
from heapq import heappop, heappush

import numpy as np






def   lowerCAmelCase_						(					_snake_case      :  np.ndarray      ,   _snake_case      :  tuple[int, int]      ,   _snake_case      :  tuple[int, int]      ,   _snake_case      :  bool      ,   )				->		tuple[float | int, list[tuple[int, int]]]:







	'''simple docstring'''


	__magic_name__   ,    __magic_name__		:		Union[str, Any]	   =     grid.shape
	__magic_name__		:		List[Any]	   =     [-1, 1, 0, 0]
	__magic_name__		:		Union[str, Any]	   =     [0, 0, -1, 1]
	if allow_diagonal:
		dx += [-1, -1, 1, 1]
		dy += [-1, 1, -1, 1]

	__magic_name__   ,    __magic_name__		:		List[Any]	   =     [(0, source)], set()
	__magic_name__		:		Tuple	   =     np.full((rows, cols)      ,   np.inf   )
	__magic_name__		:		int	   =     0
	__magic_name__		:		Optional[int]	   =     np.empty((rows, cols)      ,   dtype=_snake_case   )
	__magic_name__		:		Optional[Any]	   =     None

	while queue:
		((__magic_name__)   ,    (__magic_name__))		:		Any	   =     heappop(_snake_case   )
		if (x, y) in visited:
			continue
		visited.add((x, y)   )

		if (x, y) == destination:
			__magic_name__		:		Optional[int]	   =     []
			while (x, y) != source:
				path.append((x, y)   )
				__magic_name__   ,    __magic_name__		:		List[Any]	   =     predecessors[x, y]
			path.append(_snake_case   )  # add the source manually
			path.reverse()
			return matrix[destination], path

		for i in range(len(_snake_case   )   ):
			__magic_name__   ,    __magic_name__		:		Optional[Any]	   =     x + dx[i], y + dy[i]
			if 0 <= nx < rows and 0 <= ny < cols:
				__magic_name__		:		Optional[int]	   =     grid[nx][ny]
				if next_node == 1 and matrix[nx, ny] > dist + 1:
					heappush(_snake_case      ,   (dist + 1, (nx, ny))   )
					__magic_name__		:		List[str]	   =     dist + 1
					__magic_name__		:		Any	   =     (x, y)

	return np.inf, []


if __name__ == "__main__":
				import doctest

				doctest.testmod()


def   lowerCAmelCase_						(					_snake_case      :  list[list[int | float]]   )				->		int:







	'''simple docstring'''


	__magic_name__		:		Any	   =     len(_snake_case   )
	__magic_name__		:		Optional[Any]	   =     len(matrix[0]   )
	__magic_name__		:		Union[str, Any]	   =     min(_snake_case      ,   _snake_case   )

	for row in range(_snake_case   ):
		# Check if diagonal element is not zero
		if matrix[row][row] != 0:
			# Eliminate all the elements below the diagonal
			for col in range(row + 1      ,   _snake_case   ):
				__magic_name__		:		Optional[Any]	   =     matrix[col][row] / matrix[row][row]
				for i in range(_snake_case      ,   _snake_case   ):
					matrix[col][i] -= multiplier * matrix[row][i]
		else:
			# Find a non-zero diagonal element to swap rows
			__magic_name__		:		str	   =     True
			for i in range(row + 1      ,   _snake_case   ):
				if matrix[i][row] != 0:
					__magic_name__   ,    __magic_name__		:		List[str]	   =     matrix[i], matrix[row]
					__magic_name__		:		Union[str, Any]	   =     False
					break
			if reduce:
				rank -= 1
				for i in range(_snake_case   ):
					__magic_name__		:		Any	   =     matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
			row -= 1

	return rank


if __name__ == "__main__":
				import doctest

				doctest.testmod()
