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

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

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

This problem uses Array, Heap (Priority Queue), Simulation. Understanding these concepts is essential for solving this Medium problem efficiently.

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

Insight 1: The key insight is that we always need to pick the two smallest numbers to perform the operation, making a priority queue (heap) the ideal data structure. Insight 2: Since the operation involves repeated extraction of minimum elements, a min-heap is suitable to efficiently maintain the order of elements.

Which companies ask LeetCode 3066. Minimum Operations to Exceed Threshold Value II in interviews?

This problem is frequently asked at tcs.

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Minimum Operations to Exceed Threshold Value II - LeetCode 3066 Solution

Minimum Operations to Exceed Threshold Value II - Complete Solution Guide

Minimum Operations to Exceed Threshold Value II is LeetCode problem 3066, 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

You are given a 0-indexed integer array nums , and an integer k . You are allowed to perform some operations on nums , where in a single operation, you can: Select the two smallest integers x and y from nums . Remove x and y from nums . Insert (min(x, y) * 2 + max(x, y)) at any position in the array. Note that you can only apply the described operation if nums contains at least two elements. Return the minimum number of operations needed so that all elements of the array are greater than or equa

Detailed Explanation

The problem requires us to find the minimum number of operations needed to make all elements in an array `nums` greater than or equal to a given threshold `k`. In each operation, we select the two smallest elements `x` and `y` from `nums`, remove them, and insert a new element `(min(x, y) * 2 + max(x, y))` back into the array. We continue this process until all elements in `nums` are greater than or equal to `k`. The input consists of an array of integers `nums` and an integer `k`. The output is the minimum number of operations.

Solution Approach

The solution uses a min-heap (priority queue) to efficiently find and extract the two smallest elements in the array. The algorithm iteratively performs the defined operation until all elements in the heap are greater than or equal to `k`. In each iteration, it retrieves the two smallest elements, calculates the new value, and inserts it back into the heap. The number of operations performed is tracked and returned as the result.

Step-by-Step Algorithm

Step 1: Build a min-heap from the input array `nums`. This allows efficient retrieval of the smallest elements.
Step 2: Initialize a counter `operations` to 0. This will track the number of operations performed.
Step 3: While the heap contains more than one element AND the smallest element in the heap (heap's root) is less than `k`, perform the following steps:
Step 4: Extract the two smallest elements `x` and `y` from the heap using `heapq.heappop()` or equivalent.
Step 5: Calculate the new value as `new_val = min(x, y) * 2 + max(x, y)`. This follows the problem's operation rule.
Step 6: Insert the `new_val` back into the heap using `heapq.heappush()` or equivalent.
Step 7: Increment the `operations` counter.
Step 8: After the loop terminates, return the `operations` counter, which represents the minimum number of operations needed.

Key Insights

Insight 1: The key insight is that we always need to pick the two smallest numbers to perform the operation, making a priority queue (heap) the ideal data structure.
Insight 2: Since the operation involves repeated extraction of minimum elements, a min-heap is suitable to efficiently maintain the order of elements.
Insight 3: The problem guarantees that a solution always exists, so we don't need to handle cases where it's impossible to reach the threshold.

Complexity Analysis

Time Complexity: O(nlogn)

Space Complexity: O(1)

Topics

This problem involves: Array, Heap (Priority Queue), Simulation.

Companies

Asked at: tcs.

Minimum Operations to Exceed Threshold Value II | LeetCode 3066

Medium

Array Heap (Priority Queue)Simulation

Time: O(nlogn)Space: O(1)

Solution Code

Available in:

import java.util.PriorityQueue;

class Solution {
    public int minOperations(int[] nums, int k) {
        PriorityQueue<Integer> pq = new PriorityQueue<>();
        
        for (int num : nums) {
            pq.offer(num);
        }
        
        int operations = 0;
        
        while (pq.size() > 1 && pq.peek() < k) {
            int x = pq.poll();
            int y = pq.poll();
            
            int new_val = x * 2 + y;
            
            pq.offer(new_val);
            
            operations++;
        }
        
        return operations;
    }
}

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Problem Info

Description

Problem 3066: Minimum Operations to Exceed Threshold Value II - Detailed explanation and solution approaches.

Topics

Array Heap (Priority Queue)Simulation

Companies

tcs

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:3066

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

8 steps

1
Step 1: Build a min-heap from the input array `nums`. This allows efficient retrieval of the smallest elements.
2
Step 2: Initialize a counter `operations` to 0. This will track the number of operations performed.
3
Step 3: While the heap contains more than one element AND the smallest element in the heap (heap's root) is less than `k`, perform the following steps:
4
Step 4: Extract the two smallest elements `x` and `y` from the heap using `heapq.heappop()` or equivalent.
5
Step 5: Calculate the new value as `new_val = min(x, y) * 2 + max(x, y)`. This follows the problem's operation rule.
6
Step 6: Insert the `new_val` back into the heap using `heapq.heappush()` or equivalent.
7
Step 7: Increment the `operations` counter.
8
Step 8: After the loop terminates, return the `operations` counter, which represents the minimum number of operations needed.

💡

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(nlogn)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is dominated by the heap operations. Building the heap initially takes O(n) time. In the worst case, we might need to perform the operation until only one element remains in the heap. Each operation involves two heap pops (O(log n) each) and one heap push (O(log n)). Since we perform at most n operations, the total time complexity is O(n log n). Space complexity is O(n) since it is the max space required by the priority queue.

📖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 Iteration

Instead of using a heap, we could sort the array and iteratively select the two smallest elements, perform the operation, and then re-sort the array. This is less efficient.

Time: O(n^2 log n)Space: O(1)

Trade-offs: The heap-based approach is generally preferred because of its better time complexity. Sorting repeatedly is inefficient. The sorting approach might be simpler to implement for beginners, but it's not scalable for larger input sizes.

✨

Key Insights

1Insight 1: The key insight is that we always need to pick the two smallest numbers to perform the operation, making a priority queue (heap) the ideal data structure.
2Insight 2: Since the operation involves repeated extraction of minimum elements, a min-heap is suitable to efficiently maintain the order of elements.
3Insight 3: The problem guarantees that a solution always exists, so we don't need to handle cases where it's impossible to reach the threshold.

📚

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: `nums` contains elements all greater than or equal to `k` initially. The loop condition ensures that no operations are performed, and 0 is returned, which is correct.
Edge case 2: `nums` contains only two elements. The algorithm correctly performs the operation and returns 1 if needed, or 0 if not.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not using a heap (priority queue) and attempting to find the smallest elements by iterating through the array repeatedly. This results in a much higher time complexity.

✗Common mistake 2: Modifying the original array without considering the impact on subsequent operations. The heap data structure ensures that the smallest elements are always readily available and updated correctly.

✅

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 needing to combine smaller tasks (represented by their estimated completion time) to create larger tasks. Minimizing the number of combined tasks while ensuring each resulting task is large enough maps directly to this problem.

🏦Real-world scenario 2: Data compression. This problem's underlying operation (combining two smallest elements) is conceptually similar to Huffman coding, where symbols with lower frequencies are combined to build an efficient prefix code.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: June 7, 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 14

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

@InterviewProJul 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.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

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 "Minimum Operations to Exceed Threshold Value II"?

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 heap (priority queue) techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?