What is the time complexity of Count Subarrays With Fixed Bounds?

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

What data structures are used to solve Count Subarrays With Fixed Bounds?

This problem uses Array, Queue, Sliding Window, Monotonic Queue. Understanding these concepts is essential for solving this Hard problem efficiently.

What are the key insights for solving Count Subarrays With Fixed Bounds?

Insight 1: The subarray must contain both `minK` and `maxK`. Any subarray not containing both cannot be a valid fixed-bound subarray. Insight 2: The presence of numbers outside the range [minK, maxK] invalidates any subarray containing them. These out-of-range numbers act as boundaries for valid subarrays.

Which companies ask LeetCode 2444. Count Subarrays With Fixed Bounds in interviews?

This problem is frequently asked at MathWorks, Morgan Stanley, OKX, Snowflake.

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Count Subarrays With Fixed Bounds - LeetCode 2444 Solution

Count Subarrays With Fixed Bounds - Complete Solution Guide

Count Subarrays With Fixed Bounds is LeetCode problem 2444, a Hard level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an integer array nums and two integers minK and maxK . A fixed-bound subarray of nums is a subarray that satisfies the following conditions: The minimum value in the subarray is equal to minK . The maximum value in the subarray is equal to maxK . Return the number of fixed-bound subarrays . A subarray is a contiguous part of an array. Example 1: Input: nums = [1,3,5,2,7,5], minK = 1, maxK = 5 Output: 2 Explanation: The fixed-bound subarrays are [1,3,5] and [1,3,5,2]. Example 2: Inp

Detailed Explanation

The problem requires us to count the number of subarrays within a given array `nums` that satisfy specific conditions. These conditions define a 'fixed-bound subarray': its minimum value must be equal to `minK`, and its maximum value must be equal to `maxK`. We are given the array `nums` and the integers `minK` and `maxK` as input, and we need to return the total count of such fixed-bound subarrays. A subarray must be contiguous, meaning it consists of consecutive elements from the original array.

Solution Approach

The solution utilizes a single pass through the array `nums`. It maintains three indices: `min_k_idx` (the latest index of `minK`), `max_k_idx` (the latest index of `maxK`), and `bad_idx` (the latest index of an element outside the range [minK, maxK]). For each index `i`, the algorithm checks if the current element is out of bounds (less than `minK` or greater than `maxK`). If so, `bad_idx` is updated. The algorithm also updates `min_k_idx` and `max_k_idx` if the current element equals `minK` or `maxK` respectively. The number of valid subarrays ending at index `i` is determined by `max(0, min(min_k_idx, max_k_idx) - bad_idx)`. This is because any subarray ending at `i` must include elements from `bad_idx + 1` to `i` (inclusive), and it must also include both `minK` and `maxK`. Thus, the number of valid start positions for a fixed-bound subarray ending at index `i` is the distance between the furthest 'bad' index and the nearest of the `minK` and `maxK` indices.

Step-by-Step Algorithm

Step 1: Initialize `ans` to 0, `min_k_idx`, `max_k_idx`, and `bad_idx` to -1.
Step 2: Iterate through the `nums` array using index `i`.
Step 3: If `nums[i]` is less than `minK` or greater than `maxK`, update `bad_idx` to `i`.
Step 4: If `nums[i]` is equal to `minK`, update `min_k_idx` to `i`.
Step 5: If `nums[i]` is equal to `maxK`, update `max_k_idx` to `i`.
Step 6: Calculate the number of valid subarrays ending at index `i` as `max(0, min(min_k_idx, max_k_idx) - bad_idx)`, and add it to `ans`.
Step 7: After the loop finishes, return `ans`.

Key Insights

Insight 1: The subarray must contain both `minK` and `maxK`. Any subarray not containing both cannot be a valid fixed-bound subarray.
Insight 2: The presence of numbers outside the range [minK, maxK] invalidates any subarray containing them. These out-of-range numbers act as boundaries for valid subarrays.
Insight 3: Instead of generating and checking every subarray, we can efficiently track the latest indices of `minK`, `maxK`, and invalid elements, and calculate the count of valid subarrays ending at each index.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Queue, Sliding Window, Monotonic Queue.

Companies

Asked at: MathWorks, Morgan Stanley, OKX, Snowflake.

