3498. Reverse Degree of a String

3498. Reverse Degree of a String

Difficulty: Easy

Topics: Mid Level, String, Simulation, Biweekly Contest 153

Given a string s, calculate its reverse degree.

The reverse degree is calculated as follows:

• For each character, multiply its position in the reversed alphabet ('a' = 26, 'b' = 25, ..., 'z' = 1) with its position in the string (1-indexed).
• Sum these products for all characters in the string.

Return the reverse degree of s.

Example 1:

• Input: s = "abc"
• Output: 148
• Explanation:

Letter	Index in Reversed Alphabet	Index in String	Product
'a'	26	1	26
'b'	25	2	50
'c'	24	3	72

• The reversed degree is 26 + 50 + 72 = 148.

Example 2:

• Input: s = "zaza"
• Output: 160
• Explanation:

Letter	Index in Reversed Alphabet	Index in String	Product
'z'	1	1	1
'a'	26	2	52
'z'	1	3	3
'a'	26	4	104

• The reverse degree is 1 + 52 + 3 + 104 = 160.

Example 3:

• Input: s = "a"
• Output: 26

Example 4:

• Input: s = "z"
• Output: 1

Example 5:

• Input: s = "az"
• Output: 28

Example 6:

• Input: s = "za"
• Output: 53

Example 7:

• Input: s = "aaaa"
• Output: 260

Example 8:

• Input: s = "zzzz"
• Output: 10

Constraints:

• 1 <= s.length <= 1000
• s contains only lowercase English letters.

Hint:

1. Simulate the operations as described.

Solution:

We iterate through s, map each character to its reverse alphabet value, multiply by its 1-indexed position, and sum all products.

Approach

• Initialize sum = 0.
• Traverse s using a zero-based loop index $i.
• Convert $i to the 1-based string position: $i + 1.
• Convert the character to its reverse alphabet value:
  • ord($s[$i]) - ord('a') gives 0 for 'a', 25 for 'z'.
  • 26 - value gives 'a' -> 26, 'z' -> 1.
• Add positionInString * positionInReversedAlphabet to $sum.
• Return $sum.

Let's implement this solution in PHP: 3498. Reverse Degree of a String

<?php
/**
 * @param String $s
 * @return Integer
 */
function reverseDegree(string $s): int
{
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Test cases
echo reverseDegree("abc") . "\n";       // Output: 148
echo reverseDegree("zaza") . "\n";      // Output: 160
echo reverseDegree("a") . "\n";         // Output: 26
echo reverseDegree("z") . "\n";         // Output: 1
echo reverseDegree("az") . "\n";        // Output: 28
echo reverseDegree("za") . "\n";        // Output: 53
echo reverseDegree("aaaa") . "\n";      // Output: 260
echo reverseDegree("zzzz") . "\n";      // Output: 10
?>

Explanation:

• 'a' has reversed alphabet index 26.
• 'z' has reversed alphabet index 1.
• For "abc": (1 * 26) + (2 * 25) + (3 * 24) = 26 + 50 + 72 = 148.
• For "zaza": (1 * 1) + (2 * 26) + (3 * 1) + (4 * 26) = 1 + 52 + 3 + 104 = 160.
• The solution directly simulates the problem definition, so no sorting or extra mapping array is needed.

Complexity Analysis

• Time Complexity: O(n), where n = strlen(s), because each character is processed once.
• Space Complexity: O(1), because only a few integer variables are used.

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