Valid Mountain Array in Python

A valid mountain array is an array that rises to a peak and then falls, resembling a mountain shape. To be valid, it must have at least 3 elements, strictly increase to a peak, then strictly decrease.

Mountain Array Requirements

An array is a valid mountain if it satisfies these conditions:

• Array size >= 3
• There exists a peak index i where:
• Elements strictly increase: A[0]
• Elements strictly decrease: A[i] > A[i+1] > ... > A[length-1]

Algorithm Approach

We use a two-phase traversal approach:

1. Ascending phase: Walk up while elements are increasing
2. Descending phase: Walk down while elements are decreasing
3. Validation: Check if we reached the end after both phases

Implementation

def validMountainArray(A):
    if len(A) < 3:
        return False
    
    i = 1
    
    # Walk up - ascending phase
    while i < len(A) and A[i] > A[i-1]:
        i += 1
    
    # Peak cannot be at start or end
    if i == 1 or i == len(A):
        return False
    
    # Walk down - descending phase  
    while i < len(A) and A[i] < A[i-1]:
        i += 1
    
    # Should reach the end
    return i == len(A)

# Test examples
print(validMountainArray([0, 3, 2, 1]))     # Valid mountain
print(validMountainArray([3, 5, 5]))        # Plateau - invalid
print(validMountainArray([0, 1, 2, 3]))     # Only ascending
print(validMountainArray([3, 2, 1, 0]))     # Only descending

True
False
False
False

Step-by-Step Explanation

Let's trace through the algorithm with example [0, 3, 2, 1]:

1. Initial check: Length = 4 >= 3 ?
2. Ascending phase: i=1?2 (02 stops)
3. Peak validation: i=2, not at start/end ?
4. Descending phase: i=2?4 (3>2>1)
5. Final check: i=4 equals array length ?

Edge Cases

Conclusion

A valid mountain array requires strict ascending followed by strict descending phases. The algorithm uses two-pointer traversal to verify both phases exist and cover the entire array.