Minimum Deletions to Make String Balanced

You are given a string s consisting only of characters 'a' and 'b'.

You can delete any number of characters in s to make s balanced. s is balanced if there is no pair of indices (i,j) such that i < j and s[i] = 'b' and s[j]= 'a'.

Return the minimum number of deletions needed to make s balanced.

Example 1:

Input: s = "aababbab"
Output: 2
Explanation: You can either:
Delete the characters at 0-indexed positions 2 and 6 ("aababbab" -> "aaabbb"), or
Delete the characters at 0-indexed positions 3 and 6 ("aababbab" -> "aabbbb").

Example 2:

Input: s = "bbaaaaabb"
Output: 2
Explanation: The only solution is to delete the first two characters.

Constraints:

1 <= s.length <= 105
s[i] is 'a' or 'b'.

Solution:

class Solution {
    
    public int minimumDeletions(String s) {
        int n = s.length();
        // min Deleteion of substring (0, i]
        int[] dp = new int[n];
        int b = s.charAt(0) == 'b' ? 1 : 0;
        for (int i = 1; i < n; i ++) {
            if (s.charAt(i) == 'a') {
                // 1. remove current a
                // 2. remove all prev b
                dp[i] = Math.min(dp[i - 1] + 1, b);
            } else {
                // 1. do nothing
                dp[i] = dp[i - 1];
                b ++;
            }
        }
        return dp[n - 1];
    }
}