'''

Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix.

This matrix has the following properties:

- Integers in each row are sorted in ascending from left to right.

- Integers in each column are sorted in ascending from top to bottom.

Input: target = 21

[

[1, 4, 7, 11, 15],

[2, 5, 8, 12, 19],

[3, 6, 9, 16, 22],

[10, 13, 14, 17, 24],

[18, 21, 23, 26, 30]

]

Output: True

=========================================

Start from bottom left corner and search in top right direction.

Time Complexity: O(N + M)

Space Complexity: O(1)

'''

############

# Solution #

############

def search_2d_matrix(matrix, target):

n = len(matrix)

m = len(matrix[0])

j = 0

i = n - 1

while (i >= 0) and (j < m):

if matrix[i][j] > target:

i -= 1

elif matrix[i][j] < target:

j += 1

else:

return True

return False

###########

# Testing #

###########

# Test 1

# Correct result => True

print(search_2d_matrix([[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]], 21))

# Test 2

# Correct result => False

print(search_2d_matrix([[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]], 20))