Minimum Number of Pushes to Type Word I

Problem Description

You are given a string word containing distinct lowercase English letters. Telephone keypads can be remapped to distinct collections of letters. Each letter must be mapped to exactly one key, and you need to find the minimum number of times the keys will be pushed to type the string word after remapping the keys.

Key Insights

• Each key can be remapped to any distinct collection of letters.
• The cost of typing a letter corresponds to its position in the remapped collection (1 push for the first letter, 2 pushes for the second, etc.).
• The goal is to minimize the total number of pushes required to type the entire word.

Space and Time Complexity

Time Complexity: O(n) where n is the length of the word, as we only need to iterate through the letters once. Space Complexity: O(1) since we only need a fixed amount of space for indices and counters, regardless of the input size.

Solution

To solve the problem, we can utilize a greedy approach:

1. Sort the letters in the word.
2. Assign the first letter to the first key and continue assigning letters to keys based on their sorted order.
3. Calculate the total number of pushes required based on their assigned positions.

The sorted letters will ensure that letters assigned to the same key minimize the total pushes required, as lower indexed letters incur lower push costs.

Code Solutions