from typing import List, Dict

def build_placements(shoes: List[str]) -> Dict[str, List[int]]:
    """Return a dictionary where each key is a company and each value is a
    list of placements by people wearing shoes made by that company.
    
    >>> build_placements(['Saucony', 'Asics', 'Asics', 'NB', 'Saucony', \
    'Nike', 'Asics', 'Adidas', 'Saucony', 'Asics'])
    {'Saucony': [1, 5, 9], 'Asics': [2, 3, 7, 10], 'NB': [4], 'Nike': [6], 'Adidas': [8]}
    """
    placements = {}
    
    #for shoe in shoes: # can't iterate over the elements (need the indices for this function
    for i in range(len(shoes)):
        if not shoes[i] in placements:
            placements[shoes[i]] = [i + 1]
        else:
            placements[shoes[i]].append(i + 1)
    
    
    # another way: initialize empty list and append after.  don't need the else
    
    #for i in range(len(shoes)):
        #if not shoes[i] in placements:
            #placements[shoes[i]] = []
        #placements[shoes[i]].append(i + 1)
    
    return placements