Question

373. Find K Pairs with Smallest Sums

中文文档

Description

You are given two integer arrays nums1 and nums2 sorted in non-decreasing 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.

Return _the_ k _pairs_ (u1, v1), (u2, v2), ..., (uk, vk) _with the smallest sums_.

 

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]

 

Constraints:

• 1 <= nums1.length, nums2.length <= 105
• -109 <= nums1[i], nums2[i] <= 109
• nums1 and nums2 both are sorted in non-decreasing order.
• 1 <= k <= 104
• k <= nums1.length * nums2.length

Solutions

Solution 1

class Solution:
  def kSmallestPairs(
    self, nums1: List[int], nums2: List[int], k: int
  ) -> List[List[int]]:
    q = [[u + nums2[0], i, 0] for i, u in enumerate(nums1[:k])]
    heapify(q)
    ans = []
    while q and k > 0:
      _, i, j = heappop(q)
      ans.append([nums1[i], nums2[j]])
      k -= 1
      if j + 1 < len(nums2):
        heappush(q, [nums1[i] + nums2[j + 1], i, j + 1])
    return ans

class Solution {
  public List<List<Integer>> kSmallestPairs(int[] nums1, int[] nums2, int k) {
    PriorityQueue<int[]> q = new PriorityQueue<>(Comparator.comparingInt(a -> a[0]));
    for (int i = 0; i < Math.min(nums1.length, k); ++i) {
      q.offer(new int[] {nums1[i] + nums2[0], i, 0});
    }
    List<List<Integer>> ans = new ArrayList<>();
    while (!q.isEmpty() && k > 0) {
      int[] e = q.poll();
      ans.add(Arrays.asList(nums1[e[1]], nums2[e[2]]));
      --k;
      if (e[2] + 1 < nums2.length) {
        q.offer(new int[] {nums1[e[1]] + nums2[e[2] + 1], e[1], e[2] + 1});
      }
    }
    return ans;
  }
}

class Solution {
public:
  vector<vector<int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, int k) {
    auto cmp = [&nums1, &nums2](const pair<int, int>& a, const pair<int, int>& b) {
      return nums1[a.first] + nums2[a.second] > nums1[b.first] + nums2[b.second];
    };

    int m = nums1.size();
    int n = nums2.size();
    vector<vector<int>> ans;
    priority_queue<pair<int, int>, vector<pair<int, int>>, decltype(cmp)> pq(cmp);
    for (int i = 0; i < min(k, m); i++)
      pq.emplace(i, 0);
    while (k-- && !pq.empty()) {
      auto [x, y] = pq.top();
      pq.pop();
      ans.emplace_back(initializer_list<int>{nums1[x], nums2[y]});
      if (y + 1 < n)
        pq.emplace(x, y + 1);
    }

    return ans;
  }
};

func kSmallestPairs(nums1, nums2 []int, k int) (ans [][]int) {
  m, n := len(nums1), len(nums2)
  h := hp{nil, nums1, nums2}
  for i := 0; i < k && i < m; i++ {
    h.data = append(h.data, pair{i, 0})
  }
  for h.Len() > 0 && len(ans) < k {
    p := heap.Pop(&h).(pair)
    i, j := p.i, p.j
    ans = append(ans, []int{nums1[i], nums2[j]})
    if j+1 < n {
      heap.Push(&h, pair{i, j + 1})
    }
  }
  return
}

type pair struct{ i, j int }
type hp struct {
  data     []pair
  nums1, nums2 []int
}

func (h hp) Len() int { return len(h.data) }
func (h hp) Less(i, j int) bool {
  a, b := h.data[i], h.data[j]
  return h.nums1[a.i]+h.nums2[a.j] < h.nums1[b.i]+h.nums2[b.j]
}
func (h hp) Swap(i, j int) { h.data[i], h.data[j] = h.data[j], h.data[i] }
func (h *hp) Push(v any)   { h.data = append(h.data, v.(pair)) }
func (h *hp) Pop() any   { a := h.data; v := a[len(a)-1]; h.data = a[:len(a)-1]; return v }