What is the time complexity of Minimum Subsequence in Non-Increasing Order?

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

What data structures are used to solve Minimum Subsequence in Non-Increasing Order?

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

What are the key insights for solving Minimum Subsequence in Non-Increasing Order?

Insight 1: Sorting the input array in descending order allows us to greedily select elements from the beginning to maximize the sum of the subsequence while minimizing its size. Insight 2: We can use a greedy approach by iterating through the sorted array and adding elements to the subsequence until its sum exceeds the sum of the remaining elements. This ensures we find a minimal subsequence satisfying the condition.

Which companies ask LeetCode 1403. Minimum Subsequence in Non-Increasing Order in interviews?

This problem is frequently asked at Mercari.

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Minimum Subsequence in Non-Increasing Order - LeetCode 1403 Solution

Minimum Subsequence in Non-Increasing Order - Complete Solution Guide

Minimum Subsequence in Non-Increasing Order is LeetCode problem 1403, 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

Given the array nums , obtain a subsequence of the array whose sum of elements is strictly greater than the sum of the non included elements in such subsequence. If there are multiple solutions, return the subsequence with minimum size and if there still exist multiple solutions, return the subsequence with the maximum total sum of all its elements. A subsequence of an array can be obtained by erasing some (possibly zero) elements from the array. Note that the solution with the given constraints

Detailed Explanation

The problem asks you to find the smallest subsequence (subset) of numbers from an input array `nums` such that the sum of the numbers in the subsequence is strictly greater than the sum of the remaining numbers not included in the subsequence. If multiple such subsequences exist with the same minimum size, the one with the largest sum should be chosen. The subsequence must be returned in non-increasing order.

Solution Approach

The solution employs a greedy strategy. It first sorts the input array `nums` in descending order. Then, it iteratively adds elements from the sorted array to a `result` subsequence, updating the `currentSum` (sum of the subsequence) and `totalSum` (sum of the remaining elements). The loop continues until the `currentSum` becomes strictly greater than `totalSum - currentSum`, at which point the algorithm terminates and returns the `result` subsequence.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` in descending order.
Step 2: Calculate the `totalSum` of all elements in `nums`.
Step 3: Initialize `currentSum` to 0 and an empty list `result`.
Step 4: Iterate through the sorted `nums` array:
Step 5: Add the current element to `result` and update `currentSum`.
Step 6: Update `totalSum` by subtracting the added element.
Step 7: Check if `currentSum > totalSum - currentSum`. If true, break the loop.
Step 8: Return the `result` list (which will be in non-increasing order due to the initial sorting).

Key Insights

Insight 1: Sorting the input array in descending order allows us to greedily select elements from the beginning to maximize the sum of the subsequence while minimizing its size.
Insight 2: We can use a greedy approach by iterating through the sorted array and adding elements to the subsequence until its sum exceeds the sum of the remaining elements. This ensures we find a minimal subsequence satisfying the condition.
Insight 3: Keeping track of the `totalSum` and the `currentSum` allows for efficient comparison and termination when the condition (`currentSum > totalSum - currentSum`) is met, avoiding unnecessary iterations.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Greedy, Sorting.

Companies

Asked at: Mercari.

Minimum Subsequence in Non-Increasing Order | LeetCode 1403

Easy

Array Greedy Sorting

Time: O(n log n)Space: O(n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

class Solution {
    public List<Integer> minSubsequence(int[] nums) {
        Arrays.sort(nums);
        int totalSum = 0;
        for (int num : nums) {
            totalSum += num;
        }

        List<Integer> result = new ArrayList<>();
        int subsequenceSum = 0;
        for (int i = nums.length - 1; i >= 0; i--) {
            result.add(nums[i]);
            subsequenceSum += nums[i];
            if (subsequenceSum > totalSum - subsequenceSum) {
                return result;
            }
        }
        return result;
    }
}

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Problem Info

Description

Problem 1403: Minimum Subsequence in Non-Increasing Order - Detailed explanation and solution approaches.

Topics

Array Greedy Sorting

Companies

Mercari

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1403

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: Sort the input array `nums` in descending order.
2
Step 2: Calculate the `totalSum` of all elements in `nums`.
3
Step 3: Initialize `currentSum` to 0 and an empty list `result`.
4
Step 4: Iterate through the sorted `nums` array:
5
Step 5: Add the current element to `result` and update `currentSum`.
6
Step 6: Update `totalSum` by subtracting the added element.
7
Step 7: Check if `currentSum > totalSum - currentSum`. If true, break the loop.
8
Step 8: Return the `result` list (which will be in non-increasing order due to the initial sorting).

💡

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 log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operation is sorting the array, which takes O(n log n) time using efficient algorithms like merge sort or quicksort. The subsequent iteration through the array and the space used for the `result` list are both linear, O(n).

📖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

Using a Priority Queue (Heap)

Instead of sorting, we can use a max-heap data structure to efficiently extract the largest elements. This would still maintain the greedy approach but with slightly different implementation.

Time: O(n log n)Space: O(n)

Trade-offs: While the time complexity remains similar, the heap approach might be slightly less efficient in practice than a straightforward sort for this specific problem due to the overhead of heap operations. It offers more flexibility if elements need to be added or removed dynamically.

✨

Key Insights

1Insight 1: Sorting the input array in descending order allows us to greedily select elements from the beginning to maximize the sum of the subsequence while minimizing its size.
2Insight 2: We can use a greedy approach by iterating through the sorted array and adding elements to the subsequence until its sum exceeds the sum of the remaining elements. This ensures we find a minimal subsequence satisfying the condition.
3Insight 3: Keeping track of the `totalSum` and the `currentSum` allows for efficient comparison and termination when the condition (`currentSum > totalSum - currentSum`) is met, avoiding unnecessary iterations.

📚

Key Terms Explained

For Students

Array

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

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty input array. The code handles this gracefully, returning an empty list.
Edge case 2: All elements in the array are equal. The algorithm correctly identifies a minimum-length subsequence that satisfies the condition.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to sort the array before starting the iterative process. This would result in an incorrect subsequence.

✗Common mistake 2: Incorrectly managing the `totalSum` and `currentSum` during iterations which leads to an inaccurate comparison and potentially wrong results.

✅

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 assigning tasks to workers where the total work done by a subset of workers (subsequence) must exceed the work remaining. This algorithm finds the smallest team of workers.

🏦Real-world scenario 2: Investment portfolio optimization. Selecting a small set of investments whose return must significantly outperform the remaining assets in the portfolio.

💡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: October 22, 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 are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

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 Subsequence in Non-Increasing Order"?

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 greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?