# We reuse the following binary operators from last time
def add(x, y):
    return x + y

def mul(x, y):
    return x * y

def lesser(x, y):
    if x < y:
        return x
    else:
        return y

def greater(x, y):
    if x > y:
        return x
    else:
        return y

# Also consider the following higher order functions
map
reduce
from toolz import accumulate

# When showing off numpy we used the cumulative sum method

import numpy as np
X = np.arange(20)

X[X>=10].cumsum()

# Accumulate is a general version of this

data = range(10, 20)

list(accumulate(add, data))

X[X>=10].cumprod()

list(accumulate(mul, data))

data1 = [1, 2, 3, 4, 5]
data2 = [10, 20, 30, 40, 50]
map(add, data1, data2)

reduce(lesser, [5, 3, 2, 7, 3], 999999999)

list(accumulate(lesser, [5, 3, 2, 7, 3]))

map(lesser, [5, 3, 2, 7, 3], [1, 9, 2, 6, 6])  # Pairwise lesser across the two lists

def longer(a, b):
    ...
    
assert longer('cat', 'mouse') == 'mouse'  # because cat is of length 3 and mouse is of length 5

# Use reduce to find the longest word

animals = ['cat', 'mouse', 'lion', 'goose', 'giraffe', 'mule']

# Use accumulate to track the longest word over time.
# This should be a list where the first element is 'cat', the last is 'giraffe', 
# and each intermediate element is the longest word up to that point


# Use map to create a list of the pairwise longest among the following two lists
animals = ['cat', 'mouse', 'lion', 'goose', 'giraffe', 'mule']
fruits  = ['apple', 'orange', 'banana', 'date', 'grape', 'strawberry']