What is the time complexity of Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold?

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

What data structures are used to solve Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold?

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

What are the key insights for solving Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold?

Insight 1: The key is to avoid recalculating the sum of each sub-array from scratch. Use a sliding window technique to efficiently update the sum as we move across the array. Insight 2: Multiplying the threshold by `k` allows us to work with the sum directly instead of repeatedly calculating the average, which can improve efficiency.

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Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold - LeetCode 1343 Solution

Q: Which companies ask LeetCode 1343. Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold in interviews?

This problem is frequently asked at Turo.

Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold - Complete Solution Guide

Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold is LeetCode problem 1343, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an array of integers arr and two integers k and threshold , return the number of sub-arrays of size k and average greater than or equal to threshold . Example 1: Input: arr = [2,2,2,2,5,5,5,8], k = 3, threshold = 4 Output: 3 Explanation: Sub-arrays [2,5,5],[5,5,5] and [5,5,8] have averages 4, 5 and 6 respectively. All other sub-arrays of size 3 have averages less than 4 (the threshold). Example 2: Input: arr = [11,13,17,23,29,31,7,5,2,3], k = 3, threshold = 5 Output: 6 Explanation: The fir

Detailed Explanation

The problem asks us to find the number of sub-arrays of a given array `arr` that meet two criteria: (1) they have a length of `k`, and (2) their average is greater than or equal to a given `threshold`. The input consists of the array `arr` of integers, the length of the sub-array `k`, and the minimum average `threshold`. The output is the count of sub-arrays meeting these conditions.

Solution Approach

The provided solution employs a sliding window technique to efficiently calculate the sum of each sub-array of length `k`. First, it calculates the sum of the first `k` elements. Then, it iterates through the rest of the array, subtracting the leftmost element of the current window and adding the next element on the right to update the sum. After each update, it checks if the sum is greater than or equal to `k * threshold` and increments the count if it is.

Step-by-Step Algorithm

Step 1: Calculate `target_sum` by multiplying `k` by `threshold`. This avoids repeatedly calculating the average.
Step 2: Initialize a variable `count` to 0 to store the number of sub-arrays that meet the condition.
Step 3: Calculate the sum of the first `k` elements of the array `arr` and store it in `current_sum`.
Step 4: Check if `current_sum` is greater than or equal to `target_sum`. If it is, increment `count`.
Step 5: Iterate from `i = k` to the end of the array. In each iteration, update `current_sum` by subtracting `arr[i-k]` (the element leaving the window) and adding `arr[i]` (the element entering the window).
Step 6: Check if the updated `current_sum` is greater than or equal to `target_sum`. If it is, increment `count`.
Step 7: Return the final value of `count`.

Key Insights

Insight 1: The key is to avoid recalculating the sum of each sub-array from scratch. Use a sliding window technique to efficiently update the sum as we move across the array.
Insight 2: Multiplying the threshold by `k` allows us to work with the sum directly instead of repeatedly calculating the average, which can improve efficiency.
Insight 3: The problem constraints indicate that brute-force solutions might not be efficient enough due to potentially large input array sizes. Optimization is required.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Sliding Window.

Companies

Asked at: Turo.

Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold | LeetCode 1343

Medium

Array Sliding Window

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

Solution Code

Available in:

class Solution {
    public int numOfSubarrays(int[] arr, int k, int threshold) {
        int target_sum = k * threshold;
        int count = 0;
        
        if (arr.length < k) {
            return 0;
        }

        int current_sum = 0;
        for (int i = 0; i < k; i++) {
            current_sum += arr[i];
        }
        
        if (current_sum >= target_sum) {
            count += 1;
        }
        
        for (int i = k; i < arr.length; i++) {
            current_sum = current_sum - arr[i-k] + arr[i];
            if (current_sum >= target_sum) {
                count += 1;
            }
        }
        
        return count;
    }
}

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Problem Info

Description

Problem 1343: Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold - Detailed explanation and solution approaches.

Topics

Array Sliding Window

Companies

Turo

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1343

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: Calculate `target_sum` by multiplying `k` by `threshold`. This avoids repeatedly calculating the average.
2
Step 2: Initialize a variable `count` to 0 to store the number of sub-arrays that meet the condition.
3
Step 3: Calculate the sum of the first `k` elements of the array `arr` and store it in `current_sum`.
4
Step 4: Check if `current_sum` is greater than or equal to `target_sum`. If it is, increment `count`.
5
Step 5: Iterate from `i = k` to the end of the array. In each iteration, update `current_sum` by subtracting `arr[i-k]` (the element leaving the window) and adding `arr[i]` (the element entering the window).
6
Step 6: Check if the updated `current_sum` is greater than or equal to `target_sum`. If it is, increment `count`.
7
Step 7: Return the final value of `count`.

💡

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 only iterate through the array once with a sliding window of size k. The space complexity is constant because the algorithm uses a fixed amount of extra memory, irrespective of the input size.

📖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

Brute-force approach

Iterate through all possible sub-arrays of size `k`, calculate the average of each, and check if it is greater than or equal to the threshold.

Time: O(n*k), where n is the length of the arraySpace: O(1)

Trade-offs: While simple to implement, this approach is less efficient than the sliding window technique, especially for larger arrays and values of `k`. It is acceptable for small input sizes, but the sliding window approach is preferred for larger datasets.

✨

Key Insights

1Insight 1: The key is to avoid recalculating the sum of each sub-array from scratch. Use a sliding window technique to efficiently update the sum as we move across the array.
2Insight 2: Multiplying the threshold by `k` allows us to work with the sum directly instead of repeatedly calculating the average, which can improve efficiency.
3Insight 3: The problem constraints indicate that brute-force solutions might not be efficient enough due to potentially large input array sizes. Optimization is required.

📚

Key Terms Explained

For Students

Array

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

Sliding Window

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

Edge Cases

Edge case 1: `k` is equal to the length of `arr`. The solution correctly handles this case by computing the sum of the entire array and comparing it against the `target_sum`.
Edge case 2: Empty array. Although not explicitly handled by a check for `arr.length == 0`, the loops will not execute, and the `count` will remain 0, which is the correct behavior for an empty array since there are no sub-arrays of size k.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Recalculating the sum of each sub-array from scratch in each iteration. This leads to a time complexity of O(n*k) instead of O(n).

✗Common mistake 2: Incorrectly implementing the sliding window update. For example, forgetting to subtract the element leaving the window or adding the wrong element entering the window can lead to incorrect results.

✗Common mistake 3: Integer overflow. If the array contains large numbers and k is also large, the sum can exceed the maximum value of the int data type. This can be avoided by using long integers in Java or C++ if necessary, although the problem constraints limit the size such that integer overflow is unlikely in this case.

✅

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: Signal processing. Identifying segments of a signal (e.g., audio or stock prices) that meet a certain average threshold. For example, detecting periods of high trading volume in stock market data.

🏦Real-world scenario 2: Data analysis. Finding consecutive periods of time (e.g., days, weeks) where the average performance of a system (e.g., server response time, energy consumption) exceeds a certain limit.

💡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

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ 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: August 23, 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

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 14

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

@TechLeadJul 7

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

@DevExpert92Jun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What data structures complement sliding window?

Hash maps track character frequencies within the window. Deques enable O(1) access to both window boundaries. Heaps help find min/max within the window. Choose based on what property you need to maintain as the window slides.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold"?

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

🤖 Need help with this problem?