What is the brute force solution for Split a String Into the Max Number of Unique Substrings?

The brute force approach for Split a String Into the Max Number of Unique Substrings is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible substrings of the given string and checking each combination to see if they are unique. This method is straightforward but can be inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(n * 2^n).

What algorithm or data structure is used to solve Split a String Into the Max Number of Unique Substrings?

Split a String Into the Max Number of Unique Substrings uses the following concepts: Hash Table, String, Backtracking. The recommended patterns to study are: Hash Map, Backtracking.

What are the interview tips for Split a String Into the Max Number of Unique Substrings?

Explain your thought process clearly while coding. Discuss edge cases and constraints upfront. Practice writing clean and efficient code.

What are common mistakes when solving Split a String Into the Max Number of Unique Substrings?

Not using a set to track unique substrings. Forgetting to backtrack properly, leading to incorrect counts.

#1593

Split a String Into the Max Number of Unique Substrings

Medium

Hash TableStringBacktrackingHash MapBacktracking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * 2^n)
Space	O(1)	O(n)

💡

Intuition

Time O(n * 2^n)Space O(n)

The optimal solution uses backtracking with memoization to avoid recalculating results for the same starting index and set of used substrings. This significantly reduces the number of computations and improves efficiency.

⚙️

Algorithm

3 steps

1Step 1: Use a recursive function with memoization to store results for each starting index.
2Step 2: At each index, try all possible substrings and track unique ones using a set.
3Step 3: Return the maximum count of unique substrings found.

solution.py17 lines

1# Full working Python code
2from typing import Set
3from functools import lru_cache
4
5class Solution:
6    def maxUniqueSplit(self, s: str) -> int:
7        @lru_cache(None)
8        def backtrack(start: int, used: frozenset) -> int:
9            if start == len(s):
10                return len(used)
11            max_count = 0
12            for end in range(start + 1, len(s) + 1):
13                substring = s[start:end]
14                if substring not in used:
15                    max_count = max(max_count, backtrack(end, used | {substring}))
16            return max_count
17        return backtrack(0, frozenset())

ℹ

Complexity note: The time complexity is O(n * 2^n) due to the exponential number of subsets of substrings we can create, but memoization helps reduce redundant calculations. The space complexity is O(n) for storing the memoization map.

1Using a set helps track uniqueness efficiently.
2Backtracking allows exploring all combinations while pruning invalid paths.

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