[Array] Valid Mountain Array - Easy

A valid mountain array is an array that follows certain rules. It forms a peak where the numbers first go up and then go down. To check if an array is a valid mountain array, it needs to have at least three elements. It should start with a sequence that increases. Then it must reach a peak and follow with a sequence that decreases. This problem is important in algorithm design. We can solve it using many programming languages like Java, Python, and C++.

In this article, we will look at the valid mountain array in detail. We will talk about the problem overview and the rules that make a valid mountain array. We will also give solutions in Java, Python, and C++. Plus, we will discuss the best algorithms, edge cases, performance analysis, common mistakes, and answer frequently asked questions.

  • Array Valid Mountain Array Problem Overview
  • Understanding the Valid Mountain Array Criteria
  • Java Solution for Valid Mountain Array
  • Python Implementation of Valid Mountain Array
  • C++ Approach to Valid Mountain Array
  • Optimal Algorithm for Valid Mountain Array
  • Edge Cases in Valid Mountain Array
  • Performance Analysis of Valid Mountain Array Solutions
  • Common Errors in Valid Mountain Array Implementation
  • Frequently Asked Questions

If you want to read more about related array problems, you can check out articles like Array Two Sum and Array Best Time to Buy and Sell Stock.

Understanding the Valid Mountain Array Criteria

We define a valid mountain array by certain rules. An array must meet these rules to be called a mountain array. Here are the main points that show a valid mountain array:

  1. Length Requirement: The array needs to have at least three elements. If it has less than three, it can’t be a mountain.

  2. Strictly Increasing and Decreasing:

    • The array must first go up to a peak, which is the highest point. Then it must go down.
    • There must be at least one number before the peak and one number after the peak.

  3. Peak Position:

    • The peak can’t be the first or last number in the array.

Example of a Valid Mountain Array

For example, the array [0, 2, 3, 4, 3, 2, 1] is a valid mountain array. - It goes up from 0 to 4, and then it goes down from 4 to 1.

Example of an Invalid Mountain Array

On the other hand, [1, 2, 3] is not a valid mountain array. It does not go down after the peak. Also, [3, 2, 1] is not valid because it does not go up first.

Criteria Summary

  • Length must be 3 or more
  • There needs to be one part that goes up and one part that goes down
  • The peak should not be at the start or the end of the array

These rules help us create algorithms that check if an array is a valid mountain array or not.

Java Solution for Valid Mountain Array

To check if an array is a valid mountain array in Java, we need to follow some rules. A valid mountain array must meet these conditions:

  1. The array must have at least three elements.
  2. There should be a peak. The elements must increase to the peak and then decrease after the peak.

Here is a simple way to do this in Java:

public class ValidMountainArray {
    public boolean validMountainArray(int[] arr) {
        int n = arr.length;
        if (n < 3) return false;

        int i = 0;

        // Ascend to peak
        while (i + 1 < n && arr[i] < arr[i + 1]) {
            i++;
        }

        // Peak cannot be the first or last element
        if (i == 0 || i == n - 1) return false;

        // Descend from peak
        while (i + 1 < n && arr[i] > arr[i + 1]) {
            i++;
        }

        return i == n - 1;
    }
}

Explanation of Code:

  • First, we check if the length of the array is less than 3. We return false if it is.
  • We use a variable i to go through the array. The first while loop increases i while the current element is smaller than the next one. This shows we are going up.
  • After we reach the peak, we check if i is the first or the last index. If it is, the array is not a valid mountain.
  • The second while loop decreases i while the current element is bigger than the next one. This shows we are going down.
  • Lastly, we check if i is at the last index. This means we have gone through the whole array.

This Java solution checks the rules for a valid mountain array in O(n) time. For more related array problems, we can check the Array Two Sum and Array Monotonic Array articles.

Python Implementation of Valid Mountain Array

To check if an array is a valid mountain array in Python, we need to follow some simple rules. A valid mountain array must meet these conditions:

  1. The array must have at least three elements.
  2. There must be a peak element that is greater than the ones next to it.
  3. The elements before the peak must go up in value.
  4. The elements after the peak must go down in value.

