#2207

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Maximize Number of Subsequences in a String

Maximize the number of subsequences by optimally adding a character to a given string to match a specified pattern.

Problem Statement

You are given a string text and a two-character string pattern, both consisting of only lowercase English letters. Your task is to add either pattern[0] or pattern[1] at exactly one position in text, ensuring that the character can be added at the beginning, middle, or end of the string.

The challenge is to determine the maximum number of times the pattern can appear as a subsequence in the modified string. You must identify the optimal position for inserting the character that will result in the maximum subsequences of pattern.

Examples

Example 1

Input: text = "abdcdbc", pattern = "ac"

Output: 4

If we add pattern[0] = 'a' in between text[1] and text[2], we get "abadcdbc". Now, the number of times "ac" occurs as a subsequence is 4. Some other strings which have 4 subsequences "ac" after adding a character to text are "aabdcdbc" and "abdacdbc". However, strings such as "abdcadbc", "abdccdbc", and "abdcdbcc", although obtainable, have only 3 subsequences "ac" and are thus suboptimal. It can be shown that it is not possible to get more than 4 subsequences "ac" by adding only one character.

Example 2

Input: text = "aabb", pattern = "ab"

Output: 6

Some of the strings which can be obtained from text and have 6 subsequences "ab" are "aaabb", "aaabb", and "aabbb".

Constraints

1 <= text.length <= 105
pattern.length == 2
text and pattern consist only of lowercase English letters.

Solution Approach

Greedy Choice to Maximize Subsequences

To solve the problem efficiently, use a greedy approach. Focus on determining the best position to insert either pattern[0] or pattern[1] to maximize subsequences. Iterate through the string, tracking potential subsequences formed by adding the chosen character and validating positions accordingly.

Prefix Sum Calculation for Efficient Counting

Use a prefix sum array to efficiently track the number of valid subsequences formed as you iterate through the string. By leveraging the prefix sum, you can calculate how many subsequences can be made after inserting a character without re-scanning the entire string repeatedly.

Invariant Validation of Subsequences

Ensure that the insertion of the character adheres to an invariant that maximizes subsequences. Validate positions to check the number of valid subsequences, ensuring that no additional subsequences are lost or undercounted after the character insertion.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the final approach chosen. If using a prefix sum with a greedy selection process, the time complexity is typically O(n) where n is the length of the string. Space complexity may be O(n) for the prefix sum array and other auxiliary data structures used.

What Interviewers Usually Probe

The candidate effectively demonstrates the ability to apply a greedy approach for subsequences.
The candidate uses prefix sums or dynamic counting to reduce time complexity in their solution.
The candidate ensures the optimal placement of characters using invariant validation, avoiding suboptimal solutions.

Common Pitfalls or Variants

Common pitfalls

Not considering the best position to insert the character, which leads to suboptimal solutions.
Failing to handle edge cases such as when inserting at the beginning or end of the string.
Misunderstanding how subsequences are counted and invalidating potential subsequences after insertion.

Follow-up variants

What happens if the pattern length is greater than 2?
Can the pattern contain repeated characters and still maintain the same approach?
What if the pattern length increases dynamically during the insertion?

FAQ

What is the primary strategy for solving the "Maximize Number of Subsequences in a String" problem?

The primary strategy involves applying a greedy approach combined with prefix sum calculations to determine the best position to insert a character from the pattern, maximizing the subsequences formed.

How do prefix sums help in the solution of this problem?

Prefix sums enable efficient tracking of subsequences across the string, allowing the solution to calculate subsequences formed after character insertion without re-scanning the string multiple times.

What are some common mistakes candidates make while solving this problem?

Common mistakes include failing to insert the pattern character at the optimal position, miscounting subsequences, and neglecting edge cases like inserting at the beginning or end of the string.

What if the pattern contains the same character twice? Does the approach change?

The approach remains similar even if the pattern contains duplicate characters, but it’s crucial to track how each position contributes to the subsequences formed to avoid errors in counting.

How can GhostInterview help me with greedy choice-based problems?

GhostInterview provides insights into greedy strategy applications, offering guidance on making optimal decisions for subsequence problems and helping you identify the best choices for inserting characters.

terminal

Solution

Solution 1: Traversal + Counting

We can use two variables $x$ and $y$ to record the current counts of $\textit{pattern}[0]$ and $\textit{pattern}[1]$ in the string, respectively.

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class Solution:
    def maximumSubsequenceCount(self, text: str, pattern: str) -> int:
        ans = x = y = 0
        for c in text:
            if c == pattern[1]:
                y += 1
                ans += x
            if c == pattern[0]:
                x += 1
        ans += max(x, y)
        return ans

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