Problem

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[B.length - 1]

Example 1:

Input: [2,1]
Output: false

Example 2:

Input: [3,5,5]
Output: false

Example 3:

Input: [0,3,2,1]
Output: true

Note:

1. 0 <= A.length <= 10000
2. 0 <= A[i] <= 10000 

Solution

Use has_up and has_down to track whether we have A[i] > A[i – 1] and A[i] < A[i – 1] receptively.

return false if any of the following happened:

1. size(A) < 3
2. has_down happened before has_up
3. not has_down or not has_up
4. A[i – 1] < A[i] after has_down
5. A[i – 1] > A[i] before has_up

Time complexity: O(n)

Space complexity: O(n)