Here is a simple Python code to check if an array is a valid mountain array:

def validMountainArray(arr):
    n = len(arr)
    if n < 3:
        return False
    
    i = 0
    
    # Go up to the peak
    while i + 1 < n and arr[i] < arr[i + 1]:
        i += 1
    
    # Peak cannot be the first or last element
    if i == 0 or i == n - 1:
        return False
    
    # Go down from the peak
    while i + 1 < n and arr[i] > arr[i + 1]:
        i += 1
    
    return i == n - 1

# Example usage
arr = [2, 1]
print(validMountainArray(arr))  # Output: False

arr = [0, 3, 2, 1]
print(validMountainArray(arr))  # Output: True

This code first checks how long the array is. Then it uses two loops to go through the array. One loop is for going up to the peak and the other is for going down. The last check makes sure we look at the whole array, confirming it is a valid mountain shape.

For more information on array problems, we can look at other articles like Array Contains Duplicate and Array Best Time to Buy and Sell Stock.

C++ Approach to Valid Mountain Array

We want to check if an array is a valid mountain array in C++. To do this, we need to make sure it follows some rules. First, it should increase to a peak. Then it should decrease after that peak. Also, the array must have at least three elements to be a valid mountain.

Here is a simple C++ code that checks these rules:

#include <vector>

bool validMountainArray(std::vector<int>& arr) {
    int n = arr.size();
    if (n < 3) return false;

    int i = 0;

    // Climb up
    while (i + 1 < n && arr[i] < arr[i + 1]) {
        i++;
    }

    // Peak can't be the first or the last element
    if (i == 0 || i == n - 1) return false;

    // Climb down
    while (i + 1 < n && arr[i] > arr[i + 1]) {
        i++;
    }

    return i == n - 1; // Check if we reached the end
}

Explanation of the Code:

  • The function validMountainArray takes a vector of integers as input.
  • First, it checks if the size of the array is less than 3. If yes, it returns false.
  • It uses a loop to increase i while the current element is less than the next. This shows the climbing up part of the array.
  • Then it checks if i is at the start or end of the array. This would not be a valid mountain.
  • Next, a second loop decreases i while the current element is greater than the next. This shows the climbing down part.
  • Finally, it checks if i reached the end of the array. This means we have a valid mountain.

Example Usage:

#include <iostream>

int main() {
    std::vector<int> arr = {0, 2, 3, 4, 3, 2, 1};
    if (validMountainArray(arr)) {
        std::cout << "The array is a valid mountain array." << std::endl;
    } else {
        std::cout << "The array is not a valid mountain array." << std::endl;
    }
    return 0;
}

Performance:

  • The time complexity is O(n) because we go through the array at most two times.
  • The space complexity is O(1) since we only use a small amount of extra space.

This way, we can easily find out if an array forms a valid mountain shape. For more array problems, you can check out the Array Best Time to Buy and Sell Stock article.

Optimal Algorithm for Valid Mountain Array

We can find out if an array is a valid mountain array in a smart way by using a two-pointer method. This method helps us go through the array just one time. So, it has a time complexity of O(n).

Criteria for a Valid Mountain Array

  1. The array must have at least three elements.
  2. There must be a peak element. It cannot be the first or last element.
  3. The elements before the peak should go up in value.
  4. The elements after the peak should go down in value.

Implementation Steps

  1. We start with two pointers. One pointer is at the beginning of the array (left) and the other is at the end (right).
  2. We move the left pointer to the right while the next element is bigger than the current one. This means it is strictly increasing.
  3. We move the right pointer to the left while the previous element is bigger than the current one. This means it is strictly decreasing.
  4. We check if the two pointers meet at a valid peak.

