# 373 Find K Pairs with Smallest Sums

### Problem:

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 1:

``````Given nums1 = [1,7,11], nums2 = [2,4,6],  k = 3

Return: [1,2],[1,4],[1,6]

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:

``````Given nums1 = [1,1,2], nums2 = [1,2,3],  k = 2

Return: [1,1],[1,1]

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:

``````Given nums1 = [1,2], nums2 = [3],  k = 3

Return: [1,3],[2,3]

All possible pairs are returned from the sequence:
[1,3],[2,3]
``````

### Solutions:

``````public class Solution {
public List<int[]> kSmallestPairs(int[] nums1, int[] nums2, int k) {
int[] index = new int[nums1.length];
for (int i = 0; i < k; i ++) {
int min = Integer.MAX_VALUE;
int chosen = -1;
for (int j = 0; j < nums1.length; j ++) {
if (index[j] >= nums2.length) {
continue;
}
int tmp = nums1[j] + nums2[index[j]];
if (tmp < min) {
min = tmp;
chosen = j;
}
}
if (chosen != -1) {
index[chosen] ++;
}
}
return result;
}
}
``````
``````public class Solution {
private class Pair implements Comparable<Pair>{
private int i1;
private int i2;
private int sum;
public Pair(int i1, int i2, int sum) {
this.i1 = i1;
this.i2 = i2;
this.sum = sum;
}
public int compareTo(Pair p) {
return this.sum - p.sum;
}
}
public List<int[]> kSmallestPairs(int[] nums1, int[] nums2, int k) {
int[] index = new int[nums1.length];
if (nums1.length == 0 || nums2.length == 0) {
return result;
}
PriorityQueue<Pair> q = new PriorityQueue<Pair>();
for (int i = 0; i < nums1.length; i ++) {
q.add(new Pair(i, 0, nums1[i] + nums2[0]));
index[i] ++;
}
while (k > 0 && !q.isEmpty()) {
Pair p = q.poll();
k --;
if (index[p.i1] < nums2.length) {
q.add(new Pair(p.i1, index[p.i1], nums1[p.i1] + nums2[index[p.i1]]));
index[p.i1] ++;
}
}
return result;
}
}
``````