[LeetCode] 88. Merge Sorted Array

Problem

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?

Solution

Logic

1. 배열 nums1의 길이가 m + n이고 배열의 뒷 부분에 값이 0인 요소들이 n개 있다.

2. 값이 0인 n개의 요소에 배열 nums2의 요소를 할당해준다.

3. 배열 nums1을 오름차순으로 정렬해준다.

   Code

   class Solution {
    public void merge(int[] nums1, int m, int[] nums2, int n) {
        for (int i = 0; i < n; i++)
            nums1[m + i] = nums2[i];
        Arrays.sort(nums1);
    }
   }
   

   Time Complexity

   • 배열 nums2의 길이가 n일 때, 아래 반복문은 O(n)의 시간 복잡도를 가진다.

     for (int i = 0; i < n; i++)
      nums1[m + i] = nums2[i];
     

   • 배열 nums1의 길이가 m + n일 떄, 아래 함수 호출에서 O(nlog(m + n))의 시간 복잡도를 가진다. 따라서 본 문제는 O(nlog(m + n))의 시간 복잡도를 가진다.

     Arrays.sort(nums1);