How to Think Like a Computer Scientist - Learning with Python, 2008a

9.7 Many buckets 103
bucketWidth = 1.0 / numBuckets
for i in range(numBuckets):
low = i * bucketWidth
high = low + bucketWidth
print low, "to", high
To compute the low end of each bucket, we multiply the loop variable by the
bucket width. The high end is just a bucketWidth away.
With numBuckets = 8, the output is:
0.0 to 0.125
0.125 to 0.25
0.25 to 0.375
0.375 to 0.5
0.5 to 0.625
0.625 to 0.75
0.75 to 0.875
0.875 to 1.0
You can confirm that each bucket is the same width, that they don’t overlap, and
that they cover the entire range from 0.0 to 1.0.
Now back to the first problem. We need a way to store eight integers, using the
loop variable to indicate one at a time. By now you should be thinking, “List!”
We have to create the bucket list outside the loop, because we only want to do it
once. Inside the loop, we’ll call inBucket repeatedly and update the i-eth element
of the list:
numBuckets = 8
buckets = [0] * numBuckets
bucketWidth = 1.0 / numBuckets
for i in range(numBuckets):
low = i * bucketWidth
high = low + bucketWidth
buckets[i] = inBucket(t, low, high)
print buckets
With a list of 1000 values, this code produces this bucket list:
[138, 124, 128, 118, 130, 117, 114, 131]
These numbers are fairly close to 125, which is what we expected. At least, they
are close enough that we can believe the random number generator is working.
As an exercise, test this function with some longer lists, and see if the
number of values in each bucket tends to level off.