LeetCode-373 Find K Pairs with Smallest Sums

题目描述

You are given two integer arrays nums1 and nums2 sorted in ascending order and an integer k.

Define a pair (u,v) which consists of one element from the first array and one element from the second array.

Find the k pairs (u1,v1),(u2,v2) ...(uk,vk) with the smallest sums.

题目大意

从两个给定的整数数组中依次取出两个数字求和，求能够取出的前k小的数对的和，将数对存入结果当中。

示例

E1

Input: nums1 = [1,7,11], nums2 = [2,4,6], k = 3
Output: [[1,2],[1,4],[1,6]] 
Explanation: The first 3 pairs are returned from the sequence: 
             [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]

E2

Input: nums1 = [1,1,2], nums2 = [1,2,3], k = 2
Output: [1,1],[1,1]
Explanation: The first 2 pairs are returned from the sequence: 
             [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]

E3

Input: nums1 = [1,2], nums2 = [3], k = 3
Output: [1,3],[2,3]
Explanation: All possible pairs are returned from the sequence: [1,3],[2,3]

解题思路

简单利用数据结构 map<int, set<pair<int,int>>> ，遍历所有的数对可能性，取出前k个作为结果即可（map会自动按照第一个主参数排序）。

复杂度分析

时间复杂度：O(M * N)

空间复杂度：O(M * N)

代码

class Solution {
public:
    vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
        map<int, multiset<pair<int, int> > > pairSum;
        // 遍历所有可能的数对，保存数对以及它们的和
        for(int j = 0; j < nums2.size(); ++j) {
            for(int i = 0; i < nums1.size(); ++i) {
                pairSum[nums1[i] + nums2[j]].insert(make_pair(nums1[i], nums2[j]));
            }
        }
        
        vector<vector<int> > res;
        // 取出上述保存的前k个数对
        for(auto iter = pairSum.begin(); iter != pairSum.end(); ++iter) {
            for(auto it = iter->second.begin(); it != iter->second.end(); ++it) {
                if(res.size() >= k)
                    break;
                vector<int> tmp;
                tmp.push_back(it->first);
                tmp.push_back(it->second);
                res.push_back(tmp);
            }
            if(res.size() >= k)
                break;
        }
        
        return res;
    }
};