506. Relative Ranks

[mah-shamim]

Topics: Array, Sorting, Heap (Priority Queue)

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 [1^st, 2^nd, 3^rd, 4^th, 5^th].

Example 2:

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

Constraints:

• n == score.length
• 1 <= n <= 104
• 0 <= score[i] <= 1066
• All the values in score are unique.

[topugit]

We can follow these steps:

1. Sort the Scores: We need to know the relative order of each score, so we sort the scores in descending order.
2. Assign Ranks: Once we have the sorted scores, we can map the ranks to the original scores based on their positions.
3. Map the Ranks Back to the Original Array: Using the original indices of the scores, assign the appropriate ranks.

Let's implement this solution in PHP: 506. Relative Ranks

<?php
function findRelativeRanks($score) {
    $n = count($score);
    $ranked = $score;
    
    // Step 1: Sort the scores in descending order while keeping track of original indices
    arsort($ranked);
    
    // Step 2: Assign ranks
    $ranks = array();
    $index = 0;
    
    foreach ($ranked as $originalIndex => $value) {
        $index++;
        if ($index == 1) {
            $ranks[$originalIndex] = "Gold Medal";
        } elseif ($index == 2) {
            $ranks[$originalIndex] = "Silver Medal";
        } elseif ($index == 3) {
            $ranks[$originalIndex] = "Bronze Medal";
        } else {
            $ranks[$originalIndex] = (string)$index;
        }
    }
    
    // Step 3: Prepare the result array based on the original scores' indices
    $result = array();
    for ($i = 0; $i < $n; $i++) {
        $result[$i] = $ranks[$i];
    }
    
    return $result;
}

// Test cases
print_r(findRelativeRanks([5, 4, 3, 2, 1])); // Output: ["Gold Medal","Silver Medal","Bronze Medal","4","5"]
print_r(findRelativeRanks([10, 3, 8, 9, 4])); // Output: ["Gold Medal","5","Bronze Medal","Silver Medal","4"]
?>

Explanation:

1. Sorting the Scores:

   • We use arsort() to sort the scores in descending order while maintaining the original indices. This is important because we need to assign ranks back to the original positions.

2. Assigning Ranks:

   • After sorting, the highest score gets the "Gold Medal", the second-highest gets the "Silver Medal", the third-highest gets the "Bronze Medal", and so on. For the 4th place and beyond, we simply assign the numeric rank as a string.

3. Mapping Ranks to the Original Array:

   • We then loop over the original score array and fill in the result array using the ranks we calculated, maintaining the original order.

Test Cases:

• [5, 4, 3, 2, 1]: The output is ["Gold Medal","Silver Medal","Bronze Medal","4","5"], as the scores are already in descending order.
• [10, 3, 8, 9, 4]: The output is ["Gold Medal","5","Bronze Medal","Silver Medal","4"], based on the descending order of scores [10, 9, 8, 4, 3].

This solution efficiently handles the problem within the constraints provided.

[mah-shamim]

Thanks to solve the problem of determining the relative ranks of athletes based on their scores

[topugit]

Thanks