





from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def 			__UpperCamelCase				(			lowercase__	:       np.ndarray		,    lowercase__	:       np.ndarray		,    lowercase__	:       np.ndarray		)	->      np.ndarray:
    '''simple docstring'''





    lowerCAmelCase_					:	List[Any]						=   np.stack((horizontal_flow, vertical_flow)		,    2		)

    # Create a grid of all pixel coordinates and subtract the flow to get the
    # target pixels coordinates
    lowerCAmelCase_					:	int						=   np.stack(
        np.meshgrid(np.arange(0		,    image.shape[1]		)		,    np.arange(0		,    image.shape[0]		)		)		,    2		)
    lowerCAmelCase_					:	str						=   np.round(grid - flow		).astype(np.intaa		)

    # Find the locations outside of the original image
    lowerCAmelCase_					:	Dict						=   (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]		))
    lowerCAmelCase_					:	Optional[int]						=   0

    lowerCAmelCase_					:	Union[str, Any]						=   image[grid[:, :, 1], grid[:, :, 0]]

    # Set pixels at invalid locations to 0
    lowerCAmelCase_					:	int						=   0

    return warped
def 			__UpperCamelCase				(			lowercase__	:       np.ndarray		,    lowercase__	:       np.ndarray		,    lowercase__	:       SupportsIndex		,    lowercase__	:       float | None = None		,    )	->      tuple[np.ndarray, np.ndarray]:
    '''simple docstring'''





    if alpha is None:
        lowerCAmelCase_					:	Tuple						=   0.1

    # Initialize flow
    lowerCAmelCase_					:	Optional[int]						=   np.zeros_like(lowercase__		)
    lowerCAmelCase_					:	List[str]						=   np.zeros_like(lowercase__		)

    # Prepare kernels for the calculation of the derivatives and the average velocity
    lowerCAmelCase_					:	Tuple						=   np.array([[-1, 1], [-1, 1]]		) * 0.25
    lowerCAmelCase_					:	Any						=   np.array([[-1, -1], [1, 1]]		) * 0.25
    lowerCAmelCase_					:	Union[str, Any]						=   np.array([[1, 1], [1, 1]]		) * 0.25
    lowerCAmelCase_					:	List[str]						=   np.array(
        [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]		)

    # Iteratively refine the flow
    for _ in range(lowercase__		):
        lowerCAmelCase_					:	List[str]						=   warp(lowercase__		,    lowercase__		,    lowercase__		)
        lowerCAmelCase_					:	Optional[Any]						=   convolve(lowercase__		,    lowercase__		) + convolve(lowercase__		,    lowercase__		)
        lowerCAmelCase_					:	Tuple						=   convolve(lowercase__		,    lowercase__		) + convolve(lowercase__		,    lowercase__		)
        lowerCAmelCase_					:	Optional[int]						=   convolve(lowercase__		,    lowercase__		) + convolve(lowercase__		,    -kernel_t		)

        lowerCAmelCase_					:	List[Any]						=   convolve(lowercase__		,    lowercase__		)
        lowerCAmelCase_					:	Dict						=   convolve(lowercase__		,    lowercase__		)

        # This updates the flow as proposed in the paper (Step 12)
        lowerCAmelCase_					:	Any						=   (
            derivative_x * avg_horizontal_velocity
            + derivative_y * avg_vertical_velocity
            + derivative_t
        )
        lowerCAmelCase_					:	Any						=   update / (alpha**2 + derivative_x**2 + derivative_y**2)

        lowerCAmelCase_					:	Optional[int]						=   avg_horizontal_velocity - derivative_x * update
        lowerCAmelCase_					:	List[Any]						=   avg_vertical_velocity - derivative_y * update

    return horizontal_flow, vertical_flow


if __name__ == "__main__":
  import doctest

  doctest.testmod()









from __future__ import annotations

import sys

class 		__a							:



       def __init__(     self	:   Any					,			UpperCAmelCase	:   str					,			UpperCAmelCase	:   int			):
           lowerCAmelCase_					:	str						=   letter
           lowerCAmelCase_					:	int						=   freq
           lowerCAmelCase_					:	dict[str, str]						=   {}



       def __repr__(     self	:   Optional[int]			):
           return F'{self.letter}:{self.freq}'






class 		__a							:



       def __init__(     self	:   Any					,			UpperCAmelCase	:   int					,			UpperCAmelCase	:   Letter | TreeNode					,			UpperCAmelCase	:   Letter | TreeNode			):
           lowerCAmelCase_					:	int						=   freq
           lowerCAmelCase_					:	Letter | TreeNode						=   left
           lowerCAmelCase_					:	Letter | TreeNode						=   right






def 			__UpperCamelCase				(			lowercase__	:       str		)	->      list[Letter]:
    '''simple docstring'''





    lowerCAmelCase_					:	dict[str, int]						=   {}
    with open(lowercase__		) as f:
        while True:
            lowerCAmelCase_					:	int						=   f.read(1		)
            if not c:
                break
            lowerCAmelCase_					:	Optional[Any]						=   chars[c] + 1 if c in chars else 1
    return sorted((Letter(lowercase__		,    lowercase__		) for c, f in chars.items())		,    key=lambda lowercase__		: x.freq		)
def 			__UpperCamelCase				(			lowercase__	:       list[Letter]		)	->      Letter | TreeNode:
    '''simple docstring'''





    lowerCAmelCase_					:	list[Letter | TreeNode]						=   letters  # type: ignore
    while len(lowercase__		) > 1:
        lowerCAmelCase_					:	str						=   response.pop(0		)
        lowerCAmelCase_					:	Any						=   response.pop(0		)
        lowerCAmelCase_					:	Union[str, Any]						=   left.freq + right.freq
        lowerCAmelCase_					:	Union[str, Any]						=   TreeNode(lowercase__		,    lowercase__		,    lowercase__		)
        response.append(lowercase__		)
        response.sort(key=lambda lowercase__		: x.freq		)
    return response[0]
def 			__UpperCamelCase				(			lowercase__	:       Letter | TreeNode		,    lowercase__	:       str		)	->      list[Letter]:
    '''simple docstring'''





    if isinstance(lowercase__		,    lowercase__		):
        lowerCAmelCase_					:	Dict						=   bitstring
        return [root]
    lowerCAmelCase_					:	TreeNode						=   root  # type: ignore
    lowerCAmelCase_					:	Union[str, Any]						=   []
    letters += traverse_tree(treenode.left		,    bitstring + """0"""		)
    letters += traverse_tree(treenode.right		,    bitstring + """1"""		)
    return letters
def 			__UpperCamelCase				(			lowercase__	:       str		)	->      None:
    '''simple docstring'''





    lowerCAmelCase_					:	Any						=   parse_file(lowercase__		)
    lowerCAmelCase_					:	int						=   build_tree(lowercase__		)
    lowerCAmelCase_					:	Tuple						=   {
        k: v for letter in traverse_tree(lowercase__		,    """"""		) for k, v in letter.bitstring.items()
    }
    print(f'Huffman Coding  of {file_path}: '		)
    with open(lowercase__		) as f:
        while True:
            lowerCAmelCase_					:	List[str]						=   f.read(1		)
            if not c:
                break
            print(letters[c]		,    end=""" """		)
    print()


if __name__ == "__main__":
  # pass the file path to the huffman function
  huffman(sys.argv[1])


