Solution Explanation

The problem involves finding the minimum time to type a given word using a special typewriter where characters are arranged in a circle. The solution leverages a greedy approach, focusing on minimizing the movement of the pointer at each step.

Core Idea:

The optimal strategy is to always move the pointer in the shortest direction (clockwise or counter-clockwise) to reach the next character. The time taken to type a character is the sum of the time to move the pointer and the time to type the character itself (which is always 1 second).

Algorithm:

1. Initialization:

   • ans: Variable to store the total time. Initialized to 0.
   • prev: Variable to keep track of the index of the previously typed character (initially 'a', index 0).

2. Iteration:

   • Iterate through each character (c) in the input word.
   • Calculate the current character's index (curr) by subtracting the ASCII value of 'a' from c.
   • Calculate the shortest distance (t) between the previous character's index (prev) and the current character's index (curr). This involves finding the minimum of the absolute difference and its complement (26 - absolute difference) to account for the circular nature of the arrangement.
   • Add the shortest distance (t) plus 1 (for typing the character) to the total time (ans).
   • Update prev with curr for the next iteration.

3. Return:

   • Return the total time (ans).

Time Complexity: O(n), where n is the length of the word. We iterate through the word once.

Space Complexity: O(1). We use only a few constant extra variables.

Code Explanation (Python)

class Solution:
    def minTimeToType(self, word: str) -> int:
        ans = prev = 0
        for c in word:
            curr = ord(c) - ord('a') #Efficiently gets the index of the character
            t = abs(prev - curr)      #Distance between previous and current
            t = min(t, 26 - t)        #Shortest distance considering circularity
            ans += t + 1              #Time to move + time to type
            prev = curr               #Update previous character index
        return ans

The Python code directly implements the algorithm described above. The ord() function is used for efficient index calculation. The min() function elegantly handles the shortest-distance calculation.

Code Explanation (Other Languages)

The Java, C++, and Go code follow the same logic as the Python code, with minor syntactic differences to reflect the specific features of each language. All of them maintain the same time and space complexity. The key aspects—the iteration, distance calculation (including the circularity handling), and time accumulation—remain consistent across all implementations.