Question

You are given an Array of numbers and they are unsorted/random order. You are supposed to find the longest sequence of consecutive numbers in the array. Note the sequence need not be in sorted order within the array. Here is an example :

Input :

A[] = {10,21,45,22,7,2,67,19,13,45,12,11,18,16,17,100,201,20,101}  

Output is :

{16,17,18,19,20,21,22}  

The solution needs to be of O(n) complexity.

I am told that the solution involves using a hash table and I did come across few implementations that used 2 hash tables. One cannot sort and solve this because sorting would take O(nlgn) which is not what is desired.

Answer 1

Here is a solution in Python that uses just a single hash set and doesn’t do any fancy interval merging.

def destruct_directed_run(num_set, start, direction):
  while start in num_set:
    num_set.remove(start)
    start += direction
  return start

def destruct_single_run(num_set):
  arbitrary_member = iter(num_set).next()
  bottom = destruct_directed_run(num_set, arbitrary_member, -1) 
  top = destruct_directed_run(num_set, arbitrary_member + 1, 1)
  return range(bottom + 1, top)

def max_run(data_set):
  nums = set(data_set)
  best_run = []
  while nums:
    cur_run = destruct_single_run(nums)
    if len(cur_run) > len(best_run):
      best_run = cur_run
  return best_run

def test_max_run(data_set, expected):
  actual = max_run(data_set)
  print data_set, actual, expected, 'Pass' if expected == actual else 'Fail'

print test_max_run([10,21,45,22,7,2,67,19,13,45,12,11,18,16,17,100,201,20,101], range(16, 23))
print test_max_run([1,2,3], range(1, 4))
print max_run([1,3,5]), 'any singleton output fine'