What is the time complexity of Monotonic Array?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Monotonic Array?

This problem uses Array. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Monotonic Array?

Insight 1: An array can be both monotonically increasing and monotonically decreasing if all elements are the same. Insight 2: We can check for both increasing and decreasing properties in a single pass through the array.

Which companies ask LeetCode 896. Monotonic Array in interviews?

This problem is frequently asked at Ozon.

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Monotonic Array - LeetCode 896 Solution

Q: How to solve Monotonic Array?

The provided solution uses a simple and efficient approach. It initializes two boolean variables, `increasing` and `decreasing`, to `true`. Then, it iterates through the array, comparing each element to the previous one. If it finds an element that violates the increasing property, it sets `increasing` to `false`. Similarly, if it finds an element that violates the decreasing property, it sets `decreasing` to `false`. Finally, it returns `true` if either `increasing` or `decreasing` is still `true`, indicating that the array is monotonic.

Monotonic Array - Complete Solution Guide

Monotonic Array is LeetCode problem 896, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

An array is monotonic if it is either monotone increasing or monotone decreasing. An array nums is monotone increasing if for all i <= j , nums[i] <= nums[j] . An array nums is monotone decreasing if for all i <= j , nums[i] >= nums[j] . Given an integer array nums , return true if the given array is monotonic, or false otherwise . Example 1: Input: nums = [1,2,2,3] Output: true Example 2: Input: nums = [6,5,4,4] Output: true Example 3: Input: nums = [1,3,2] Output: false Constraints: 1 <= nums.

Detailed Explanation

The problem asks us to determine if a given array of integers is monotonic. An array is monotonic if it is either monotone increasing (every element is less than or equal to the next) or monotone decreasing (every element is greater than or equal to the next). We need to return `true` if the array satisfies either of these conditions, and `false` otherwise. The constraints specify the array's length and the range of values the elements can hold.

Solution Approach

The provided solution uses a simple and efficient approach. It initializes two boolean variables, `increasing` and `decreasing`, to `true`. Then, it iterates through the array, comparing each element to the previous one. If it finds an element that violates the increasing property, it sets `increasing` to `false`. Similarly, if it finds an element that violates the decreasing property, it sets `decreasing` to `false`. Finally, it returns `true` if either `increasing` or `decreasing` is still `true`, indicating that the array is monotonic.

Step-by-Step Algorithm

Step 1: Initialize two boolean variables, `increasing` and `decreasing`, to `true`.
Step 2: Iterate through the array from the second element (index 1) to the end.
Step 3: In each iteration, compare the current element `nums[i]` to the previous element `nums[i-1]`.
Step 4: If `nums[i] < nums[i-1]`, set `increasing` to `false`.
Step 5: If `nums[i] > nums[i-1]`, set `decreasing` to `false`.
Step 6: After iterating through the entire array, return `increasing || decreasing`.

Key Insights

Insight 1: An array can be both monotonically increasing and monotonically decreasing if all elements are the same.
Insight 2: We can check for both increasing and decreasing properties in a single pass through the array.
Insight 3: No need to create new arrays, it can be determined in O(1) space by using flags.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array.

Companies

Asked at: Ozon.

Monotonic Array | LeetCode 896

Easy

Array

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public boolean isMonotonic(int[] nums) {
        boolean increasing = true;
        boolean decreasing = true;
        for (int i = 1; i < nums.length; i++) {
            if (nums[i] < nums[i - 1]) {
                increasing = false;
            }
            if (nums[i] > nums[i - 1]) {
                decreasing = false;
            }
        }
        return increasing || decreasing;
    }
}

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Problem Info

Description

Problem 896: Monotonic Array - Detailed explanation and solution approaches.

Topics

Array

Companies

Ozon

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:896

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Initialize two boolean variables, `increasing` and `decreasing`, to `true`.
2
Step 2: Iterate through the array from the second element (index 1) to the end.
3
Step 3: In each iteration, compare the current element `nums[i]` to the previous element `nums[i-1]`.
4
Step 4: If `nums[i] < nums[i-1]`, set `increasing` to `false`.
5
Step 5: If `nums[i] > nums[i-1]`, set `decreasing` to `false`.
6
Step 6: After iterating through the entire array, return `increasing || decreasing`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n) because the algorithm iterates through the array once. The space complexity is O(1) because the algorithm uses a constant amount of extra space regardless of the input size (only two boolean variables).

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Two separate loops

One loop checks for increasing, and another checks for decreasing. If either is true, return true.

Time: O(n)Space: O(1)

Trade-offs: This approach might be slightly less efficient due to the potential for two full array traversals, but it might be easier to read for some.

✨

Key Insights

1Insight 1: An array can be both monotonically increasing and monotonically decreasing if all elements are the same.
2Insight 2: We can check for both increasing and decreasing properties in a single pass through the array.
3Insight 3: No need to create new arrays, it can be determined in O(1) space by using flags.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: Empty array or array with a single element. The solution handles this correctly because the loop will not execute, and both `increasing` and `decreasing` will remain `true`, so the function returns `true`.
Edge case 2: Array with all elements equal. The solution handles this correctly because neither `increasing` nor `decreasing` will be set to `false`, so the function returns `true`.
Edge case 3: Array with only two elements, one increasing and one decreasing. The solution correctly identifies this case and returns false.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Only checking for strictly increasing or strictly decreasing, forgetting that elements can be equal in a monotonic array.

✗Common mistake 2: Not handling the case of an empty array or an array with only one element properly. These arrays are considered monotonic.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Trend analysis in financial data. Determining if a stock price is generally increasing or decreasing over a certain period.

🏦Real-world scenario 2: Monitoring system logs. Checking if the number of errors is consistently increasing or decreasing over time.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 24, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Monotonic Array"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether standard techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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