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non_neg_int.py
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non_neg_int.py
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# Given an array arr of n unique non-negative integers, how can you most efficiently find a non-negative integer that is not in the array?
# Your solution should return such an integer or null if arr contains all possible integers.
# Analyze the runtime and space complexity of your solution.
import sys
def find_int(arr):
""" Takes an array and returns a non-negative integer that is not in the original array. Returns null if all integers are in the array.
Runtime: O(n)
Spacetime: O(n)
>>> find_int([0, 2, 1, 3, 4, 5, 11, 32, 42, 50, 100, 6])
7
>>> find_int([2, 4, 5, 1, 3])
0
>>> find_int([0, 2, 4, 5, 1, 3])
6
>>> find_int([0, 2, 4, 5, 1, 3, 6, 8])
7
>>> find_int([])
0
"""
arr2 = {}
# If the length of the array is equal to the maximum allowed integers, there are no missing integers in the array.
if len(arr) == sys.maxint:
return None
# Create an O(1) lookup hashtable using the integers from the array as the key, and set the value to True
for i in range(len(arr)):
arr2[arr[i]] = True
# Loop through the length of the array + 1 and check if the number is a key in the hashtable. If it isn't return that number.
for i in range(len(arr) + 1):
if not arr2.get(i):
return i
return None
if __name__ == '__main__':
import doctest
results = doctest.testmod()
if results.failed == 0:
print 'ALL TESTS PASSED!'