

def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )      ->     Tuple:






    '''simple docstring'''
    __UpperCAmelCase									=			len(SCREAMING_SNAKE_CASE      )
    # Create a stack and push index of fist element to it
    __UpperCAmelCase									=			[]
    st.append(0      )

    # Span value of first element is always 1
    __UpperCAmelCase									=			1

    # Calculate span values for rest of the elements
    for i in range(1       ,   SCREAMING_SNAKE_CASE      ):
        # Pop elements from stack while stack is not
        # empty and top of stack is smaller than price[i]
        while len(SCREAMING_SNAKE_CASE      ) > 0 and price[st[0]] <= price[i]:
            st.pop()

        # If stack becomes empty, then price[i] is greater
        # than all elements on left of it, i.e. price[0],
        # price[1], ..price[i-1]. Else the price[i]  is
        # greater than elements after top of stack
        __UpperCAmelCase									=			i + 1 if len(SCREAMING_SNAKE_CASE      ) <= 0 else (i - st[0])

        # Push this element to stack
        st.append(SCREAMING_SNAKE_CASE      )


def       __a       (   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )      ->     Tuple:






    '''simple docstring'''
    for i in range(0       ,   SCREAMING_SNAKE_CASE      ):
        print(arr[i]       ,   end=''' '''      )


# Driver program to test above function
A_		:			List[Any]										=   [10, 4, 5, 90, 120, 80]
A_		:			Union[str, Any]										=   [0 for i in range(len(price) + 1)]

# Fill the span values in array S[]
calculation_span(price, S)
print_array(S, len(price))







import numpy as np


def       __a       (   SCREAMING_SNAKE_CASE      )      ->     Tuple:






    '''simple docstring'''
    __UpperCAmelCase					,     __UpperCAmelCase									=			a.shape
    __UpperCAmelCase									=			min(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE      )
    __UpperCAmelCase									=			np.eye(SCREAMING_SNAKE_CASE      )
    __UpperCAmelCase									=			a.copy()

    for k in range(t - 1      ):
        # select a column of modified matrix A':
        __UpperCAmelCase									=			r[k:, [k]]
        # construct first basis vector
        __UpperCAmelCase									=			np.zeros_like(SCREAMING_SNAKE_CASE      )
        __UpperCAmelCase									=			1.0
        # determine scaling factor
        __UpperCAmelCase									=			np.linalg.norm(SCREAMING_SNAKE_CASE      )
        # construct vector v for Householder reflection
        __UpperCAmelCase									=			x + np.sign(x[0]      ) * alpha * ea
        v /= np.linalg.norm(SCREAMING_SNAKE_CASE      )

        # construct the Householder matrix
        __UpperCAmelCase									=			np.eye(m - k      ) - 2.0 * v @ v.T
        # pad with ones and zeros as necessary
        __UpperCAmelCase									=			np.block([[np.eye(SCREAMING_SNAKE_CASE      ), np.zeros((k, m - k)      )], [np.zeros((m - k, k)      ), q_k]]      )

        __UpperCAmelCase									=			q @ q_k.T
        __UpperCAmelCase									=			q_k @ r

    return q, r


if __name__ == "__main__":
       import doctest

       doctest.testmod()




