# a1q3 (Python)
    
def ave(data, index, width):
    # returns (data[i] + data[i+1] + ... + data[index+width-1])/width 
    sum = 0.0
    for j in range(index, index+width):
        sum += data[j]
    return sum/width

def averageAndScale(data):
    # harcode the number of bins
    size = 20
    # bins will store the data for each "bin" (averaged values) 
    bins = [0]*size

    # determine how many values will be used in each bin
    # (i.e., the number of values for each average except maybe the last)
    width = 0
    if len(data) % size == 0:
        width = len(data) // size
    else:
        width = (len(data) // size) + 1
    
    # add this many averages using width numbers for the average
    first = len(data) // width # integer division will round down automatically
    for index in range(0, first):
        bins[index] = ave(data, index*width, width)
    
    # add the rest of the bin data now
    if first*width < len(data):
        # need another average with less numbers
        bins[first] = ave(data, first*width, len(data)-first*width)
    
    # find the largest value of the bins
    biggest = bins[0]
    for i in range(size):
        if biggest < bins[i]:
            biggest = bins[i]

    # determine the scaling factor
    # biggest * scale = 20
    scale = 20 / biggest

    # compute the scaled bins and put in a new list
    # for output
    out = [0]*size
    for i in range(size):
        out[i] = bins[i]*scale
    
    # print statements to trace what is happening in the function
    print(f'        width={width} first={first} biggest={biggest} scale={scale}')
    print(' bins =' + str(bins))
    return out

def main():
    # for testing
    in1 = [2*i for i in range(1,21)]
    print('##\n##', 'len(data) = 20')
    print('input =' + str(in1))
    print('output=' + str(averageAndScale(in1)))

    print('##\n##', 'len(data) = 40')
    in2 = [2*i for i in range(1,41)]
    print('input =' + str(in2))
    print('output=' + str(averageAndScale(in2)))

    print('##\n##', 'len(data) = 17')
    in3 = [2*i for i in range(1,18)]
    print('input =' + str(in3))
    print('output=' + str(averageAndScale(in3)))

    print('##\n##', 'len(data) = 38')
    in4 = [2*i for i in range(1,39)]
    print('input =' + str(in4))
    print('output=' + str(averageAndScale(in4)))


if __name__ == '__main__':
    main()