numegil numegil - 3 years ago 137
Python Question

Expected number of hash collisions

I feel like I'm way overthinking this problem, but here goes anyway...

I have a hash table with M slots in its internal array. I need to insert N elements into the hash table. Assuming that I have a hash function that randomly inserts am element into a slot with equal probability for each slot, what's the expected value of the total number of hash collisions?

(Sorry that this is more of a math question than a programming question).

Here's some code I have to simulate it using Python. I'm getting numerical answers, but having trouble generalizing it to a formula and explaining it.

import random
import pdb

N = 5
M = 8

NUM_ITER = 100000

def get_collisions(table):
col = 0
for item in table:
if item > 1:
col += (item-1)
return col

def run():
table = [0 for x in range(M)]

for i in range(N):
table[int(random.random() * M)] += 1

#print table
return get_collisions(table)

# Main

total = 0
for i in range(NUM_ITER):
total += run()

print float(total)/NUM_ITER

Answer Source

You'll find the answer here: The expected number of collisions for m buckets and n inserts is

n - m * (1 - ((m-1)/m)^n).

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