373 Find K Pairs with Smallest Sums 查找和最小的K对数字
Description:
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.
Example:
Example 1:
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]
Example 2:
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]
Example 3:
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]
题目描述:
给定两个以升序排列的整形数组 nums1 和 nums2, 以及一个整数 k。
定义一对值 (u,v)，其中第一个元素来自 nums1，第二个元素来自 nums2。
找到和最小的 k 对数字 (u1,v1), (u2,v2) ... (uk,vk)。
示例 :
示例 1:
输入: nums1 = [1,7,11], nums2 = [2,4,6], k = 3
输出: [1,2],[1,4],[1,6]
解释: 返回序列中的前 3 对数：
[1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]
示例 2:
输入: nums1 = [1,1,2], nums2 = [1,2,3], k = 2
输出: [1,1],[1,1]
解释: 返回序列中的前 2 对数：
[1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]
示例 3:
输入: nums1 = [1,2], nums2 = [3], k = 3
输出: [1,3],[2,3]
解释: 也可能序列中所有的数对都被返回:[1,3],[2,3]
思路:
求前 k个一般使用堆
使用小顶堆, 固定 nums1中的数, 找到 nums2中的数加入结果中
时间复杂度O((k + n)lgn), 空间复杂度O(n)
代码:
C++:
class Solution
{
public:
vector> kSmallestPairs(vector& nums1, vector& nums2, int k)
{
vector> result;
if (nums1.empty() or nums2.empty()) return result;
int n = nums1.size(), m = nums2.size();
k = min(n * m, k);
priority_queue>> heap;
for (int i = 0; i < n; i++) heap.push({-nums1[i] - nums2[0], {i, 0}});
while (result.size() < k)
{
auto cur = heap.top();
heap.pop();
int i = cur.second.first, j = cur.second.second;
result.push_back({nums1[i], nums2[j++]});
if (j < m) heap.push({-nums1[i] - nums2[j], {i, j}});
}
return result;
}
};
Java:
class Solution {
public List> kSmallestPairs(int[] nums1, int[] nums2, int k) {
PriorityQueue queue = new PriorityQueue<>((o1, o2) -> compare(o2, o1));
for (int i : nums1) {
if (queue.size() == k && compare(queue.peek(), new int[]{i, nums2[0]}) < 0) break;
for (int j : nums2) {
int[] arr = new int[]{i, j};
if (queue.size() < k) queue.offer(arr);
else if (!queue.isEmpty() && compare(queue.peek(), arr) > 0) {
queue.poll();
queue.offer(arr);
} else break;
}
}
List> result = new ArrayList<>();
while (!queue.isEmpty()) {
int[] cur = queue.poll();
result.add(0, Arrays.asList(cur[0], cur[1]));
}
return result;
}
private int compare(int[] arr1, int[] arr2) {
return (arr1[0] + arr1[1]) - (arr2[0] + arr2[1]);
}
}
Python:
class Solution:
def kSmallestPairs(self, nums1: List[int], nums2: List[int], k: int) -> List[List[int]]:
return map(list, heapq.nsmallest(k, itertools.product(nums1, nums2), key=sum))