#3403

Medium

auto_awesomeTwo-pointer scanning with invariant tracking

LeetCode Problem Workspace

Find the Lexicographically Largest String From the Box I

This problem involves finding the lexicographically largest string from a given word using a two-pointer approach.

Problem Statement

Given a string word and an integer numFriends, Alice is organizing a game where the goal is to find the lexicographically largest string from the box. After multiple rounds, your task is to determine the largest possible string that can be formed based on the constraints of the game.

In each round, you are to find the lexicographically largest substring of size n - numFriends + 1 or less starting at every index. The final output is the lexicographically largest result from all possible splits of the word.

Examples

Example 1

Input: word = "dbca", numFriends = 2

Output: "dbc"

All possible splits are:

Example 2

Input: word = "gggg", numFriends = 4

Output: "g"

The only possible split is: "g" , "g" , "g" , and "g" .

Constraints

1 <= word.length <= 5 * 103
word consists only of lowercase English letters.
1 <= numFriends <= word.length

Solution Approach

Two-pointer Scanning

Use a two-pointer approach to iterate through the string. For each index, check substrings starting from that index and track the largest one.

Invariant Tracking

Ensure that while scanning, the invariant is maintained to correctly track the largest lexicographically substring at every step of the iteration.

Efficient Enumeration

Enumerate through all potential substrings but limit the enumeration to substrings that are feasible based on the number of friends, ensuring optimal time complexity.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity is O(n) because the solution scans through the string only once, and space complexity is O(n) for storing the largest lexicographically substring during the process.

What Interviewers Usually Probe

Candidate demonstrates knowledge of two-pointer techniques.
Candidate efficiently handles lexicographical comparisons in string processing.
Candidate applies constraints like numFriends and substring lengths effectively in their solution.

Common Pitfalls or Variants

Common pitfalls

Not maintaining the invariant of lexicographical order.
Incorrectly calculating the valid range for substring lengths.
Failing to optimize the solution for time complexity with large inputs.

Follow-up variants

Using a sliding window technique instead of two pointers.
Considering edge cases where numFriends is close to the length of the word.
Optimizing the solution with a stack-based approach for larger inputs.

FAQ

How does the two-pointer approach work for this problem?

The two-pointer approach involves iterating through the string while maintaining a window of potential substrings. At each index, you evaluate the largest lexicographically possible substring within the constraints.

What is the role of invariant tracking in this problem?

Invariant tracking ensures that as you iterate through the string, you can always maintain the largest substring at any given point without losing the optimal result.

How does the `numFriends` parameter affect the substring size?

The numFriends parameter determines the maximum size of the substring that can be selected. It limits the number of splits and reduces the range of substrings that can be considered.

What is the expected time complexity for this problem?

The expected time complexity is O(n) since we are scanning through the string linearly with no nested loops.

How does this problem relate to the Two Pointers pattern?

This problem uses the Two Pointers pattern by scanning through the string with two pointers to determine the largest lexicographically valid substring at each index.

terminal

Solution

Solution 1: Enumerate Substring Left Endpoints

If we fix the left endpoint of the substring, the longer the substring, the larger its lexicographical order. Suppose the left endpoint of the substring is $i$, and the minimum length of the remaining substrings is $\text{numFriends} - 1$, then the right endpoint of the substring can be up to $\min(n, i + n - (\text{numFriends} - 1))$, where $n$ is the length of the string. Note that we are talking about left-closed, right-open intervals.

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class Solution:
    def answerString(self, word: str, numFriends: int) -> str:
        if numFriends == 1:
            return word
        n = len(word)
        return max(word[i : i + n - (numFriends - 1)] for i in range(n))

Continue Practicing

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