Solve merging-ranges

Write a function to merge meeting times. Added an in-place solution, which the
"Bonus" section suggested attempting to solve.

- Added some simple benchmarks to test the performance differences between the
  in-place and not-in-place variants. To my surprise, the in-place solution was
  consistently slower than the not-in-place solution.

scratch/deepmind/part_two/merging-ranges.py

@@ -0,0 +1,115 @@
+import unittest
+import timeit
+
+
+# Solution that uses O(n) space to store the result.
+def not_in_place(xs):
+    xs.sort()
+    result = [xs[0]]
+    for ca, cb in xs[1:]:
+        pa, pb = result[-1]
+        if ca <= pb:
+            result[-1] = (pa, max(pb, cb))
+        else:
+            result.append((ca, cb))
+    return result
+
+
+# Solution that uses O(1) space to store the result.
+def in_place(xs):
+    xs.sort()
+    i = 0
+    j = i + 1
+    while j < len(xs):
+        pa, pb = xs[i]
+        ca, cb = xs[j]
+        if ca <= pb:
+            xs[i] = (pa, max(pb, cb))
+            del xs[j]
+        else:
+            i = j
+            j += 1
+    return xs
+
+
+def test_nip():
+    inputs = [
+        [(1, 3), (2, 4)],
+        [(5, 6), (6, 8)],
+        [(1, 8), (2, 5)],
+        [(1, 3), (4, 8)],
+        [(1, 4), (2, 5), (5, 8)],
+        [(5, 8), (1, 4), (6, 8)],
+        [(1, 10), (2, 5), (6, 8), (9, 10), (10, 12)],
+        [(0, 1), (3, 5), (4, 8), (10, 12), (9, 10)],
+    ]
+    for x in inputs:
+        not_in_place(x)
+
+
+def test_ip():
+    inputs = [
+        [(1, 3), (2, 4)],
+        [(5, 6), (6, 8)],
+        [(1, 8), (2, 5)],
+        [(1, 3), (4, 8)],
+        [(1, 4), (2, 5), (5, 8)],
+        [(5, 8), (1, 4), (6, 8)],
+        [(1, 10), (2, 5), (6, 8), (9, 10), (10, 12)],
+        [(0, 1), (3, 5), (4, 8), (10, 12), (9, 10)],
+    ]
+    for x in inputs:
+        in_place(x)
+
+
+merge_ranges = in_place
+
+setup = 'from __main__ import test_nip, test_ip'
+print(timeit.timeit('test_nip()', number=10000, setup=setup))
+print(timeit.timeit('test_ip()', number=10000, setup=setup))
+
+
+# Tests
+class Test(unittest.TestCase):
+    def test_meetings_overlap(self):
+        actual = merge_ranges([(1, 3), (2, 4)])
+        expected = [(1, 4)]
+        self.assertEqual(actual, expected)
+
+    def test_meetings_touch(self):
+        actual = merge_ranges([(5, 6), (6, 8)])
+        expected = [(5, 8)]
+        self.assertEqual(actual, expected)
+
+    def test_meeting_contains_other_meeting(self):
+        actual = merge_ranges([(1, 8), (2, 5)])
+        expected = [(1, 8)]
+        self.assertEqual(actual, expected)
+
+    def test_meetings_stay_separate(self):
+        actual = merge_ranges([(1, 3), (4, 8)])
+        expected = [(1, 3), (4, 8)]
+        self.assertEqual(actual, expected)
+
+    def test_multiple_merged_meetings(self):
+        actual = merge_ranges([(1, 4), (2, 5), (5, 8)])
+        expected = [(1, 8)]
+        self.assertEqual(actual, expected)
+
+    def test_meetings_not_sorted(self):
+        actual = merge_ranges([(5, 8), (1, 4), (6, 8)])
+        expected = [(1, 4), (5, 8)]
+        self.assertEqual(actual, expected)
+
+    def test_one_long_meeting_contains_smaller_meetings(self):
+        actual = merge_ranges([(1, 10), (2, 5), (6, 8), (9, 10), (10, 12)])
+        expected = [(1, 12)]
+        self.assertEqual(actual, expected)
+
+    def test_sample_input(self):
+        actual = merge_ranges([(0, 1), (3, 5), (4, 8), (10, 12), (9, 10)])
+        expected = [(0, 1), (3, 8), (9, 12)]
+        self.assertEqual(actual, expected)
+
+
+unittest.main(verbosity=2)