





# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint

class 		__a							:

       '''simple docstring'''





       def __init__(     self	:   Dict					,			UpperCAmelCase	:   Any					,			UpperCAmelCase	:   Tuple			):
           lowerCAmelCase_					:	Union[str, Any]						=   key
           lowerCAmelCase_					:	int						=   freq



       def __str__(     self	:   Tuple			):
           return F'Node(key={self.key}, freq={self.freq})'






def 			__UpperCamelCase				(			lowercase__	:       Optional[int]		,    lowercase__	:       Optional[int]		,    lowercase__	:       str		,    lowercase__	:       List[str]		,    lowercase__	:       str		,    lowercase__	:       List[str]		)	->      Dict:
    '''simple docstring'''





    if i > j or i < 0 or j > len(_A		) - 1:
        return

    lowerCAmelCase_					:	List[Any]						=   root[i][j]
    if parent == -1:  # root does not have a parent
        print(f'{key[node]} is the root of the binary search tree.'		)
    elif is_left:
        print(f'{key[node]} is the left child of key {parent}.'		)
    else:
        print(f'{key[node]} is the right child of key {parent}.'		)

    print_binary_search_tree(_A		,    _A		,    _A		,    node - 1		,    key[node]		,    _A		)
    print_binary_search_tree(_A		,    _A		,    node + 1		,    _A		,    key[node]		,    _A		)
def 			__UpperCamelCase				(			lowercase__	:       Optional[Any]		)	->      Optional[int]:
    '''simple docstring'''





    nodes.sort(key=lambda lowercase__		: node.key		)

    lowerCAmelCase_					:	Tuple						=   len(_A		)

    lowerCAmelCase_					:	str						=   [nodes[i].key for i in range(_A		)]
    lowerCAmelCase_					:	Optional[int]						=   [nodes[i].freq for i in range(_A		)]

    # This 2D array stores the overall tree cost (which's as minimized as possible);
    # for a single key, cost is equal to frequency of the key.
    lowerCAmelCase_					:	List[Any]						=   [[freqs[i] if i == j else 0 for j in range(_A		)] for i in range(_A		)]
    # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
    # array
    lowerCAmelCase_					:	Optional[int]						=   [[freqs[i] if i == j else 0 for j in range(_A		)] for i in range(_A		)]
    # stores tree roots that will be used later for constructing binary search tree
    lowerCAmelCase_					:	Any						=   [[i if i == j else 0 for j in range(_A		)] for i in range(_A		)]

    for interval_length in range(2		,    n + 1		):
        for i in range(n - interval_length + 1		):
            lowerCAmelCase_					:	Any						=   i + interval_length - 1

            lowerCAmelCase_					:	Optional[Any]						=   sys.maxsize  # set the value to "infinity"
            lowerCAmelCase_					:	Optional[int]						=   total[i][j - 1] + freqs[j]

            # Apply Knuth's optimization
            # Loop without optimization: for r in range(i, j + 1):
            for r in range(root[i][j - 1]		,    root[i + 1][j] + 1		):  # r is a temporal root
                lowerCAmelCase_					:	Union[str, Any]						=   dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                lowerCAmelCase_					:	str						=   dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
                lowerCAmelCase_					:	List[str]						=   left + total[i][j] + right

                if dp[i][j] > cost:
                    lowerCAmelCase_					:	Any						=   cost
                    lowerCAmelCase_					:	Optional[int]						=   r

    print("""Binary search tree nodes:"""		)
    for node in nodes:
        print(_A		)

    print(f'\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'		)
    print_binary_search_tree(_A		,    _A		,    0		,    n - 1		,    -1		,    _A		)
def 			__UpperCamelCase				(			)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	str						=   [Node(_A		,    randint(1		,    50		)		) for i in range(10		,    0		,    -1		)]
    find_optimal_binary_search_tree(_A		)


if __name__ == "__main__":
  main()









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])


