LeetCode #88 Merge Sorted Array explained and Extra Space solution translated into English
Problem description: given two sorted arrays nums1 and nums2 with sizes m and n respectively, merge the elements of both into nums1 in sorted order. The Extra Space solution creates an auxiliary list with the first m elements of nums1 and all n elements of nums2, sorts that list, and copies the result back into nums1.
Time complexity O((m + n) log(m + n))
Breakdown by operations: first pass adding m elements from nums1 O(m), second pass adding n elements from nums2 O(n), Collections.sort O((m + n) log(m + n)) which dominates the cost, and final copy back to nums1 O(m + n). Total O((m + n) log(m + n)).
Space complexity O(m + n)
Auxiliary list numList stores m + n elements using O(m + n) additional space. Collections.sort may use O(log(m + n)) additional space for the call stack depending on the implementation. Auxiliary variables are O(1). Total O(m + n) auxiliary space.
Example Java code for the Extra Space solution
class Solution { public void merge(int[] nums1, int m, int[] nums2, int n) { List<Integer> numList = new ArrayList<>(); for (int i = 0; i < m; i++) { numList.add(nums1[i]); } for (int i = 0; i < n; i++) { numList.add(nums2[i]); } Collections.sort(numList); for (int i = 0; i < numList.size(); i++) { nums1[i] = numList.get(i); } } }
Notes and considerations: this solution is simple and easy to implement, although it is not optimal in space. For cases where O(1) additional space is required, the two-pointer technique starting from the end of the arrays is recommended to insert into nums1 without an auxiliary list.
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