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Find the Lexicographically Largest String From the Box I

Difficulty: Medium

Problem Description

You are given a string word, and an integer numFriends. Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round the string word is split into numFriends non-empty strings, such that no previous round has had the exact same split. All the split words are put into a box. Find the lexicographically largest string from the box after all the rounds are finished.

Key Insights

  • The task requires generating all possible splits of the string word into numFriends parts.
  • The splits must be unique across rounds, meaning we need to avoid duplicating previous splits.
  • We need to track and compare the generated substrings to determine the lexicographically largest one.
  • The problem can be efficiently approached by considering the order and positions of characters when creating the splits.

Space and Time Complexity

Time Complexity: O(n^2) - where n is the length of the string, due to the need to consider all split combinations. Space Complexity: O(n) - for storing potential splits.

Solution

To solve the problem, we can use a recursive or iterative approach to generate all possible splits of the string word. We maintain a set to track the unique splits, then compare each generated substring to find the largest one in lexicographical order. The algorithm will iterate through the string, attempting to split it at every possible position for numFriends - 1 times, thus creating the required number of substrings.

Code Solutions

def findLargestString(word: str, numFriends: int) -> str:
    n = len(word)
    if numFriends == 1:
        return word  # Only one friend, return the whole word
    
    largest = ""
    
    def backtrack(index: int, friends_left: int, current: str):
        nonlocal largest
        if friends_left == 1:  # Last friend takes the remaining string
            last_part = word[index:]
            candidate = current + last_part
            largest = max(largest, candidate)
            return
        
        for i in range(index + 1, n - friends_left + 2):  # Ensure non-empty splits
            part = word[index:i]
            backtrack(i, friends_left - 1, current + part)
    
    backtrack(0, numFriends, "")
    return largest
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