Minimum Number of Pushes to Type Word I — C++

// Time:  O(4)
// Space: O(1)

// greedy
class Solution {
public:
    int minimumPushes(string word) {
        const auto& ceil_divide = [](int a, int b) {
            return (a + b - 1) / b;
        };

        int result = 0;
        const int l = ceil_divide(size(word), (9 - 2 + 1));
        for (int i = 0; i < l; ++i) {
            result += (i + 1) * min(static_cast<int>(size(word)) - i * (9 - 2 + 1), (9 - 2 + 1));
        }
        return result;
    }
};

// Time:  O(26)
// Space: O(26)
// freq table, greedy
class Solution2 {
public:
    int minimumPushes(string word) {
        vector<int> cnt(26);
        for (const auto& x : word) {
            ++cnt[x - 'a'];
        }
        sort(rbegin(cnt), rend(cnt));
        int result = 0;
        for (int i = 0; i < size(cnt); ++i) {
            result += cnt[i] * (i / (9 - 2 + 1) + 1);
        }
        return result;
    }
};