What is the time complexity of Minimum Operations to Exceed Threshold Value I?

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

What data structures are used to solve Minimum Operations to Exceed Threshold Value I?

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

What are the key insights for solving Minimum Operations to Exceed Threshold Value I?

Insight 1: We only need to consider elements smaller than `k`. Elements greater than or equal to `k` don't require any operations. Insight 2: No sorting is needed. We can simply count the number of elements smaller than `k` by iterating through the array once.

Which companies ask LeetCode 3065. Minimum Operations to Exceed Threshold Value I in interviews?

This problem is frequently asked at tcs.

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Minimum Operations to Exceed Threshold Value I | LeetCode 3065

Easy

Array

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

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int minOperations(int[] nums, int k) {
        int operations = 0;
        Arrays.sort(nums);
        for (int num : nums) {
            if (num < k) {
                operations++;
            } else {
                break;
            }
        }
        return operations;
    }
}

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Problem Info

Description

Problem 3065: Minimum Operations to Exceed Threshold Value I - Detailed explanation and solution approaches.

Topics

Array

Companies

tcs

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:3065

Problem Explanation

The problem asks you to find the minimum number of operations needed to make all elements in an array greater than or equal to a given threshold `k`. In each operation, you remove the smallest element from the array. The input is a 0-indexed integer array `nums` and an integer `k`. The output is the minimum number of operations. The problem guarantees that at least one element in `nums` is greater than or equal to `k`.

💡

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

The solution iterates through the input array `nums`. For each element, it checks if the element is less than `k`. If it is, a counter (`operations`) is incremented. Finally, the counter, representing the minimum number of operations, is returned.

📋

Step-by-Step Solution

4 steps

1
Step 1: Initialize a counter `operations` to 0.
2
Step 2: Iterate through each element `num` in the array `nums`.
3
Step 3: If `num` is less than `k`, increment `operations`.
4
Step 4: After iterating through all elements, return the value of `operations`.

💡

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 each element in the array is processed exactly once. The space complexity is constant because the memory usage does not depend on the size of the input array.

📖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

Sorting and Binary Search

Sort the array and then use binary search to find the index of the first element greater than or equal to k. The number of elements before this index would be the number of operations.

Time: O(n log n) due to sortingSpace: O(log n) or O(n) depending on the sorting algorithm

Trade-offs: This approach is less efficient than the linear approach, but it would be preferable if we needed to perform multiple queries with different values of k on the same array. The linear approach is better for a single query.

✨

Key Insights

1Insight 1: We only need to consider elements smaller than `k`. Elements greater than or equal to `k` don't require any operations.
2Insight 2: No sorting is needed. We can simply count the number of elements smaller than `k` by iterating through the array once.
3Insight 3: The problem statement ensures there's at least one element >=k, eliminating the need for special handling of cases where all elements are below k.

📚

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: All elements are greater than or equal to `k`. In this case, the algorithm correctly returns 0 operations.
Edge case 2: All elements are less than `k`. In this case, the algorithm correctly returns the length of the array as the number of operations.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly using a sorting algorithm (like the Java example initially showing). Sorting is unnecessary and increases the time complexity. The problem doesn't require the elements to be sorted before the operation count.

✗Common mistake 2: Forgetting to handle edge cases where all elements are larger or smaller than k. The problem statement guarantees at least one element >=k which simplifies things but a robust solution should account for potential edge cases in a more general sense (although this problem does not actually need to).

✅

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: Resource allocation. Imagine you have a set of tasks with varying resource requirements. You want to determine how many tasks you need to remove to ensure all remaining tasks can be handled with available resources (`k`).

🏦Real-world scenario 2: Data filtering. You might need to remove low-value data points from a dataset to ensure the remaining data meets a certain quality threshold (`k`).

💡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.

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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: June 6, 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

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

@DevExpert92Jul 14

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

@AlgoMasterJul 7

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

@InterviewProJun 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 should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 "Minimum Operations to Exceed Threshold Value I"?

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.

🤖 Need help with this problem?

Minimum Operations to Exceed Threshold Value I - Complete Solution Guide

Problem Statement

Detailed Explanation

Solution Approach

Step-by-Step Algorithm

Key Insights

Complexity Analysis

Topics

Companies

Minimum Operations to Exceed Threshold Value I | LeetCode 3065

Solution Code

Problem Info

Description

Topics

Companies

Stats

Problem Explanation

Think Before You Code

🤔 Ask Yourself

✏️ Try This First

Solution Approach

Step-by-Step Solution

Pro Tip for Students

Complexity Analysis

Time Complexity

Space Complexity

Why?

Big O Notation - Quick Guide

Alternative Approaches

Sorting and Binary Search

Key Insights

Key Terms Explained

Array

Edge Cases

Common Mistakes to Avoid

Learning Tip

Where is This Used in Real Life?

Author's Notes

About the Author

Community Tips & Insights

Frequently Asked Questions

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

What should I learn from easy problems?

What is the importance of time and space complexity analysis?

What is the optimal approach for "Minimum Operations to Exceed Threshold Value I"?

Minimum Operations to Exceed Threshold Value I | LeetCode 3065

Solution Code

Problem Info

Description

Topics

Companies

Stats

Problem Explanation

Think Before You Code

🤔 Ask Yourself

✏️ Try This First

Solution Approach

Step-by-Step Solution

Pro Tip for Students

Complexity Analysis

Time Complexity

Space Complexity

Why?

Big O Notation - Quick Guide

Alternative Approaches

Sorting and Binary Search

Key Insights

Key Terms Explained

Array

Edge Cases

Common Mistakes to Avoid

Learning Tip

Where is This Used in Real Life?

Author's Notes

About the Author

Community Tips & Insights

Frequently Asked Questions

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

What should I learn from easy problems?

What is the importance of time and space complexity analysis?