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Relative Ranks

You are given an integer array score of size n, where score[i] is the score of the ith athlete in a competition. All the scores are guaranteed to be unique.

The athletes are placed based on their scores, where the 1st place athlete has the highest score, the 2nd place athlete has the 2nd highest score, and so on. The placement of each athlete determines their rank:

  • The 1st place athlete's rank is "Gold Medal".
  • The 2nd place athlete's rank is "Silver Medal".
  • The 3rd place athlete's rank is "Bronze Medal".
  • For the 4th place to the nth place athlete, their rank is their placement number (i.e., the xth place athlete's rank is "x").

Return an array answer of size n where answer[i] is the rank of the ith athlete.

 

Example 1:

Input: score = [5,4,3,2,1]
Output: ["Gold Medal","Silver Medal","Bronze Medal","4","5"]
Explanation: The placements are [1st, 2nd, 3rd, 4th, 5th].

Example 2:

Input: score = [10,3,8,9,4]
Output: ["Gold Medal","5","Bronze Medal","Silver Medal","4"]
Explanation: The placements are [1st, 5th, 3rd, 2nd, 4th].

 

Constraints:

  • n == score.length
  • 1 <= n <= 104
  • 0 <= score[i] <= 106
  • All the values in score are unique.

Solution Explanation: Relative Ranks

This problem requires us to determine the ranks of athletes based on their scores and return them in an array. The ranks follow a specific pattern: 1st place is "Gold Medal", 2nd is "Silver Medal", 3rd is "Bronze Medal", and subsequent places are represented by their numerical rank (e.g., 4th place is "4").

Approach: Sorting with Index Tracking

The most efficient approach involves sorting the scores while keeping track of the original indices of the athletes. This allows us to map the sorted ranks back to the original order. We'll use an array of indices to maintain this mapping.

Algorithm:

  1. Create Index Array: Generate an array idx containing the indices 0 to n-1, where n is the length of the score array. Each index represents the position of a score in the original input.

  2. Sort Indices: Sort the idx array based on the corresponding scores in the score array in descending order. This ensures that the highest score is at the beginning of the sorted idx array. Many languages allow custom sort functions to achieve this.

  3. Rank Assignment: Create a result array to store the ranks (strings). Iterate through the sorted idx array:

    • For the top 3 indices, assign the corresponding medal ("Gold Medal", "Silver Medal", "Bronze Medal").
    • For the remaining indices, assign their rank as a string (e.g., "4", "5", ...).

  4. Map Ranks to Original Order: Use the original indices from idx to place the ranks correctly in the result array, reflecting the original order of athletes in the score array.

  5. Return Result: Return the result array containing the string ranks.

Time and Space Complexity

  • Time Complexity: O(n log n) due to the sorting operation. The other steps are linear time.
  • Space Complexity: O(n) to store the idx array and the result array.

Code Implementation (Python)

class Solution:
    def findRelativeRanks(self, score: List[int]) -> List[str]:
        n = len(score)
        idx = list(range(n))  # Create index array
 
        # Sort indices by score in descending order
        idx.sort(key=lambda i: score[i], reverse=True) 
 
        ranks = ["Gold Medal", "Silver Medal", "Bronze Medal"] + [str(i + 4) for i in range(n - 3)]
 
        result = [""] * n  # Initialize result array
        for i, index in enumerate(idx):  # Map ranks to original order
            result[index] = ranks[i]
        
        return result

The other languages (Java, C++, Go, TypeScript) follow a very similar structure, with the primary difference lying in the syntax and built-in functions for sorting and string manipulation. The core algorithm remains the same. The provided code examples in the question illustrate these variations effectively.