This notebook was prepared by Donne Martin. Source and license info is on GitHub.

# Solution Notebook¶

## Constraints¶

• Does A have enough space for B?
• Yes
• Can the inputs have duplicate array items?
• Yes
• Can we assume the inputs are valid?
• No
• Does the inputs also include the actual size of A and B?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• A or B is None -> Exception
• index of last A or B < 0 -> Exception
• A or B is empty
• General case
• A = [1, 3, 5, 7, 9, None, None, None]
• B = [4, 5, 6]
• A = [1, 3, 4, 5, 5, 6, 7, 9]

## Algorithm¶

                     i                 k
A = [1,  3,  5,  7,  9,  None,  None,  None]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i                 k
A = [1,  3,  5,  7,  9,  None,  None,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i              k
A = [1,  3,  5,  7,  9,  None,  7,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i           k
A = [1,  3,  5,  7,  9,  6,  7,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i       k
A = [1,  3,  5,  7,  5,  6,  7,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i       k
A = [1,  3,  5,  5,  5,  6,  7,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
i   k
A = [1,  3,  4,  5,  5,  6,  7,  9]
j
B = [4,  5,  6]

---

A[k] = max(A[i], B[j])
ik
A = [1,  3,  4,  5,  5,  6,  7,  9]

B = [4,  5,  6]

---

A = [1, 3, 4, 5, 5, 6, 7, 9]



Complexity:

• Time: O(m + n)
• Space: O(1)

## Code¶

In [1]:
class Array(object):

def merge_into(self, source, dest, source_end_index, dest_end_index):
if source is None or dest is None:
raise TypeError('source or dest cannot be None')
if source_end_index < 0 or dest_end_index < 0:
raise ValueError('end indices must be >= 0')
if not source:
return dest
if not dest:
return source
source_index = source_end_index - 1
dest_index = dest_end_index - 1
insert_index = source_end_index + dest_end_index - 1
while dest_index >= 0:
if source[source_index] > dest[dest_index]:
source[insert_index] = source[source_index]
source_index -= 1
else:
source[insert_index] = dest[dest_index]
dest_index -= 1
insert_index -= 1
return source


## Unit Test¶

In [2]:
%%writefile test_merge_into.py
import unittest

class TestArray(unittest.TestCase):

def test_merge_into(self):
array = Array()
self.assertRaises(TypeError, array.merge_into, None, None, None, None)
self.assertRaises(ValueError, array.merge_into, [1], [2], -1, -1)
a = [1, 2, 3]
self.assertEqual(array.merge_into(a, [], len(a), 0), [1, 2, 3])
a = [1, 2, 3]
self.assertEqual(array.merge_into(a, [], len(a), 0), [1, 2, 3])
a = [1,  3,  5,  7,  9,  None,  None,  None]
b = [4,  5,  6]
expected = [1, 3, 4, 5, 5, 6, 7, 9]
self.assertEqual(array.merge_into(a, b, 5, len(b)), expected)
print('Success: test_merge_into')

def main():
test = TestArray()
test.test_merge_into()

if __name__ == '__main__':
main()

Overwriting test_merge_into.py

In [3]:
%run -i test_merge_into.py

Success: test_merge_into