Minimum Time to Type Word Using Special Typewriter
Easy
There is a special typewriter with lowercase English letters 'a' to 'z' arranged in a circle with a pointer. A character can only be typed if the pointer is pointing to that character. The pointer is initially pointing to the character 'a'. Each second, you may perform one of the following operations:
- Move the pointer one character counterclockwise or clockwise.2. Type the character the pointer is currently on.
Given a string word, return the minimum number of seconds to type out the characters in word.
For example:
- If
word = "abc", the output is 5. The explanation is:- Type 'a' (1 second).
- Move to 'b' (1 second).
- Type 'b' (1 second).
- Move to 'c' (1 second).
- Type 'c' (1 second).
- If
word = "bza", the output is 7.- Move to 'b' (1 second).
- Type 'b' (1 second).
- Move to 'z' (2 seconds).
- Type 'z' (1 second).
- Move to 'a' (1 second).
- Type 'a' (1 second).
- If
word = "zjpc", the output is 34.
What is the most efficient way to solve this problem? What is the time and space complexity of your solution? Can you identify any potential edge cases?
Solution
Naive Approach
The simplest approach is to simulate the typewriter's movements and count the seconds. We start at 'a' and iterate through the word. For each character, we calculate the distance to move clockwise and counterclockwise, choose the minimum, and add it to the total seconds. Finally, add one second for typing the character.
Code (Python)
def min_seconds_naive(word):
current = 'a'
total_seconds = 0
for char in word:
diff = abs(ord(char) - ord(current))
move_seconds = min(diff, 26 - diff)
total_seconds += move_seconds + 1 # 1 for typing
current = char
return total_seconds
Time and Space Complexity
- Time Complexity: O(n), where n is the length of the
word. We iterate through the word once. - Space Complexity: O(1). We use a constant amount of extra space.
Optimal Approach
The optimal approach is essentially the same as the naive approach, as the core logic of calculating the minimum distance between characters is already optimal. The main improvement could involve minor code optimizations, but the underlying algorithm remains the same.
Code (Python)
def min_seconds_optimal(word):
current = 'a'
total_seconds = 0
for char in word:
diff = abs(ord(char) - ord(current))
move_seconds = min(diff, 26 - diff)
total_seconds += move_seconds + 1
current = char
return total_seconds
Time and Space Complexity
- Time Complexity: O(n), where n is the length of the
word. - Space Complexity: O(1).
Edge Cases
- Empty word: If the input
wordis empty, the function should return 0. - Single-character word: If the word contains a single character, the function correctly calculates the distance from 'a' and adds 1 for typing.
- Words with repeated characters: The function should handle repeated characters correctly, accounting for the movements between them.
- Words with characters close to 'a' and 'z': The logic to calculate the minimum distance between clockwise and counter-clockwise movements should ensure correctness, especially when the characters are near the start or end of the alphabet.
Edge case handling in Python:
def min_seconds(word):
if not word:
return 0
current = 'a'
total_seconds = 0
for char in word:
diff = abs(ord(char) - ord(current))
move_seconds = min(diff, 26 - diff)
total_seconds += move_seconds + 1
current = char
return total_seconds
