Find the Lexicographically Largest String From the Box I

Find the Lexicographically Largest String From the Box I - Problem

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:

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.

Input & Output

Example 1 — Basic Case

$ Input: word = "abc", numFriends = 2

› Output: "c"

💡 Note: Possible splits: ["a","bc"], ["ab","c"]. All substrings: "a", "bc", "ab", "c". Lexicographically largest is "c".

Example 2 — Single Friend

$ Input: word = "aba", numFriends = 1

› Output: "aba"

💡 Note: Only one split possible: ["aba"]. The answer is the word itself.

Example 3 — Multiple Friends

$ Input: word = "abac", numFriends = 3

› Output: "c"

💡 Note: Many possible splits into 3 parts. All possible substrings include "a", "b", "c", "ab", "ba", "ac", etc. The largest is "c".

Constraints

1 ≤ word.length ≤ 10³
1 ≤ numFriends ≤ word.length
word consists of lowercase English letters

Visualization

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Asked in

G Google 25 M Microsoft 20

The key insight is that the answer is always the lexicographically largest substring of the original word, regardless of how we split it. Best approach is to find all substrings and return the largest one. Time: O(n³), Space: O(n)

Common Approaches

✓ Frequency Count

⏱️ Time: N/A Space: N/A

Direct Substring Search

⏱️ Time: O(n³) Space: O(n)

The key insight is that the answer is always the lexicographically largest substring of the original word. We can find this by comparing all possible substrings without generating actual splits.

Generate All Splits

⏱️ Time: O(C(n-1, k-1) * n) Space: O(C(n-1, k-1) * n)

Generate all ways to split the word into numFriends parts, collect all substrings, then find the lexicographically largest one. This involves using combinations to place dividers.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

⚡ Linearithmic Space

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Medium Frequency

~25 min Avg. Time

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Smart Actions

💡 Explanation

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