What is the Maximum Number of Subsequences problem and how can it be solved using a greedy algorithm?

What is the Maximum Number of Subsequences problem and how can it be solved using a greedy algorithm?

The Maximum Number of Subsequences problem is a problem where we are given a string and we need to find the maximum number of non-empty subsequences such that each subsequence contains only distinct characters.

This problem can be solved using a greedy algorithm. The algorithm works as follows:

1. Initialize a count variable to 0 to keep track of the number of subsequences.
2. Initialize a set to store the distinct characters encountered so far.
3. Iterate through each character in the string.
4. If the character is not present in the set, add it to the set and increment the count variable.
5. If the character is already present in the set, it means we have encountered a duplicate character. In this case, we reset the set to empty and start a new subsequence.
6. Repeat steps 4 and 5 until all characters in the string are processed.
7. Return the count variable as the maximum number of subsequences.

The greedy algorithm works by greedily selecting the maximum number of distinct characters in each subsequence. By resetting the set whenever a duplicate character is encountered, we ensure that each subsequence contains only distinct characters.