Valid mountain array [One Pass]

Time: O(N); Space: O(1); easy

Given an array A of integers, return true if and only if it is a valid mountain array.

Recall that A is a mountain array if and only if:

  • A.length >= 3

  • There exists some i with 0 < i < A.length - 1 such that:

    • A[0] < A[1] < … A[i-1] < A[i]

    • A[i] > A[i+1] > … > A[A.length - 1]

Example 1:

Input: A = [2, 1]

Output: False

Example 2:

Input: A = [3, 5, 5]

Output: False

Example 3:

Input: A = [0, 3, 2, 1]

Output: True

Notes:

  • 0 <= A.length <= 10000

  • 0 <= A[i] <= 10000

One Pass

Intuition If we walk along the mountain from left to right, we have to move strictly up, then strictly down.

Algorithm Let’s walk up from left to right until we can’t: that has to be the peak. We should ensure the peak is not the first or last element. Then, we walk down. If we reach the end, the array is valid, otherwise its not.

[5]:

class Solution1(object):
    def validMountainArray(self, A):
        """
        :type A: List[int]
        :rtype: bool
        """
        i = 0
        # walk up
        while i + 1 < len(A) and A[i] < A[i+1]:
            i += 1

        # peak can't be first or last
        j = len(A) - 1
        while j - 1 >= 0 and A[j-1] > A[j]:
            j -= 1
        return 0 < i == j < len(A)-1

[6]:

s = Solution1()
A = [2, 1]
assert s.validMountainArray(A) == False
A = [3, 5, 5]
assert s.validMountainArray(A) == False
A = [0, 3, 2, 1]
assert s.validMountainArray(A) == True

[7]:

class Solution2(object):
    def validMountainArray(self, A):
        N = len(A)
        i = 0

        # walk up
        while i+1 < N and A[i] < A[i+1]:
            i += 1

        # peak can't be first or last
        if i == 0 or i == N-1:
            return False

        # walk down
        while i + 1 < N and A[i] > A[i+1]:
            i += 1

        return i == N-1

[8]:

s = Solution2()
A = [2, 1]
assert s.validMountainArray(A) == False
A = [3, 5, 5]
assert s.validMountainArray(A) == False
A = [0, 3, 2, 1]
assert s.validMountainArray(A) == True