# lab10.py
# YOUR NAME(S) AND NETID(S) HERE
# DATE COMPLETED HERE
"""Loop functions for lab 10"""


def numberof(thelist, v):
    """Returns: number of times v occurs in thelist.
    
    Precondition: thelist is a list of ints
                  v is an int"""
    count = 0
         
    # IMPLEMENT THIS WITH A WHILE LOOP HERE
    return count


def replace_copy(thelist,a,b):
    """Returns: a COPY of thelist but with all occurrences of a replaced by b. 
    
    Example: replace([1,2,3,1], 1, 4) is [4,2,3,4].
        
    Precondition: thelist is a list of ints
                  a and b are ints"""
    copy = []
    
    # IMPLEMENT THIS WITH A WHILE LOOP HERE
    return copy
        


def replace(thelist,a,b):
    """MODIFY thelist so that all occurrences of a replaced by b. 
    
    This function should have NO RETURN STATEMENT
    
    Example: if a = [1,2,3,1] then a becomes [4,2,3,4] after the
    function call replace(a,1,4).
        
    Precondition: thelist is a list of ints
                  a and b are ints"""
    # IMPLEMENT THIS WITH A WHILE LOOP
    pass


# OPTIONAL FUNCTION
def cuberoot(c,err=1e-6):
    """Returns: the (postive) cube root of c to with the given margin of error.
    
    Use Newton's Method to find a root of the polynomial f(x) = x^3-c
    
    Newton's Method produces a sequence where
    
        x_(n+1) = x_n - f(x_n)/f'(x_n) = x_n - (x_n*x_n*x_n-c)/(3x_n*x_n)
    
    which we simplify to
    
        x_(n+1) = 2*x_n/3 + c/(3*x_n*x_n)
    
    We can stop this process and use x_n as an approximation of the
    square root of c.  The error when we do this is less than
    |x_n*x_n*x_n - c|.  So we loop until this error is less than err.
    
    Precondition: c, err > 0 is a number."""
    # IMPLEMENT THIS WITH A WHILE LOOP   
    return 0 # STUB RETURN