[LeetCode] 350. Intersection of Two Arrays II 两个数组相交II

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

Example 1:

Input: nums1 = [1,2,2,1], nums2 = [2,2]
Output: [2,2]

Example 2:

Input: nums1 = [4,9,5], nums2 = [9,4,9,8,4]
Output: [4,9]

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?

解法1：Hashmap

解法2：双指针

Python:

class Solution(object):
    def intersect(self, nums1, nums2):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: List[int]
        """
        if len(nums1) > len(nums2):
            return self.intersect(nums2, nums1)
 
        lookup = collections.defaultdict(int)
        for i in nums1:
            lookup[i] += 1
 
        res = []
        for i in nums2:
            if lookup[i] > 0:
                res += i,
                lookup[i] -= 1
 
        return res

# If the given array is already sorted, and the memory is limited, and (m << n or m >> n).
# Time:  O(min(m, n) * log(max(m, n)))
# Space: O(1)
# Binary search solution.
class Solution(object):
    def intersect(self, nums1, nums2):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: List[int]
        """
        if len(nums1) > len(nums2):
            return self.intersect(nums2, nums1)
 
        def binary_search(compare, nums, left, right, target):
            while left < right:
                mid = left + (right - left) / 2
                if compare(nums[mid], target):
                    right = mid
                else:
                    left = mid + 1
            return left
 
        nums1.sort(), nums2.sort()  # Make sure it is sorted, doesn't count in time.
 
        res = []
        left = 0
        for i in nums1:
            left = binary_search(lambda x, y: x >= y, nums2, left, len(nums2), i)
            if left != len(nums2) and nums2[left] == i:
                res += i,
                left += 1
 
        return res

# If the given array is already sorted, and the memory is limited or m ~ n.
# Time:  O(m + n)
# Soace: O(1)
# Two pointers solution.
class Solution(object):
    def intersect(self, nums1, nums2):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: List[int]
        """
        nums1.sort(), nums2.sort()  # Make sure it is sorted, doesn't count in time.
 
        res = []
 
        it1, it2 = 0, 0
        while it1 < len(nums1) and it2 < len(nums2):
            if nums1[it1] < nums2[it2]:
                it1 += 1
            elif nums1[it1] > nums2[it2]:
                it2 += 1
            else:
                res += nums1[it1],
                it1 += 1
                it2 += 1
 
        return res

# If the given array is not sorted, and the memory is limited.
# Time:  O(max(m, n) * log(max(m, n)))
# Space: O(1)
# Two pointers solution.
class Solution(object):
    def intersect(self, nums1, nums2):
        """
        :type nums1: List[int]
        :type nums2: List[int]
        :rtype: List[int]
        """
        nums1.sort(), nums2.sort()  # O(max(m, n) * log(max(m, n)))
 
        res = []
 
        it1, it2 = 0, 0
        while it1 < len(nums1) and it2 < len(nums2):
            if nums1[it1] < nums2[it2]:
                it1 += 1
            elif nums1[it1] > nums2[it2]:
                it2 += 1
            else:
                res += nums1[it1],
                it1 += 1
                it2 += 1
 
        return res

C++:

// If the given array is not sorted and the memory is unlimited.
// Time:  O(m + n)
// Space: O(min(m, n))
// Hash solution.
class Solution {
public:
    vector<int> intersect(vector<int>& nums1, vector<int>& nums2) {
        if (nums1.size() > nums2.size()) {
            return intersect(nums2, nums1);
        }
 
        unordered_map<int, int> lookup;
        for (const auto& i : nums1) {
            ++lookup[i];
        }
 
        vector<int> result;
        for (const auto& i : nums2) {
            if (lookup[i] > 0) {
                result.emplace_back(i);
                --lookup[i];
            }
        }
 
        return result;
    }
};

C++:

// If the given array is already sorted, and the memory is limited, and (m << n or m >> n).
// Time:  O(min(m, n) * log(max(m, n)))
// Space: O(1)
// Binary search solution.
class Solution {
public:
    vector<int> intersect(vector<int>& nums1, vector<int>& nums2) {
        if (nums1.size() > nums2.size()) {
            return intersect(nums2, nums1);
        }
 
        // Make sure it is sorted, doesn't count in time.
        sort(nums1.begin(), nums1.end());
        sort(nums2.begin(), nums2.end());
 
        vector<int> result;
        auto it = nums2.cbegin();
        for (const auto& i : nums1) {
            it = lower_bound(it, nums2.cend(), i);
            if (it != nums2.end() && *it == i) {
                result.emplace_back(*it++);
            }
        }
 
        return result;
    }
};

C++:

// If the given array is already sorted, and the memory is limited or m ~ n.
// Time:  O(m + n)
// Soace: O(1)
// Two pointers solution.
class Solution {
public:
    vector<int> intersect(vector<int>& nums1, vector<int>& nums2) {
        vector<int> result;
        // Make sure it is sorted, doesn't count in time.
        sort(nums1.begin(), nums1.end());
        sort(nums2.begin(), nums2.end());
        auto it1 = nums1.cbegin(), it2 = nums2.cbegin();
        while (it1 != nums1.cend() && it2 != nums2.cend()) {
            if (*it1 < *it2) {
                ++it1;
            } else if (*it1 > *it2) {
                ++it2;
            } else {
                result.emplace_back(*it1);
                ++it1, ++it2;
            }
        }
        return result;
    }
};

C++:

// If the given array is not sorted, and the memory is limited.
// Time:  O(max(m, n) * log(max(m, n)))
// Space: O(1)
// Two pointers solution.
class Solution {
public:
    vector<int> intersect(vector<int>& nums1, vector<int>& nums2) {
        vector<int> result;
        // O(max(m, n) * log(max(m, n)))
        sort(nums1.begin(), nums1.end());
        sort(nums2.begin(), nums2.end());
        auto it1 = nums1.cbegin(), it2 = nums2.cbegin();
        while (it1 != nums1.cend() && it2 != nums2.cend()) {
            if (*it1 < *it2) {
                ++it1;
            } else if (*it1 > *it2) {
                ++it2;
            } else {
                result.emplace_back(*it1);
                ++it1, ++it2;
            }
        }
        return result;
    }
};

　　

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