################
+    # Additional examples from InterviewCake.com
+    ############################################################################
+    def test_example_a(self):
+        # len(xs) even
+        actual = find_duplicate([3, 4, 2, 3, 1, 5])
+        expected = 3
+        self.assertTrue(actual, expected)
+
+    def test_example_b(self):
+        # len(xs) even
+        actual = find_duplicate([3, 1, 2, 2])
+        expected = 2
+        self.assertEqual(actual, expected)
+
+    def test_example_c(self):
+        # len(xs) odd BUT multiple duplicates
+        actual = find_duplicate([4, 3, 1, 1, 4])
+        self.assertTrue(actual in {1, 4})
+
+
+unittest.main(verbosity=2)
diff --git a/scratch/deepmind/part_two/todo.org b/scratch/deepmind/part_two/todo.org
index 5d296b9b5287..ee91e47551c7 100644
--- a/scratch/deepmind/part_two/todo.org
+++ b/scratch/deepmind/part_two/todo.org
@@ -26,7 +26,7 @@
 ** DONE 2nd Largest Item in a Binary Search Tree
 ** DONE Graph Coloring
 ** DONE MeshMessage
-** TODO Find Repeat, Space Edition BEAST MODE
+** DONE Find Repeat, Space Edition BEAST MODE
 * Dynamic programming and recursion
 ** TODO Recursive String Permutations
 ** TODO Compute nth Fibonacci Number
@@ -45,7 +45,7 @@
 ** TODO Does This Linked List Have A Cycle?
 ** TODO Reverse A Linked List
 ** TODO Kth to Last Node in a Singly-Linked List
-** TODO Find Repeat, Space Edition BEAST MODE
+** DONE Find Repeat, Space Edition BEAST MODE
 * System design
 ** TODO URL Shortener
 ** TODO MillionGazillion