How to Solve Largest Merge Of Two Strings

To solve Largest Merge Of Two Strings, build the result one character at a time by comparing the remaining substrings of word1 and word2. Use a two-pointer greedy scan to always pick the lexicographically larger choice. Continue until both strings are exhausted, ensuring the merge is maximized at every step.

Problem Statement

Given two strings word1 and word2, you need to create a new string merge by repeatedly choosing either the first character of word1 or word2 until both strings are empty. Each choice should aim to make merge lexicographically as large as possible.

Return the resulting lexicographically largest merge. A string a is larger than string b if at the first differing character a has a higher letter than b. For example, 'abcd' is larger than 'abcc' because 'd' > 'c' at the fourth position.

Examples

Example 1

Input: word1 = "cabaa", word2 = "bcaaa"

Output: "cbcabaaaaa"

One way to get the lexicographically largest merge is:

• Take from word1: merge = "c", word1 = "abaa", word2 = "bcaaa"
• Take from word2: merge = "cb", word1 = "abaa", word2 = "caaa"
• Take from word2: merge = "cbc", word1 = "abaa", word2 = "aaa"
• Take from word1: merge = "cbca", word1 = "baa", word2 = "aaa"
• Take from word1: merge = "cbcab", word1 = "aa", word2 = "aaa"
• Append the remaining 5 a's from word1 and word2 at the end of merge.

Example 2

Input: word1 = "abcabc", word2 = "abdcaba"

Output: "abdcabcabcaba"

Example details omitted.

Constraints

• 1 <= word1.length, word2.length <= 3000
• word1 and word2 consist only of lowercase English letters.

Solution Approach

Two-Pointer Greedy Scanning

Use two pointers starting at the beginning of word1 and word2. At each step, compare the current substrings starting from the pointers. Append the character from the string whose substring is lexicographically larger. Move that pointer forward and repeat until both strings are consumed.

Efficient Substring Comparison

Instead of comparing full remaining strings each time, consider using simple string slicing or built-in comparison operators to efficiently decide which character to pick. This preserves the invariant that merge remains lexicographically maximal at each choice.

Edge Case Handling

Handle cases where one string becomes empty before the other. In such scenarios, append all remaining characters from the non-empty string to merge. This ensures correctness without breaking the greedy invariant.

Complexity Analysis

Time complexity is O(n + m) if comparisons of remaining substrings are optimized, where n and m are the lengths of word1 and word2. Space complexity is O(n + m) for storing the merged string.

What Interviewers Usually Probe

• Looking for two-pointer and greedy understanding.
• Expect efficient lexicographical comparison without redundant scanning.
• Check for correct handling when one string is exhausted before the other.

Common Pitfalls or Variants

Common pitfalls

• Naively concatenating characters without checking remaining substrings can fail on ties.
• Comparing only the first characters instead of full remaining substrings may produce a smaller merge.
• Forgetting to append the leftover of the non-empty string after the other is exhausted.

Follow-up variants

• Return the lexicographically smallest merge instead of largest.
• Merge more than two strings simultaneously using a generalized two-pointer greedy approach.
• Apply the same merge logic with uppercase letters or custom lexicographical orders.

How GhostInterview Helps

• Highlights the two-pointer scanning pattern to make correct greedy choices.
• Provides step-by-step verification of why a particular character is chosen over the other.
• Detects common failure modes like mishandling ties or leftover characters to ensure correct merge construction.

Topic Pages

• Two Pointers
• String
• Greedy

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FAQ

What is the main strategy for Largest Merge Of Two Strings?

The main strategy is two-pointer greedy scanning, choosing the lexicographically larger remaining substring at each step.

How do I handle ties between the first characters of word1 and word2?

Compare the remaining substrings starting from the tie point and choose the one that is lexicographically larger.

Can this approach work efficiently for long strings?

Yes, with optimized substring comparisons or slicing, the two-pointer method achieves linear time relative to total string length.

What if one string runs out before the other?

Simply append all remaining characters from the non-empty string to the merge; this maintains the maximal lexicographical result.

Does this solution pattern appear in other string problems?

Yes, two-pointer scanning with greedy invariant tracking is common in string merging and lexicographical optimization problems.