What is the time complexity of Relative Ranks?

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

What data structures are used to solve Relative Ranks?

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

What are the key insights for solving Relative Ranks?

Insight 1: The problem requires sorting the scores to determine the ranks. Insight 2: It's crucial to maintain the original index of each score so we can assign the correct rank to each athlete.

Which companies ask LeetCode 506. Relative Ranks in interviews?

This problem is frequently asked at Electronic Arts.

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Relative Ranks - LeetCode 506 Solution

Relative Ranks - Complete Solution Guide

Relative Ranks is LeetCode problem 506, 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

You are given an integer array score of size n , where score[i] is the score of the i th athlete in a competition. All the scores are guaranteed to be unique . The athletes are placed based on their scores, where the 1 st place athlete has the highest score, the 2 nd place athlete has the 2 nd highest score, and so on. The placement of each athlete determines their rank: The 1 st place athlete's rank is "Gold Medal" . The 2 nd place athlete's rank is "Silver Medal" . The 3 rd place athlete's ran

Detailed Explanation

The problem asks you to rank athletes based on their scores in a competition. You are given an array `score` where `score[i]` represents the score of the i-th athlete. The task is to return an array of strings where each string represents the rank of the corresponding athlete. The top three athletes receive "Gold Medal", "Silver Medal", and "Bronze Medal", respectively. The remaining athletes receive their numerical rank (e.g., the 4th place athlete receives "4"). All scores are guaranteed to be unique.

Solution Approach

The solution involves sorting the scores while preserving the original index of each score. We then iterate through the sorted scores and assign the appropriate rank (either a medal or a numerical rank) based on the position in the sorted list. Finally, we create a result array where the index corresponds to the original athlete index and the value is their rank.

Step-by-Step Algorithm

Step 1: Create a data structure (e.g., an array of pairs or tuples) to store each score along with its original index in the input array.
Step 2: Sort the data structure in descending order based on the score.
Step 3: Create a result array of strings with the same size as the input array. Initialize it with empty strings.
Step 4: Iterate through the sorted data structure. For the first three elements, assign "Gold Medal", "Silver Medal", and "Bronze Medal" to the corresponding index in the result array.
Step 5: For the remaining elements, assign their rank (position + 1) as a string to the corresponding index in the result array.
Step 6: Return the result array.

Key Insights

Insight 1: The problem requires sorting the scores to determine the ranks.
Insight 2: It's crucial to maintain the original index of each score so we can assign the correct rank to each athlete.
Insight 3: The top 3 ranks are special string cases while the rest are numerical ranks.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

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

Companies

Asked at: Electronic Arts.

Relative Ranks | LeetCode 506

Easy

Array Sorting Heap (Priority Queue)

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

Solution Code

Available in:

class Solution {
    public String[] findRelativeRanks(int[] score) {
        int n = score.length;
        int[][] scoreWithIndex = new int[n][2];
        for (int i = 0; i < n; i++) {
            scoreWithIndex[i][0] = score[i];
            scoreWithIndex[i][1] = i;
        }
        Arrays.sort(scoreWithIndex, (a, b) -> b[0] - a[0]);
        String[] result = new String[n];
        for (int i = 0; i < n; i++) {
            int index = scoreWithIndex[i][1];
            if (i == 0) {
                result[index] = "Gold Medal";
            } else if (i == 1) {
                result[index] = "Silver Medal";
            } else if (i == 2) {
                result[index] = "Bronze Medal";
            } else {
                result[index] = String.valueOf(i + 1);
            }
        }
        return result;
    }
}

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Problem Info

Description

Problem 506: Relative Ranks - Detailed explanation and solution approaches.

Topics

Array Sorting Heap (Priority Queue)

Companies

Electronic Arts

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:506

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

6 steps

1
Step 1: Create a data structure (e.g., an array of pairs or tuples) to store each score along with its original index in the input array.
2
Step 2: Sort the data structure in descending order based on the score.
3
Step 3: Create a result array of strings with the same size as the input array. Initialize it with empty strings.
4
Step 4: Iterate through the sorted data structure. For the first three elements, assign "Gold Medal", "Silver Medal", and "Bronze Medal" to the corresponding index in the result array.
5
Step 5: For the remaining elements, assign their rank (position + 1) as a string to the corresponding index in the result array.
6
Step 6: Return the result array.

💡

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?

Sorting an array of size 'n' has a time complexity of O(n log n). The rest of the operations involve iterating through the array once, which takes O(n) time. The space complexity is O(n) because we need extra space to store the score-index pairs/tuples and the result.

📖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 the entire array, you can use a max-heap (priority queue) to extract the scores one by one in descending order. This might be beneficial if you only need to find the top k elements (in this case, the top 3).

Time: O(n log n) in the worst case (when all elements need to be extracted). However, if you only need the top k elements, it can be O(n + k log n).Space: O(n) to store all elements in the heap.

Trade-offs: The heap approach could be slightly faster if you only need to determine the ranks for a small number of athletes (e.g., top 3) and 'n' is very large. Sorting is simpler and usually faster if you need to rank all elements.

✨

Key Insights

1Insight 1: The problem requires sorting the scores to determine the ranks.
2Insight 2: It's crucial to maintain the original index of each score so we can assign the correct rank to each athlete.
3Insight 3: The top 3 ranks are special string cases while the rest are numerical ranks.

📚

Key Terms Explained

For Students

Array

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

Sorting

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

Edge Cases

Edge case 1: When the number of athletes is less than 3. The code correctly handles this by checking the size of the input array before assigning the medal ranks.
Edge case 2: Input array with only one element. The code works correctly by assigning "Gold Medal" to the first element.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to preserve the original index of each score during the sorting process. This leads to incorrect rank assignments.

✗Common mistake 2: Not handling the edge case where the number of athletes is less than 3, which can lead to index out-of-bounds errors when assigning the medal ranks.

✗Common mistake 3: Using incorrect string formatting or concatenation when assigning the numerical ranks.

✅

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: Leaderboard ranking in online games or competitions. The algorithm can be used to determine the rank of players based on their scores.

🏦Real-world scenario 2: Ranking search results based on relevance. The algorithm can be adapted to rank documents or web pages based on their relevance scores.

💡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 25, 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 13

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

@InterviewProJul 6

❓

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 should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 "Relative Ranks"?

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

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