Solution.java

class Solution {
    public int getLengthOfOptimalCompression(String s, int k) {
        // dp[i][k] := the length of the optimal compression of s[i..n) with at most
        // k deletion
        dp = new int[s.length()][k + 1];
        Arrays.stream(dp).forEach(A -> Arrays.fill(A, K_MAX));
        return compression(s, 0, k);
    }

    private static final int K_MAX = 101;
    private int[][] dp;

    private int compression(final String s, int i, int k) {
        if (k < 0) {
            return K_MAX;
        }
        if (i == s.length() || s.length() - i <= k) {
            return 0;
        }
        if (dp[i][k] != K_MAX) {
            return dp[i][k];
        }
        int maxFreq = 0;
        int[] count = new int[128];
        // Make letters in s[i..j] be the same.
        // Keep the letter that has the maximum frequency in this range and remove
        // the other letters.
        for (int j = i; j < s.length(); ++j) {
            maxFreq = Math.max(maxFreq, ++count[s.charAt(j)]);
            dp[i][k] = Math.min(
                dp[i][k], getLength(maxFreq) + compression(s, j + 1, k - (j - i + 1 - maxFreq)));
        }
        return dp[i][k];
    }

    // Returns the length to compress `maxFreq`.
    private int getLength(int maxFreq) {
        if (maxFreq == 1) {
            return 1; // c
        }
        if (maxFreq < 10) {
            return 2; // [1-9]c
        }
        if (maxFreq < 100) {
            return 3; // [1-9][0-9]c
        }
        return 4; // [1-9][0-9][0-9]c
    }
}