Java Solution

public boolean validMountainArray(int[] arr) {
    int n = arr.length;
    if (n < 3) return false;

    int left = 0, right = n - 1;

    while (left + 1 < n && arr[left] < arr[left + 1]) {
        left++;
    }
    while (right - 1 >= 0 && arr[right] < arr[right - 1]) {
        right--;
    }

    return left > 0 && right < n - 1 && left == right;
}

Python Implementation

def validMountainArray(arr):
    n = len(arr)
    if n < 3:
        return False

    left, right = 0, n - 1

    while left + 1 < n and arr[left] < arr[left + 1]:
        left += 1
    while right - 1 >= 0 and arr[right] < arr[right - 1]:
        right -= 1

    return left > 0 and right < n - 1 and left == right

C++ Approach

class Solution {
public:
    bool validMountainArray(vector<int>& arr) {
        int n = arr.size();
        if (n < 3) return false;

        int left = 0, right = n - 1;

        while (left + 1 < n && arr[left] < arr[left + 1]) {
            left++;
        }
        while (right - 1 >= 0 && arr[right] < arr[right - 1]) {
            right--;
        }

        return left > 0 && right < n - 1 && left == right;
    }
};

This good algorithm for checking a valid mountain array is efficient and clear. It works well even with large datasets. For more related topics, we can check articles on Array Contains Duplicate and Array Maximum Subarray.

Edge Cases in Valid Mountain Array

When we look at the problem of a valid mountain array, we need to think about some special cases. These cases can change if our solution is right or not. Here are some important edge cases we should remember when we check a mountain array:

  1. Array Lengths:
    • An array with less than 3 elements can’t be a mountain array. For example, both [1] and [1, 2] are not valid.
  2. Flat Terrain:
    • Arrays where all numbers are the same, like [2, 2, 2, 2], should give false. There are no slopes here.
  3. Strictly Increasing or Decreasing Arrays:
    • Arrays that only go up, like [1, 2, 3, 4], or only go down, like [4, 3, 2, 1], should also return false because they do not have a peak.
  4. Valid Mountain Arrays with Repeats:
    • Arrays like [0, 3, 2, 1] are valid. But [0, 3, 3, 2, 1] is not valid because a peak can’t have the same number twice.
  5. Single Peak:
    • Arrays with one peak, like [1, 2, 3, 2], are valid. We need to make sure there are numbers before and after the peak.
  6. Multiple Peaks:
    • Arrays like [1, 3, 2, 4] are not valid since they have more than one peak.
  7. Boundary Values:
    • We should think about numbers at the limits of the input rules. This means arrays with the highest or lowest allowed numbers.
  8. Input Types:
    • We must check that the input is always an integer array. We should handle cases where the input has non-integer types.

By finding and testing these edge cases, we can make sure our solution for the valid mountain array problem works well and can handle all situations.

Here’s a sample code snippet that checks these edge cases:

public boolean validMountainArray(int[] A) {
    int n = A.length;
    if (n < 3) return false;

    int i = 0;

    // Ascend
    while (i + 1 < n && A[i] < A[i + 1]) {
        i++;
    }

    // Peak can't be first or last
    if (i == 0 || i == n - 1) return false;

    // Descend
    while (i + 1 < n && A[i] > A[i + 1]) {
        i++;
    }

    return i == n - 1;
}

This function checks the edge cases and sees if the input array is a valid mountain array or not.

Performance Analysis of Valid Mountain Array Solutions

We can look at how well the solutions for the “Valid Mountain Array” problem perform by checking their time and space complexity. This problem is about finding out if an array is a mountain array. A mountain array must go up to a peak and then go down.

Time Complexity

  • Optimal Solution: The best solution works in O(n) time. Here, n is the length of the array. We can do this by going through the array once to find the peak and check the rules at the same time.
  • Brute Force Solution: A simple way that checks all possible peaks takes O(n^2) time because it goes through the array two times.

Space Complexity

  • Optimal Solution: The space used is O(1). This means it only needs a small amount of extra space for some variables. This does not change with the input size.
  • Brute Force Solution: The space can also stay O(1) if we do not use any extra data structures.

Example Analysis

For an array like [2, 1], it does not meet the mountain array rules because it has no peak. The best solution can quickly tell that this array is not a mountain array in one go.

But for an array like [0, 3, 2, 1], the steps are: 1. Go through the array to find the peak at index 1. 2. Check that the numbers before and after the peak follow the strict increase and strict decrease rules.

Performance Metrics

  • Best Case: If the array is only increasing or only decreasing, the algorithm can finish early. It will still keep O(n) time.
  • Worst Case: The worst case happens when the peak is at one end of the array. This means we have to check every element.

