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In a special typewriter keyboard designed for a word processing application, there are only two buttons:

  1. “Push” – Move the cursor to the right and type the next character of the word.
  2. “Backspace” – Move the cursor to the left, which deletes the last typed character if no characters are left.

Given a string I, the starting position of the cursor is always on the first character, and the goal is to figure out the minimum number of “Push” operations required to type the given word I without making any mistakes or using any backspaces.

Clarifying Questions

  1. Can the word contain special characters or is it limited to alphabetical letters?
    • Assume it can be any characters since the problem does not specify any restrictions.
  2. Does the cursor always start from a blank slate where positions are counted from 1?
    • Yes, the cursor starts from position 1, before the first character of the word.
  3. Are we considering only “push” operations to type the word?
    • Yes, only count “push” operations required to type each character of the string.

Strategy

Given the problem, we should break it down as follows:

  1. “Push” operations are required to type each character in the string from left to right.
  2. The number of “Push” operations needed is directly equal to the length of the string since each character needs one “Push”.

Thus, the minimal operations needed to type out the entire word I will simply be the length of the string.

Code

Here is a Python function that implements the solution:

def minPushOperations(word: str) -> int:
    # The minimum number of pushes is simply the length of the word
    return len(word)

# Example usage:
word = "I-out"
print(minPushOperations(word)) # Output: 5

Time Complexity

The time complexity of this solution is O(1). Since the length of the string can be obtained in constant time in Python, our function will execute in constant time regardless of the input size. The space complexity is also O(1) since we are not using any additional space that scales with the input.

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