1593. Split a String Into the Max Number of Unique Substrings

Problem

Given a string s, return the maximum number of unique substrings that the given string can be split into.

You can split string s into any list of non-empty substrings, where the concatenation of the substrings forms the original string. However, you must split the substrings such that all of them are unique.

A substring is a contiguous sequence of characters within a string.

  Example 1:

Input: s = "ababccc"
Output: 5
Explanation: One way to split maximally is ['a', 'b', 'ab', 'c', 'cc']. Splitting like ['a', 'b', 'a', 'b', 'c', 'cc'] is not valid as you have 'a' and 'b' multiple times.

Example 2:

Input: s = "aba"
Output: 2
Explanation: One way to split maximally is ['a', 'ba'].

Example 3:

Input: s = "aa"
Output: 1
Explanation: It is impossible to split the string any further.

  Constraints:

1 <= s.length&nbsp;<= 16


s contains&nbsp;only lower case English letters.

Solution (Java)

class Solution {
    public int maxUniqueSplit(String s) {
        int lo = 1;
        int hi = s.length();
        // binary search
        while (lo < hi) {
            int mid = (lo + hi + 1) >> 1;
            if (ok(0, mid, 0, s, new HashSet<>())) {
                lo = mid;
            } else {
                hi = mid - 1;
            }
        }
        return lo;
    }

    private boolean ok(int depth, int end, int curLen, String s, Set<String> seen) {
        if (depth == end) {
            return true;
        }
        for (int j = curLen; j < s.length(); j++) {
            // not enough length remains to reach the end.
            if (s.length() - j < end - depth) {
                break;
            }
            String cur = s.substring(curLen, j + 1);
            if (seen.add(cur)) {
                if (ok(depth + 1, end, j + 1, s, seen)) {
                    return true;
                }
                seen.remove(cur);
            }
        }
        return false;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).