Intuition

The goal is to find the minimum number of pushes required to type a given string word by remapping keys on a telephone keypad. Each letter must be assigned to a key, and we need to minimize the total number of key presses.

Approach

1. Count Character Frequencies::
2. Use a vector Count of size 26 to store the frequency of each character in the input string word.

3. Iterate through the string and populate the Count vector based on character occurrences.

4. Sort Frequencies:

5. Sort the Count vector in descending order to prioritize characters with higher frequencies.
6. Calculate Pushes:
7. Initialize a result variable res to zero.
8. Iterate through the sorted Count vector and calculate the required "pushes" for each character frequency using the formula (i / 8 + 1) * Count[i]. This formula ensures that the first 8 most frequent characters require 1 push, the next 8 require 2 pushes, and so on.
9. Sum the calculated values into res.

Complexity

• Time complexity: O(N)., where N is the length of the input string word.

• Space complexity: O(1).

Code

class Solution {
public:
    int minimumPushes(string word) {
        ios_base::sync_with_stdio(0);
        cin.tie(0);
        cout.tie(0);
        vector<int> Count(26, 0);
        int res = 0;

        for (char i : word) {
            Count[i - 'a']++;
        }
        sort(Count.rbegin(), Count.rend());
        for (int i = 0; i < 26; i++) {
            if(Count[i] == 0) break;
            res += (i / 8 + 1) * Count[i];
        }
        return res;
    }
};