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sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort sort of the code. ```python def find_the_saddle_point(matrix): """ Finds the saddle point in a matrix. Args: matrix: A 2D list representing a matrix. Returns: A tuple containing the row and column indices of the saddle point, or None if no saddle point exists. """ rows = len(matrix) cols = len(matrix[0]) # Iterate through each row for i in range(rows): # Find the minimum value in the current row min_row_val = matrix[i][0] min_col = 0 for j in range(1, cols): if matrix[i][j] < min_row_val: min_row_val = matrix[i][j] min_col = j # Check if the minimum value is the maximum in its column is_saddle_point = True for k in range(rows): if matrix[k][min_col] > min_row_val: is_saddle_point = False break if is_saddle_point: return (i, min_col) # If no saddle point is found, return None return None # Example usage: matrix = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] saddle_point = find_the_saddle_point(matrix) if saddle_point: print(f"The saddle point is at row {saddle_point[0]}, column {saddle_point[1]}.") else: print("There is no saddle point in the matrix.") ``` **Explanation:** 1. **Initialization:** - `rows` and `cols` store the number of rows and columns in the matrix. - `saddle_point` is initialized to `None` to indicate that no saddle point has been found yet. 2. **Iterating through rows:** - The outer loop iterates through each row of the matrix. 3. **Finding the minimum in the row:** - Inside the loop, `min_row_val` is initialized to the first element of the current row. - The inner loop iterates through the remaining elements of the row, updating `min_row_val` and `min_col` if a smaller value is found. 4. **Checking for saddle point:** - After finding the minimum value in the row, the code checks if it's also the maximum value in its corresponding column. - It iterates through all rows and compares the minimum value with the element in the same column. - If any element in the column is greater than the minimum value, the `is_saddle_point` flag is set to `False`, indicating that the current element is not a saddle point. 5. **Returning the result:** - If `is_saddle_point` is still `True` after checking all rows, it means the current element is a saddle point, and its row and column indices are returned as a tuple. - If no saddle point is found, the function returns `None`. **Example:** In the given example matrix: ``` [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] ``` The code will find that the element `5` at row 1, column 1 is a saddle point. This is because it is the minimum value in its row and the maximum value in its column. **Output:** ``` The saddle point is at row 1, column 1. ```
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