Payment Methods Supported by LC88

Introduction
The term LC 88 often refers to various concepts depending on the field of use — from engineering LC88 and technology to law and policy. However, one of the most recognized references is to Leetcode Problem 88, titled Merge Sorted Array. This algorithmic problem is a fundamental exercise for developers and programmers, especially those preparing for technical interviews. It challenges one’s understanding of array manipulation, sorting, and in-place algorithms. In this article, we’ll explore LC 88 in detail, discussing its problem statement, logic, step-by-step solution, and its broader significance in computer science and practical applications.

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Understanding the Problem

The LC 88 (Merge Sorted Array) problem presents the following task:

You are given two sorted integer arrays, nums1 and nums2, and two integers, m and n, representing the number of elements in each array. You must merge nums2 into nums1 as one sorted array, modifying nums1 in-place without using extra memory.

Example:

Input:
nums1 = [1,2,3,0,0,0], m = 3
nums2 = [2,5,6], n = 3

Output:
[1,2,2,3,5,6]

The challenge lies in merging the two arrays efficiently while maintaining the sorted order and ensuring that no additional data structures (like a new array) are used.

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Core Logic Behind LC 88

The naive approach might be to append all elements of nums2 to nums1 and then sort the combined array. However, this approach is inefficient because it has a time complexity of O((m+n) log(m+n)), which is not optimal for large datasets.

The optimal solution uses a two-pointer approach starting from the end of both arrays:

1. Initialize three pointers — p1 at index m-1 in nums1, p2 at index n-1 in nums2, and p at index m+n-1 (the end of nums1).
2. Compare elements pointed by p1 and p2.
3. Place the larger element at position p in nums1.
4. Move the corresponding pointer backward.
5. Repeat the process until one of the arrays is fully traversed.
6. If nums2 still has elements left, copy them into the beginning of nums1.

This approach ensures O(m + n) time complexity and O(1) space complexity.

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Step-by-Step Example

Let’s walk through the earlier example:

nums1 = [1,2,3,0,0,0]
nums2 = [2,5,6]

• Start from the end:
  • Compare 3 (nums1[p1]) and 6 (nums2[p2]). Place 6 at nums1[p] → [1,2,3,0,0,6]
  • Move p2 and p backward.
• Compare 3 and 5 → place 5 → [1,2,3,0,5,6]
• Compare 3 and 2 → place 3 → [1,2,3,3,5,6]
• Continue until all elements are merged → [1,2,2,3,5,6]

The result is a fully sorted array without using additional memory.

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Why LC 88 Matters

LC 88 is not just an academic exercise; it reinforces crucial programming concepts:

• In-place modification: Teaches memory-efficient programming.
• Pointer manipulation: Strengthens understanding of indexing and iteration.
• Sorting fundamentals: Reinforces algorithmic thinking and optimization.
• Real-world application: Used in merging datasets, combining logs, and handling large sorted files in data processing systems.

Moreover, LC 88 serves https://lc88.bio/esports/ as a building block for more complex algorithms such as merge sort and multi-array merging used in distributed systems.

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Common Mistakes and Pitfalls

• Overwriting elements: If you start merging from the front instead of the end, you may lose important data.
• Ignoring edge cases: Failing to handle empty arrays or arrays with zero initialized elements can lead to incorrect results.
• Extra space usage: Using temporary arrays violates the in-place requirement and reduces efficiency.

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Conclusion

LC 88, or Merge Sorted Array, is a classic example of an elegant, efficient algorithmic problem that embodies key principles of modern programming: optimization, space management, and algorithmic design. Mastering this problem not only prepares one for coding interviews but also instills a deeper appreciation for how simple logic can yield powerful results. Whether you’re a beginner practicing data structures or an experienced engineer refining your algorithmic thinking, LC 88 remains a timeless and essential challenge in the world of software development.