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

Solution Notebook

Problem: Search a sorted matrix for an item.

Constraints

  • Are items in each row sorted?
    • Yes
  • Are items in each column sorted?
    • Yes
  • Is the sorting in ascending or descending order?
    • Ascending
  • Is the matrix a rectangle? Not jagged?
    • Yes
  • Is the matrix square?
    • Not necessarily
  • Is the output a tuple (row, col)?
    • Yes
  • Is the item you are searching for always in the matrix?
    • No
  • Can we assume the inputs are valid?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> Exception
  • General case
    • Item found -> (row, col)
    • Item not found -> None

Algorithm

Find 60 (val = 60)

 20  40  63   80
 30  50  80   90
 40  60  100 110
 50  65  105 150

* If the start of a col > val, look left
* If the end of a col < val, look right
* If the start of row > val, look up
* If the end of a row < val, look down

If we start at the upper right corner, we just need to use these cases:

* If the start of a col > val, look left
* If the end of a row < val, look down

Complexity:

  • Time: O(n + m), where n and m are the matrix dimensions
  • Space: O(1)

Code

In [1]:
class SortedMatrix(object):

    def find_val(self, matrix, val):
        if matrix is None or val is None:
            raise TypeError('matrix and val cannot be None')
        row = 0
        col = len(matrix[0]) - 1
        while row < len(matrix) and col >= 0:
            if matrix[row][col] == val:
                return (row, col)
            elif matrix[row][col] > val:
                col -= 1
            else:
                row += 1
        return None

Unit Test

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


class TestSortedMatrix(unittest.TestCase):

    def test_find_val(self):
        matrix = [[20, 40, 63, 80],
                  [30, 50, 80, 90],
                  [40, 60, 110, 110],
                  [50, 65, 105, 150]]
        sorted_matrix = SortedMatrix()
        self.assertRaises(TypeError, sorted_matrix.find_val, None, None)
        self.assertEqual(sorted_matrix.find_val(matrix, 1000), None)
        self.assertEqual(sorted_matrix.find_val(matrix, 60), (2, 1))
        print('Success: test_find_val')


def main():
    test = TestSortedMatrix()
    test.test_find_val()


if __name__ == '__main__':
    main()
Overwriting test_search_sorted_matrix.py
In [3]:
%run -i test_search_sorted_matrix.py
Success: test_find_val