



from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , ):
    __a       ,   __a						       =				coefficient_matrix.shape
    __a       ,   __a						       =				constant_matrix.shape

    if rowsa != colsa:
        __a						       =				f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
        raise ValueError(_UpperCAmelCase				)

    if colsa != 1:
        __a						       =				f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
        raise ValueError(_UpperCAmelCase				)

    if rowsa != rowsa:
        __a						       =				(
            '''Coefficient and constant matrices dimensions must be nxn and nx1 but '''
            f'received {rowsa}x{colsa} and {rowsa}x{colsa}'
        )
        raise ValueError(_UpperCAmelCase				)

    if len(_UpperCAmelCase				) != rowsa:
        __a						       =				(
            '''Number of initial values must be equal to number of rows in coefficient '''
            f'matrix but received {len(_UpperCAmelCase				)} and {rowsa}'
        )
        raise ValueError(_UpperCAmelCase				)

    if iterations <= 0:
        raise ValueError('''Iterations must be at least 1'''				)

    __a						       =				np.concatenate(
        (coefficient_matrix, constant_matrix)   , axis=1				)

    __a       ,   __a						       =				table.shape

    strictly_diagonally_dominant(_UpperCAmelCase				)

    # Iterates the whole matrix for given number of times
    for _ in range(_UpperCAmelCase				):
        __a						       =				[]
        for row in range(_UpperCAmelCase				):
            __a						       =				0
            for col in range(_UpperCAmelCase				):
                if col == row:
                    __a						       =				table[row][col]
                elif col == cols - 1:
                    __a						       =				table[row][col]
                else:
                    temp += (-1) * table[row][col] * init_val[col]
            __a						       =				(temp + val) / denom
            new_val.append(_UpperCAmelCase				)
        __a						       =				new_val

    return [float(_UpperCAmelCase				) for i in new_val]





def      __snake_case	(			_UpperCAmelCase				):
    __a       ,   __a						       =				table.shape

    __a						       =				True

    for i in range(0   , _UpperCAmelCase				):
        __a						       =				0
        for j in range(0   , cols - 1				):
            if i == j:
                continue
            else:
                total += table[i][j]

        if table[i][i] <= total:
            raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''				)

    return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
 import doctest

 doctest.testmod()










from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def      __snake_case	(			):
    __a       ,   __a						       =				9, 14  # noqa: F841
    __a						       =				[
        [0, 1, 4],
        [0, 7, 8],
        [1, 2, 8],
        [7, 8, 7],
        [7, 6, 1],
        [2, 8, 2],
        [8, 6, 6],
        [2, 3, 7],
        [2, 5, 4],
        [6, 5, 2],
        [3, 5, 14],
        [3, 4, 9],
        [5, 4, 10],
        [1, 7, 11],
    ]

    __a						       =				defaultdict(_UpperCAmelCase				)
    for nodea, nodea, cost in edges:
        adjancency[nodea].append([nodea, cost]				)
        adjancency[nodea].append([nodea, cost]				)

    __a						       =				mst(_UpperCAmelCase				)

    __a						       =				[
        [7, 6, 1],
        [2, 8, 2],
        [6, 5, 2],
        [0, 1, 4],
        [2, 5, 4],
        [2, 3, 7],
        [0, 7, 8],
        [3, 4, 9],
    ]

    for answer in expected:
        __a						       =				tuple(answer[:2]				)
        __a						       =				tuple(edge[::-1]				)
        assert edge in result or reverse in result





