passing_cars.py

"""A non-empty zero-indexed array A consisting of N integers is given.

The consecutive elements of array A represent consecutive cars on a road.

Array A contains only 0s and/or 1s:

0 represents a car traveling east,
1 represents a car traveling west.
The goal is to count passing cars. We say that a pair of cars (P, Q),
where 0 ≤ P < Q < N, is passing when P is traveling to the east and Q is
traveling to the west.

For example, consider array A such that:

  A[0] = 0
  A[1] = 1
  A[2] = 0
  A[3] = 1
  A[4] = 1
We have five pairs of passing cars: (0, 1), (0, 3), (0, 4), (2, 3), (2, 4).

Write a function:

def solution(A)

that, given a non-empty zero-indexed array A of N integers,
returns the number of pairs of passing cars.

The function should return −1 if the number of pairs of passing cars
exceeds 1,000,000,000.

For example, given:

  A[0] = 0
  A[1] = 1
  A[2] = 0
  A[3] = 1
  A[4] = 1
the function should return 5, as explained above.

Assume that:

N is an integer within the range [1..100,000];
each element of array A is an integer that can have one of the following
values: 0, 1.
Complexity:

expected worst-case time complexity is O(N);
expected worst-case space complexity is O(1), beyond input storage
(not counting the storage required for input arguments).
Elements of input arrays can be modified.
"""


def solution(numbers):
    going_east = 0
    passing = 0
    for num in numbers:
        if num == 0:
            going_east += 1
        else:
            passing += going_east
            if passing > 10 ** 9:
                return -1
    return passing