String Compression II

Run-length encoding is a string compression method that works by replacing consecutive identical characters (repeated 2 or more times) with the concatenation of the character and the number marking the count of the characters (length of the run). For example, to compress the string "aabccc" we replace "aa" by "a2" and replace "ccc" by "c3". Thus the compressed string becomes "a2bc3".

Notice that in this problem, we are not adding '1' after single characters.

Given a string s and an integer k. You need to delete at most k characters from s such that the run-length encoded version of s has minimum length.

Find the minimum length of the run-length encoded version of s after deleting at most k characters.

Example 1:

Input: s = "aaabcccd", k = 2
Output: 4
Explanation: Compressing s without deleting anything will give us "a3bc3d" of length 6. Deleting any of the characters 'a' or 'c' would at most decrease the length of the compressed string to 5, for instance delete 2 'a' then we will have s = "abcccd" which compressed is abc3d. Therefore, the optimal way is to delete 'b' and 'd', then the compressed version of s will be "a3c3" of length 4.

Example 2:

Input: s = "aabbaa", k = 2
Output: 2
Explanation: If we delete both 'b' characters, the resulting compressed string would be "a4" of length 2.

Example 3:

Input: s = "aaaaaaaaaaa", k = 0
Output: 3
Explanation: Since k is zero, we cannot delete anything. The compressed string is "a11" of length 3.

Constraints:

• 1 <= s.length <= 100

• 0 <= k <= s.length

• s contains only lowercase English letters.

class Solution {
    Integer[][][] memo;

    public int getLengthOfOptimalCompression(String s, int k) {
        List<int[]> count = new ArrayList<>();
        char prevChar = ' ';
        int cnt = 0;
        // build a list of consecutive chars count, aaabbcc -> {{a, 3}, {b, 2}, {c, 2}}
        for (char c : s.toCharArray()) {
            if (prevChar != c) {
                if (cnt != 0)
                    count.add(new int[]{prevChar - 'a', cnt});
                cnt = 1;
                prevChar = c;
            } else
                cnt++;
        }
        count.add(new int[]{prevChar - 'a', cnt});
        memo = new Integer[count.size() + 1][k + 1][s.length() + 1];
        return helper(count, 0, 0, k);
    }

    // 'extraChars' is a number of additional consecutive chars to be added, for cases like `aabbaa` and we delete two `b`
    // 'index' is the counter, we go through all `count` list elements until we reach the end
    // 'toDelete' is the remaining chars we can delete
    public int helper(List<int[]> count, int extraChars, int index, int toDelete) {
        // Reached the end of count array
        if (index == count.size())
            return 0;
        if (memo[index][toDelete][extraChars] != null)
            return memo[index][toDelete][extraChars];
        int[] curr = count.get(index);
        int countOfChar = curr[1] + extraChars;
        // first just try to keep everything
        int ans = lengthCounter(countOfChar) + helper(count, 0, index + 1, toDelete);
        // We are interested in main-changes only,
        // like a10 -> a9, a2 -> a1, a1 -> a0(Nothing ->'')
        // where string gets shorter
        for (int desired : new int[]{0, 1, 9}) {
            int toRemove = countOfChar - desired; // how many chars to be removed to achieve "desired"
            if (toRemove <= toDelete && desired < countOfChar)
                ans = Math.min(ans, helper(count, 0, index + 1, toDelete - toRemove) + lengthCounter(desired));
        }

        // now let's handle the case like `aabbaa` -> `aaaa`
        // what we do is go through all the next consecutive chars and try to remove them entirely
        // in case we encounter the same character as we have now, we just pass the current count as `a` parameter
        // e.g. `aaabbaa` -> `{{a,3},{b,2},{a,2}}
        // we remove {b,2} and call f(count, 3, j, res),
        // where res will be (k-charsWeRemovedInBetween)
        // and 3 is the count of `a` on the beginning which is passed to sum up with the two `a` we have in the end
        // which results in (2+3)=5 consecutive `a` chars, what we have when we remove both `b`
        int copyOfDelete = toDelete;
        for (int j = index + 1; j < count.size() && copyOfDelete >= 0; j++) {
            int[] next = count.get(j);
            // If we find a matching set of char, ex: 'aabbaa' -> 'a2b2a2'
            // so if we can delete 2*b, then we need to join a2a2 -> a4
            if (next[0] == curr[0]) {
                ans = Math.min(ans, helper(count, countOfChar, j, copyOfDelete));
                break;
            }
            // Assuming we will delete all the chars in between
            copyOfDelete -= next[1];
        }
        memo[index][toDelete][extraChars] = ans;
        return ans;
    }

    // length of char + its count, where n is a count of that char
    // if n == 15, l(15) = 3 -> e.g. `a15`
    public int lengthCounter(int n) {
        if (n <= 1)
            return n;
        if (n < 10)
            return 2;
        if (n < 100)
            return 3;
        return 4;
    }
}