Minimum Deletions to Make String K-Special — C++

// Time:  O(n + 26)
// Space: O(n + 26)

// freq table, counting sort, two pointers
class Solution {
public:
    int minimumDeletions(string word, int k) {
        vector<int> cnt(26);
        for (const auto& x : word) {
            ++cnt[x - 'a'];
        }
        vector<int> arr;
        for (const auto& x : cnt) {
            if (!x) {
                continue;
            }
            arr.emplace_back(x);
        }
        arr = counting_sort(arr, [](const auto& x) { return x; }, false);
        int result = size(word);
        for (int left = 0, right = 0, prev = -1, prefix = 0, suffix = size(word); left < size(arr); ++left) {
            if (left + 1 < size(arr) && arr[left + 1] == arr[left]) {
                continue;
            }
            while (right < size(arr) && arr[right] <= arr[left] + k) {
                suffix -= arr[right++];
            }
            result = min(result, prefix + (suffix - (arr[left] + k) * (static_cast<int>(size(arr)) - right)));
            prefix += arr[left] * (left - prev);
            prev = left;
        }
        return result;
    }

private:
    vector<int> counting_sort(const vector<int>& arr, const function<int(int)>& key, bool is_reverse) {
        vector<int> count(*max_element(cbegin(arr), cend(arr), [&](const auto& x, const auto& y) {
            return key(x) < key(y);
        }) + 1);
        for (const auto& x : arr) {
            ++count[key(x)];
        }
        for (int i = 1; i < size(count); ++i) {
            count[i] += count[i - 1];
        }
        vector<int> result(size(arr));
        if (!is_reverse) {
            for (int i = size(arr) - 1; i >= 0; --i) {  // stable sort
                result[--count[key(arr[i])]] = arr[i];
            }
        } else {
            for (const auto& x : arr) {  // stable sort
                result[--count[key(x)]] = x;
            }
            reverse(begin(result), end(result));
        }
        return result;
    }
};

// Time:  O(n + 26 * log(26))
// Space: O(26)
// freq table, sort, two pointers
class Solution2 {
public:
    int minimumDeletions(string word, int k) {
        vector<int> cnt(26);
        for (const auto& x : word) {
            ++cnt[x - 'a'];
        }
        vector<int> arr;
        for (const auto& x : cnt) {
            if (!x) {
                continue;
            }
            arr.emplace_back(x);
        }
        sort(begin(arr), end(arr));
        int result = size(word);
        for (int left = 0, right = 0, prev = -1, prefix = 0, suffix = size(word); left < size(arr); ++left) {
            if (left + 1 < size(arr) && arr[left + 1] == arr[left]) {
                continue;
            }
            while (right < size(arr) && arr[right] <= arr[left] + k) {
                suffix -= arr[right++];
            }
            result = min(result, prefix + (suffix - (arr[left] + k) * (static_cast<int>(size(arr)) - right)));
            prefix += arr[left] * (left - prev);
            prev = left;
        }
        return result;
    }
};

// Time:  O(n + 26^2)
// Space: O(26)
// freq table
class Solution3 {
public:
    int minimumDeletions(string word, int k) {
        vector<int> cnt(26);
        for (const auto& x : word) {
            ++cnt[x - 'a'];
        }
        int result = size(word);
        for (const auto& x : cnt) {
            if (!x) {
                continue;
            }
            int curr = 0;
            for (const auto& y : cnt) {
                if (!y) {
                    continue;
                }
                curr += y < x ? y : max(y - (x + k), 0);
            }
            result = min(result, curr);
        }
        return result;
    }
};