Merge Sorted Array

LeetCode 88 | Difficulty: Easy

Easy

Problem Description

You are given two integer arrays nums1 and nums2, sorted in non-decreasing order, and two integers m and n, representing the number of elements in nums1 and nums2 respectively.

Merge nums1 and nums2 into a single array sorted in non-decreasing order.

The final sorted array should not be returned by the function, but instead be stored inside the array nums1. To accommodate this, nums1 has a length of m + n, where the first m elements denote the elements that should be merged, and the last n elements are set to 0 and should be ignored. nums2 has a length of n.

Example 1:

Input: nums1 = [1,2,3,0,0,0], m = 3, nums2 = [2,5,6], n = 3
Output: [1,2,2,3,5,6]
Explanation: The arrays we are merging are [1,2,3] and [2,5,6].
The result of the merge is [1,2,2,3,5,6] with the underlined elements coming from nums1.

Example 2:

Input: nums1 = [1], m = 1, nums2 = [], n = 0
Output: [1]
Explanation: The arrays we are merging are [1] and [].
The result of the merge is [1].

Example 3:

Input: nums1 = [0], m = 0, nums2 = [1], n = 1
Output: [1]
Explanation: The arrays we are merging are [] and [1].
The result of the merge is [1].
Note that because m = 0, there are no elements in nums1. The 0 is only there to ensure the merge result can fit in nums1.

Constraints:

- `nums1.length == m + n`

- `nums2.length == n`

- `0 <= m, n <= 200`

- `1 <= m + n <= 200`

- `-10^9 <= nums1[i], nums2[j] <= 10^9`

Follow up: Can you come up with an algorithm that runs in O(m + n) time?

Topics: Array, Two Pointers, Sorting

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Approach

Two Pointers

Use two pointers to traverse the array, reducing the search space at each step. This avoids the need for nested loops, bringing complexity from O(n²) to O(n) or O(n log n) if sorting is involved.

When to use

Array is sorted or can be sorted, and you need to find pairs/triplets that satisfy a condition.

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Solutions

Solution 1: C# (Best: 436 ms)

Metric	Value
Runtime	436 ms
Memory	N/A
Date	2017-11-04

Solution

public class Solution {
    public void Merge(int[] nums1, int m, int[] nums2, int n) {
        
    int i = m - 1, j = n - 1, h = m + n - 1;
    while (j >= 0 && i>=0)
    {
        nums1[h--] = nums1[i] > nums2[j] ? nums1[i--] : nums2[j--];
    }
    while(j>=0)
    nums1[h--] = nums2[j--];
}
}

📜 1 more C# submission(s)

Submission (2017-11-04) — 539 ms, N/A

public class Solution {
    public void Merge(int[] nums1, int m, int[] nums2, int n) {
        
    int i = m - 1, j = n - 1, h = m + n - 1;
    while (j >= 0)
    {
        nums1[h--] = i>=0 && nums1[i] > nums2[j] ? nums1[i--] : nums2[j--];
    }
    }
}

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Complexity Analysis

Approach	Time	Space
Two Pointers	$O(n)$	$O(1)$
Sort + Process	$O(n log n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• Ask: "Can I sort the array?" — Sorting often enables two-pointer techniques.
• LeetCode provides 2 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: You can easily solve this problem if you simply think about two elements at a time rather than two arrays. We know that each of the individual arrays is sorted. What we don't know is how they will intertwine. Can we take a local decision and arrive at an optimal solution?

Hint 2: If you simply consider one element each at a time from the two arrays and make a decision and proceed accordingly, you will arrive at the optimal solution.