Python: Find a number in a given matrix which is maximum in its column and minimum in its row

Last update on May 24 2025 10:48:23 (UTC/GMT +8 hours)

Max in Column, Min in Row

Write a Python program to find a number in a given matrix that is maximum in its column and minimum in its row.

Sample Solution:

Python Code:

# Define a function named matrix_number that takes a matrix as an argument.
def matrix_number(matrix):
    # Use set operations to find the numbers that are the minimum in their row and maximum in their column.
    # The set(map(min, matrix)) finds the minimum in each row, and set(map(max, zip(*matrix))) finds the maximum in each column.
    result = set(map(min, matrix)) & set(map(max, zip(*matrix)))
    return list(result)

# Test the function with different matrices and print the results.

# Test case 1
m1 = [[1,2], [2,3]]
print("Original matrix:", m1)
print("Number in the said matrix which is maximum in its column and minimum in its row:")
print(matrix_number(m1))

# Test case 2
m1 = [[1,2,3], [3,4,5]]
print("\nOriginal matrix:", m1)
print("Number in the said matrix which is maximum in its column and minimum in its row:")
print(matrix_number(m1))

# Test case 3
m1 = [[7,5,6], [3,4,4], [6,5,7]]
print("\nOriginal matrix:", m1)
print("Number in the said matrix which is maximum in its column and minimum in its row:")
print(matrix_number(m1))

Sample Output:

Original matrix: [[1, 2], [2, 3]]
Number in the said matrix which is maximum in its column and minimum in its row:
[2]

Original matrix: [[1, 2, 3], [3, 4, 5]]
Number in the said matrix which is maximum in its column and minimum in its row:
[3]

Original matrix: [[7, 5, 6], [3, 4, 4], [6, 5, 7]]
Number in the said matrix which is maximum in its column and minimum in its row:
[5]

Explanation:

Here is a breakdown of the above Python code:

Function definition:

The code defines a function named matrix_number that takes a matrix as an argument.

Set operations:

The function uses set operations to find the numbers that are the minimum in their row and maximum in their column. The expression set(map(min, matrix)) finds the minimum in each row, and set(map(max, zip(*matrix))) finds the maximum in each column.

Return statement:

The function returns the list of numbers that satisfy both conditions.

Flowchart:

Flowchart: Python - Find a number in a given matrix which is maximum in its column and minimum in its row.

For more Practice: Solve these Related Problems:

Write a Python program to find an element in a matrix that is the smallest in its row and the largest in its column.
Write a Python program to identify a saddle point in a matrix that meets the criteria of min in its row and max in its column.
Write a Python program to search through a matrix for numbers that are simultaneously the row minimum and column maximum.
Write a Python program to determine if a given matrix has a unique element that is the maximum in its column and minimum in its row.

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Python Code Editor:

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