Problem Description

Given a string s, calculate its reverse degree.

The reverse degree is calculated as follows:

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

Return the reverse degree of s.

Intuition

The problem requires calculating a unique value, referred to as the reverse degree, for a given string. Understanding this requires two key observations:

1. Reversed Alphabet Position: For each character in the string, determine its position in the reversed alphabet. For instance, 'a' has the reverse position of 26, 'b' is 25, continuing to 'z' which is 1. This can be simply calculated using 26 - (ord(c) - ord('a')) where ord() is a function that gives the ASCII value of a character.

2. Weighting by Position: Each character's reverse position is weighted by its position in the string itself (1-indexed). This means the earlier a character appears, the more it influences the final sum due to multiplication by its positional index.

By iterating over each character, computing the reverse position, and multiplying by the character's position in the string, we can sum these results to find the reverse degree. The approach is direct as it involves iterating over the string once, making the solution efficient with a time complexity of (O(n)), where (n) is the length of the string. The space complexity is (O(1)) since we only use a fixed amount of additional space regardless of input size.

Solution Approach

The solution employs a simple iterative approach to calculate the reverse degree. Here's how the algorithm is implemented:

1. Initialization: Start by initializing a variable ans to 0. This will be used to accumulate the sum of the products of character positions and their corresponding reverse alphabet positions.

2. Enumeration Over the String: Use Python's enumerate() to iterate over each character c in the string s, also retrieving its position i (1-indexed).

3. Calculate Reverse Position: For each character, determine its position in the reversed alphabet using the formula x = 26 - (ord(c) - ord('a')). This utilizes the ord() function to convert the character to its ASCII value and then transforms it to the desired reversed position.

4. Compute Product and Accumulate: Multiply the reverse position x by the character's position i and add this product to ans.

5. Return the Result: After processing all characters, return the accumulated sum ans, which represents the reverse degree.

The entire operation processes each character in a single pass with constant space usage, ensuring efficiency. The implementation effectively captures the described logic:

class Solution:
    def reverseDegree(self, s: str) -> int:
        ans = 0
        for i, c in enumerate(s, 1):
            x = 26 - (ord(c) - ord("a"))
            ans += i * x
        return ans

This solution is optimal for this problem due to its straightforward iteration and calculation, making it both time and space-efficient.

Example Walkthrough

Let's consider the string s = "abc" to demonstrate the calculation of its reverse degree using the given solution approach.

1. Initialize the accumulator: Start with ans = 0.

2. Enumerate through the string:

   • First Character: c = 'a', i = 1 (position in string)

     • Compute the reverse position:
       [ x = 26 - (ord('a') - ord('a')) = 26 ]
     • Calculate product and update the sum: [ ans += 1 \times 26 = 26 ]

   • Second Character: c = 'b', i = 2 (position in string)

     • Compute the reverse position:
       [ x = 26 - (ord('b') - ord('a')) = 25 ]
     • Calculate product and update the sum: [ ans += 2 \times 25 = 50 ]
     • New ans value:
       [ ans = 26 + 50 = 76 ]

   • Third Character: c = 'c', i = 3 (position in string)

     • Compute the reverse position:
       [ x = 26 - (ord('c') - ord('a')) = 24 ]
     • Calculate product and update the sum: [ ans += 3 \times 24 = 72 ]
     • New ans value:
       [ ans = 76 + 72 = 148 ]

3. Result: After processing all characters, the final accumulated value ans is 148. Thus, the reverse degree of the string "abc" is 148.

The overall procedure highlights how each character's position and reverse alphabet position are used to accumulate the total reverse degree in a single pass.

Solution Implementation

Time and Space Complexity

The time complexity of the function reverseDegree is O(n), where n is the length of the input string s. This is because the function iterates over each character of the string once, performing a constant amount of work for each character.

The space complexity of the function is O(1), as it uses a fixed amount of additional space that does not depend on the size of the input string. The only additional variables used are the integer ans and the loop variables i and c, which occupy constant space.

Learn more about how to find time and space complexity quickly.