Count Subarrays With Fixed Bounds | LeetCode 2444

Hard

Array Queue Sliding Window Monotonic Queue

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

Solution Code

Available in:

class Solution {
    public long countSubarrays(int[] nums, int minK, int maxK) {
        long ans = 0;
        int min_k_idx = -1;
        int max_k_idx = -1;
        int bad_idx = -1;

        for (int i = 0; i < nums.length; i++) {
            int num = nums[i];
            if (num < minK || num > maxK) {
                bad_idx = i;
            }

            if (num == minK) {
                min_k_idx = i;
            }

            if (num == maxK) {
                max_k_idx = i;
            }

            ans += Math.max(0, Math.min(min_k_idx, max_k_idx) - bad_idx);
        }

        return ans;
    }
}

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Problem Info

Description

Problem 2444: Count Subarrays With Fixed Bounds - Detailed explanation and solution approaches.

Topics

Array Queue Sliding Window Monotonic Queue

Companies

MathWorksMorgan StanleyOKXSnowflake

Stats

Difficulty:Hard

Languages:4

Companies:4

Problem #:2444

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

7 steps

1
Step 1: Initialize `ans` to 0, `min_k_idx`, `max_k_idx`, and `bad_idx` to -1.
2
Step 2: Iterate through the `nums` array using index `i`.
3
Step 3: If `nums[i]` is less than `minK` or greater than `maxK`, update `bad_idx` to `i`.
4
Step 4: If `nums[i]` is equal to `minK`, update `min_k_idx` to `i`.
5
Step 5: If `nums[i]` is equal to `maxK`, update `max_k_idx` to `i`.
6
Step 6: Calculate the number of valid subarrays ending at index `i` as `max(0, min(min_k_idx, max_k_idx) - bad_idx)`, and add it to `ans`.
7
Step 7: After the loop finishes, return `ans`.

💡

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 linear because we process each element of the input array exactly once. The space complexity is constant because the number of variables used does not depend on the size of the input.

📖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

Sliding Window with Two Pointers

Maintain a sliding window and check at each step if the current window is a valid fixed-bound subarray. Expand the window until it becomes invalid, then shift the window to the right.

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

Trade-offs: This approach can also be O(n) but might have higher constant factors, especially when verifying that the window is valid. The original solution might be slightly cleaner and easier to implement.

✨

Key Insights

1Insight 1: The subarray must contain both `minK` and `maxK`. Any subarray not containing both cannot be a valid fixed-bound subarray.
2Insight 2: The presence of numbers outside the range [minK, maxK] invalidates any subarray containing them. These out-of-range numbers act as boundaries for valid subarrays.
3Insight 3: Instead of generating and checking every subarray, we can efficiently track the latest indices of `minK`, `maxK`, and invalid elements, and calculate the count of valid subarrays ending at each index.

📚

Key Terms Explained

For Students

Array

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

Queue

FIFO structure - First In, First Out. Like a line at a store!

Sliding Window

A moving "window" over data to process subsets efficiently.

Edge Cases

Edge case 1: `nums` is very large. The `long` datatype in Java and C++ is used to avoid potential integer overflow when calculating the count of subarrays, as the number of subarrays can grow quadratically with the size of nums.
Edge case 2: `minK` and `maxK` are equal. The algorithm correctly handles this case because it always takes the minimum of `min_k_idx` and `max_k_idx`, effectively using the latest index of the value.
Edge case 3: `nums` does not contain either `minK` or `maxK`. In this case, both `min_k_idx` and `max_k_idx` remain at -1. Thus min(min_k_idx, max_k_idx) is also -1, and the count added is max(0, -1 - bad_idx), which will become 0, as expected, since no valid subarray is found.
Edge case 4: `minK > maxK`. In this case, there won't be any fixed-bound subarrays. Since no such subarrays are found, the algorithm correctly returns 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Integer Overflow: Forgetting to use `long` (or appropriate large integer type) to store the count of subarrays can lead to incorrect results due to integer overflow.

✗Common mistake 2: Incorrectly Calculating Valid Subarrays: Not properly accounting for the `bad_idx` and the positions of `minK` and `maxK` can result in counting invalid subarrays.

✗Common mistake 3: Prematurely ending the loop. It is important to process all elements in nums because the last element might still be part of a valid fixed-bound subarray.

✅

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: Data analysis. Identifying data segments within a time series that satisfy certain minimum and maximum criteria.

🏦Real-world scenario 2: Financial modeling. Finding time periods where stock prices stay within a specific range.

🎮Real-world scenario 3: Signal processing. Detecting signal segments that have a minimum amplitude and a maximum noise level.

💡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

These problems test your ability to optimize. Start with a brute force solution, then improve.

⚠️ 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: September 13, 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

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 14

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 7

❓

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 do I approach hard algorithm problems?

Hard problems often require: 1) Breaking down into subproblems, 2) Combining multiple advanced techniques, 3) Careful optimization of brute force. Start with a working solution (even O(n²) or worse), then optimize. Draw examples, identify patterns, and think about what makes this problem unique.

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 "Count Subarrays With Fixed Bounds"?

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

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