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This approach involves two main steps. First, find the minimum element in each row and keep track of the potential lucky numbers. Then, verify these potential numbers to check if they are the maximum in their respective columns.
Time Complexity: O(m * n) where m is the number of rows and n is the number of columns in the matrix.
Space Complexity: O(m) for storing the minimum indices for each row.
1class Solution:
2 def luckyNumbers (self, matrix):
3 min_row = {min(row) for row in matrix}
4 max_col = {max(col) for col in zip(*matrix)}
5 return list(min_row & max_col)Python's set operations allow an elegant solution. We find the minimum of each row and maximum of each column using set comprehension and then find the intersection.
This approach leverages set operations from mathematics to identify potential lucky numbers. We extract the row minimums and column maximums into separate sets and find the intersection of these sets for possible lucky numbers.
Time Complexity: O(m * n) where m is the number of rows and n is the number of columns.
Space Complexity: O(n) for storing column maximums.
1
This C implementation performs a mathematical check for intersection by keeping potential lucky values in a temporary array, then validating if they appear within the maximums of their columns.