LeetCode 1593 | Split a String Into the Max Number of Unique Substrings | Full Explanation and Solution

   

String manipulation is one of the most commonly tested topics in coding interviews, and LeetCode's Problem 1593: Split a String Into the Max Number of Unique Substrings gives us an interesting challenge. The goal is to split a string into as many unique substrings as possible. In this blog post, we’ll go step by step to understand the problem, come up with an efficient solution, and analyze its time and space complexity.

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Problem Statement

Given a string s, your task is to split it into the maximum number of unique substrings. You can break the string into any list of non-empty substrings as long as the concatenation of all substrings forms the original string, and all the substrings in the split are unique.

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

Example 1:

• Input: s = "ababccc"
• Output: 5
• Explanation: One way to split the string is ["a", "b", "ab", "c", "cc"]. Note that each substring is unique.

Example 2:

• Input: s = "aba"
• Output: 2
• Explanation: A valid split would be ["a", "ba"].

Example 3:

• Input: s = "aa"
• Output: 1
• Explanation: There is no valid way to split this string into more than one unique substring.

The task is straightforward: you need to split the string such that the maximum number of substrings are unique. You can think of this as a recursive or backtracking problem where, at each step, you try to form a new substring and check if it has been seen before.

The challenge lies in:

1. Exploring all possible ways of splitting the string.
2. Ensuring that no substring repeats.

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Approach to Solve the Problem

We can solve this problem using backtracking. The idea is to:

1. Start from the first character of the string.
2. Try to form substrings of increasing lengths starting from each index.
3. If the substring has not been seen before, add it to the set of unique substrings and recursively continue splitting the remaining string.
4. Keep track of the maximum number of unique substrings found during the recursive exploration.

Once the recursion reaches the end of the string (base case), the function will return the number of unique substrings found.

By recursively trying all possible ways to split the string, we can ensure that we find the maximum number of unique substrings.

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Code Implementation

Here’s the code for solving the problem: (CPP)

#include <set>
#include <string>
#include <algorithm>
using namespace std;

class Solution
{
public:
    // Helper function to solve the problem using recursion and backtracking
    int solve(string &s, int index, set<string> &st)
    {
        // Base case: when we've processed the entire string
        if (index == s.length())
            return 0;

        string current = "";
        int maxi = 0;

        // Explore all possible substrings starting from the current index
        for (int i = index; i < s.length(); i++)
        {
            current += s[i];

            // If the current substring is not already in the set
            if (st.find(current) == st.end())
            {
                // Add the current substring to the set
                st.insert(current);

                // Recursively process the remaining string and update the maximum
                int curr = 1 + solve(s, i + 1, st);
                maxi = max(curr, maxi);

                // Backtrack by removing the current substring from the set
                st.erase(current);
            }
        }
        return maxi;
    }

    // Main function that initializes the process
    int maxUniqueSplit(string s)
    {
        set<string> st;
        return solve(s, 0, st);
    }
};

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Step-by-Step Explanation

1. Function maxUniqueSplit(s):

   • This is the main function that initializes the recursive backtracking process. It takes the string s as input and passes it to the helper function solve.

2. Helper Function solve(s, index, st):

   • Base Case: If index equals the length of the string, that means we've reached the end, and we return 0.
   • Current Substring: At each step, we form a new substring starting from the current index.
   • Unique Check: For each substring, we check if it’s already present in the set st (which stores previously seen substrings). If it’s unique, we add it to the set and recursively process the remaining part of the string.
   • Backtracking: After exploring all possibilities for the current substring, we remove it from the set (backtrack) to explore other potential splits.
   • The result is the maximum number of unique substrings that can be formed.

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Time and Space Complexity

Time Complexity:

The time complexity of this approach is O(2^n) in the worst case, where n is the length of the string. This is because for each index, we try multiple substrings of varying lengths and explore all possible ways to split the string.

Space Complexity:

• O(n) for the recursive call stack. In the worst case, the recursion can go up to a depth of n, where n is the length of the string.
• O(k) for the set st that stores up to k unique substrings, where k is the maximum number of unique substrings.

So, the overall space complexity is O(n + k), which simplifies to O(n) because k cannot exceed n.

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Key Takeaways

1. Backtracking is a powerful tool for solving problems that involve exploring multiple possibilities. In this case, we explore all possible ways to split the string into unique substrings.
2. Set data structure is used to efficiently track whether a substring has been encountered before, allowing us to maintain the uniqueness of the split substrings.
3. Time Complexity is exponential due to the nature of backtracking, but this problem can be solved efficiently given the constraint that the string length is at most 16.

The problem LeetCode 1593: Split a String Into the Max Number of Unique Substrings is a great exercise in recursion and backtracking. The solution ensures that we explore all possible ways to split the string while maintaining uniqueness. By using a set to track unique substrings and recursively trying all splits, we can find the maximum number of unique substrings efficiently.

This approach is optimal given the constraints, and with time and space complexity analyzed, you’re well-equipped to tackle this problem!

I hope this post helped you understand how to solve this problem. Feel free to try it out on LeetCode and explore other backtracking problems to further strengthen your problem-solving skills.

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FAQ:

• Q: Why is backtracking necessary for this problem?
  • A: Backtracking allows us to explore all possible splits of the string while ensuring the substrings are unique. This ensures we don't miss any potential solutions.
• Q: Can I optimize this further?
  • A: Given the constraints (string length up to 16), this solution is efficient. Optimizing further might not yield significant gains due to the small input size.