7. almostIncreasingSequence

Task

Given a sequence of integers as an array, determine whether it is possible to obtain a strictly increasing sequence by removing no more than one element from the array.

Note: sequence a0, a1, …, an is considered to be a strictly increasing if a0 < a1 < … < an. Sequence containing only one element is also considered to be strictly increasing.

Example

• For sequence = [1, 3, 2, 1], the output should be almostIncreasingSequence(sequence) = false.
  There is no one element in this array that can be removed in order to get a strictly increasing sequence.

• For sequence = [1, 3, 2], the output should be almostIncreasingSequence(sequence) = true.
  You can remove 3 from the array to get the strictly increasing sequence [1, 2]. Alternately, you can remove 2 to get the strictly increasing sequence [1, 3].

Input/Output

• [execution time limit]
  4 seconds (py3)

• [input] array.integer sequence
  Guaranteed constraints: 2 ≤ sequence.length ≤ 105, -105 ≤ sequence[i] ≤ 105.

• [output] boolean
  Return true if it is possible to remove one element from the array in order to get a strictly increasing sequence, otherwise return false.

My Solution

def almostIncreasingSequence(sequence):
    removeCount = 0
    if sequence[0] >= sequence[1]:
        removeCount += 1
    i = 2
    while i < len(sequence):
        if sequence[i - 1] >= sequence[i]:
            removeCount += 1
            if sequence[i - 2] >= sequence[i]:
                sequence[i] = sequence[i - 1]
        i += 1

    return (removeCount < 2)