def key_of_min(d):
  return min(d, key = d.get)

key_of_min({'a':4, 'b':0, 'c':13}) # b

# Function to multiply two matrices
def multiply_matrices(matrix1, matrix2):
    # Check if the matrices can be multiplied
    if len(matrix1[0]) != len(matrix2):
        print("Error: The number of columns in the first matrix must be equal to the number of rows in the second matrix.")
        return None

    # Create the result matrix filled with zeros
    result = [[0 for _ in range(len(matrix2[0]))] for _ in range(len(matrix1))]

    # Perform matrix multiplication
    for i in range(len(matrix1)):
        for j in range(len(matrix2[0])):
            for k in range(len(matrix2)):
                result[i][j] += matrix1[i][k] * matrix2[k][j]

    return result

# Example matrices
matrix1 = [[1, 2, 3],
           [4, 5, 6],
           [7, 8, 9]]

matrix2 = [[10, 11],
           [12, 13],
           [14, 15]]

# Multiply the matrices
result_matrix = multiply_matrices(matrix1, matrix2)

# Display the result
if result_matrix is not None:
    print("Result:")
    for row in result_matrix:
        print(row)

""" Binary Search Algorithm 
----------------------------------------
"""
#iterative implementation of binary search in Python
def binary_search(a_list, item):
    """Performs iterative binary search to find the position of an integer in a given, sorted, list.
    a_list -- sorted list of integers
    item -- integer you are searching for the position of
    """
    first = 0
    last = len(a_list) - 1
    while first <= last:
        i = (first + last) / 2
        if a_list[i] == item:
            return ' found at position '.format(item=item, i=i)
        elif a_list[i] > item:
            last = i - 1
        elif a_list[i] < item:
            first = i + 1
        else:
            return ' not found in the list'.format(item=item)
#recursive implementation of binary search in Python
def binary_search_recursive(a_list, item):
    """Performs recursive binary search of an integer in a given, sorted, list.
    a_list -- sorted list of integers
    item -- integer you are searching for the position of
    """
    first = 0
    last = len(a_list) - 1
    if len(a_list) == 0:
        return ' was not found in the list'.format(item=item)
    else:
        i = (first + last) // 2
        if item == a_list[i]:
            return ' found'.format(item=item)
        else:
            if a_list[i] < item:
                return binary_search_recursive(a_list[i+1:], item)
            else:
                return binary_search_recursive(a_list[:i], item)

# @return a list of strings, [s1, s2]
def letterCombinations(self, digits):
    if '' == digits: return []
    kvmaps = {
        '2': 'abc',
        '3': 'def',
        '4': 'ghi',
        '5': 'jkl',
        '6': 'mno',
        '7': 'pqrs',
        '8': 'tuv',
        '9': 'wxyz'
    }
    return reduce(lambda acc, digit: [x + y for x in acc for y in kvmaps[digit]], digits, [''])

magnitude = lambda bits: 1_000_000_000_000_000_000 % (2 ** bits)
sign = lambda bits: -1 ** (1_000_000_000_000_000_000 // (2 ** bits))

print("64 bit sum:", magnitude(64) * sign(64))
print("32 bit sum:", magnitude(32) * sign(32))
print("16 bit sum:", magnitude(16) * sign(16))

#84 48 13 20 61 20 33 97 34 45 6 63 71 66 24 57 92 74 6 25 51 86 48 15 64 55 77 30 56 53 37 99 9 59 57 61 30 97 50 63 59 62 39 32 34 4 96 51 8 86 10 62 16 55 81 88 71 25 27 78 79 88 92 50 16 8 67 82 67 37 84 3 33 4 78 98 39 64 98 94 24 82 45 3 53 74 96 9 10 94 13 79 15 27 56 66 32 81 77
# xor a list of integers to find the lonely integer
res = a[0]
    for i in range(1,len(a)):
        res = res ^ a[i]