Practical Considerations

When we make solutions for the valid mountain array, we should think about these points:

  • The size of the input can change how well the solution works. So we prefer O(n) solutions.
  • We need to take care of special cases, like arrays with less than three elements, because they cannot be mountains.
  • We should test with different datasets to make sure the performance stays good.

For more information on array problems, you can check the Array Two Sum article.

Common Errors in Valid Mountain Array Implementation

When we work on a solution for the Valid Mountain Array problem, we can face some common mistakes. Knowing these errors helps us create a better implementation.

  1. Incorrect Index Range: We should make sure that the loop indices for checking mountain conditions do not go out of bounds. We need to go through the array from index 0 to n-1, where n is the length of the array.

  2. Not Checking Array Length: A valid mountain array needs at least three elements. We must check if the array length is less than 3 at the start of our function.

    if (arr.length < 3) return false;

  3. Not Distinguishing Between Up and Down: The change from going up to going down must be clear. If we do not manage this change well, we can get wrong results while checking if it is a mountain.

    int i = 0;
while (i + 1 < arr.length && arr[i] < arr[i + 1]) {
    i++;
}

  4. Allowing Flat Sections: A mountain array can’t have flat parts. We need to allow only strictly increasing or strictly decreasing parts.

  5. Final Peak Check: After we go through the array, we must check that we have passed the peak. If we stop at the start or the end of the array, it is not a valid mountain.

    return i > 0 && i < arr.length - 1;

  6. Handling Edge Cases: Sometimes arrays with negative numbers or zeros can confuse us. We should have proper checks that handle all kinds of numbers.

  7. Logic Errors: We need to make sure our logic for finding the peak and the next descent is correct. Wrong conditions can give us wrong results.

  8. Redundant Checks: We should not make unnecessary checks after we find out if the mountain structure is valid. We need to focus on a clear and quick exit from the function.

By knowing these common errors in Valid Mountain Array implementation, we can create a better solution. If we want to read more about related array problems, we can check out Array Two Sum or Array Best Time to Buy and Sell Stock.

Frequently Asked Questions

What is a valid mountain array?

A valid mountain array has some simple rules. It must have at least three elements. First, it should increase to a peak. Then, it should decrease after the peak. We can find an index i where all items before this index j < i are less than the next item arr[j+1]. And all items after this index k > i must be greater than the next item arr[k+1]. If the array follows these rules, we call it a valid mountain array.

How do I check if an array is a valid mountain array in Java?

To check if an array is a valid mountain array in Java, we can go through the array to find the peak. After that, we check if the items before the peak are increasing and those after the peak are decreasing. Here is a simple way to do it:

public boolean validMountainArray(int[] arr) {
    int n = arr.length;
    if (n < 3) return false;
    
    int i = 0;
    while (i + 1 < n && arr[i] < arr[i + 1]) i++;
    
    if (i == 0 || i == n - 1) return false;
    
    while (i + 1 < n && arr[i] > arr[i + 1]) i++;
    
    return i == n - 1;
}

What are some common mistakes when implementing valid mountain array algorithms?

When we implement valid mountain array algorithms, we can make some common mistakes. One mistake is not checking the length of the array before we start. Another mistake is not handling the peak condition correctly. We should also make sure both the increasing and decreasing parts are strict. Sometimes we forget edge cases, like arrays with only two elements or flat arrays. These can cause wrong results. For more help on array problems, we can look at resources like Array Contains Duplicate.

Can a valid mountain array contain equal elements?

No, a valid mountain array cannot have equal elements. By definition, elements must increase strictly to a peak and then decrease strictly. This means no two adjacent elements can be equal. If there are any equal elements, then the array is not a valid mountain array. For more similar ideas, we can check out Monotonic Arrays.

Are there any performance considerations for valid mountain array implementations?

Yes, we should think about performance when we implement the valid mountain array algorithm. The best time complexity for a good solution is O(n). This is because we only need to go through the array once to check if it is a mountain. Space complexity can be O(1) if we just use a few pointers to go through the array. For better algorithm strategies, we can look at the Optimal Algorithm for Valid Mountain Array.

By looking at these frequently asked questions, we can understand better how to find and use the valid mountain array algorithm. If we want to learn about related array problems, we can check out articles like Array Two Sum and Array Maximum Subarray for more information.