LeetCode Intersection of Two Arrays II

原题链接在这里：https://leetcode.com/problems/intersection-of-two-arrays-ii/

题目：

Given two arrays, write a function to compute their intersection.

Example:
Given nums1 = [1, 2, 2, 1], nums2 = [2, 2], return [2, 2].

Note:

• Each element in the result should appear as many times as it shows in both arrays.
• The result can be in any order.

Follow up:

• What if the given array is already sorted? How would you optimize your algorithm?
• What if nums1's size is small compared to nums2's size? Which algorithm is better?
• What if elements of nums2 are stored on disk, and the memory is limited such that you cannot load all elements into the memory at once?

题解：

可以使用双指针.

Time Complexity: O(nlogn). Space: O(1).

AC Java:

 public class Solution {
     public int[] intersect(int[] nums1, int[] nums2) {
         Arrays.sort(nums1);
         Arrays.sort(nums2);
         int i = 0;
         int j = 0;
         List<Integer> res = new ArrayList<Integer>();
         while(i<nums1.length && j<nums2.length){
             if(nums1[i] < nums2[j]){
                 i++;
             }else if(nums1[i] > nums2[j]){
                 j++;
             }else{
                 res.add(nums1[i]);
                 i++;
                 j++;
             }
         }
 
         int [] resArr = new int[res.size()];
         int k = 0;
         for(int num : res){
             resArr[k++] = num;
         }
         return resArr;
     }
 }

Could use HashMap as well.

Time Complexity: O(m + n).

Space: O(Math.min(m, n)).

AC Java:

 class Solution {
     public int[] intersect(int[] nums1, int[] nums2) {
         if(nums1 == null || nums2 == null){
             return new int[0];
         }
 
         HashMap<Integer, Integer> hm = new HashMap<>();
         for(int num : nums1){
             hm.put(num, hm.getOrDefault(num, 0) + 1);
         }
 
         List<Integer> res = new ArrayList<>();
         for(int num : nums2){
             if(hm.containsKey(num)){
                 res.add(num);
                 if(hm.get(num) == 1){
                     hm.remove(num);
                 }else{
                     hm.put(num, hm.get(num) - 1);
                 }
             }
         }
 
         int [] resArr = new int[res.size()];
         int i = 0;
         for(int num : res){
             resArr[i++] = num;
         }
 
         return resArr;
     }
 }

Follow up 2 nums1 length is smaller. 用双指针先sort两个array明显没有利用到num1.length小的特性. 若是用HashMap来记录num1每个element出现频率再iterate nums2, 那么Time Complexity: O(m + n), m = nums1.length, n = num2.length. Space: O(m).

或者sort nums1 再对每一个num2的element在 sorted nums1上做 binary search. Time Complexity: O(mlogm + nlogm). Space: O(1).

由此可见，当m很小时，用HashMap和binary search就是time和space的trade off.

Follow up 3 nums2 is sorted but too big for memory. I/O的操作很贵，所以首先想到的是避免I/O的次数。

若是nums1可以全部load到memory上, 先sort nums1再把nums2从小到大分开load到memory来.

　　if load进来这一段最大值, 也就是最后一个值<nums1[0] 或者 load进来这一段最小值, 也就是第一个值>nums1[nums1.length-1]可以直接跳过, load下一段. 　　else load进来这一段 和 sorted nums1做双指针.

若是nums1也太大了，就先external sort nums1, 在分开load进来nums1一段和nums2一段做双指针.

类似Find Common Characters, Intersection of Two Arrays.