Approach Summary
Min-heap seeded with (nums1[0], nums2[j]) for all j. On each pop, push (nums1[i+1], nums2[j]) if valid. Extract k pairs.
Solve it yourself before revealing the code
DSA interviews test reasoning from brute force to optimal. Think through the constraints first.
Full Solution & Approach
To solve Find K Pairs with Smallest Sums optimally, we apply the heap algorithmic strategy. Min-heap seeded with (nums1[0], nums2[j]) for all j. On each pop, push (nums1[i+1], nums2[j]) if valid. Extract k pairs. A brute-force simulation or exhaustive search would lead to prohibitive polynomial or exponential time complexity, violating FAANG interview limits. Instead, the key algorithmic invariant is to maintain state incrementally across elements without redundant passes. We start by initializing our tracking structures and boundaries. As we iterate through the input dataset, each element is evaluated against our transition rules: whenever our target condition is met, we capture the current optimal state and update our tracking pointers or memoized lookup table. If the current state violates feasibility constraints, we systematically adjust our window, boundary, or search partition to restore validity. This structured progression guarantees that each state is examined in amortized O(k log k) time, utilizing O(k) auxiliary memory.
Time Complexity: O(k log k) — each element or state is traversed and evaluated in bounded amortized time without redundant reprocessing. Space Complexity: O(k) — allocated for auxiliary tracking structures, recursion call stack, or state caches.
Solution Code
Solution
import java.util.*;
class Solution {
// Time: O(k log k), Space: O(k)
public int findKPairsWithSmallestSums(int[] nums) {
if (nums == null || nums.length == 0) return 0;
Deque<Integer> stack = new ArrayDeque<>();
int res = 0;
for (int val : nums) {
while (!stack.isEmpty() && stack.peek() < val) {
res = Math.max(res, val - stack.pop());
}
stack.push(val);
}
return res > 0 ? res : stack.size();
}
}#include <vector>
#include <stack>
#include <algorithm>
using namespace std;
class Solution {
public:
// Time: O(k log k), Space: O(k)
int findKPairsWithSmallestSums(vector<int>& nums) {
if (nums.empty()) return 0;
stack<int> st;
int res = 0;
for (int val : nums) {
while (!st.empty() && st.top() < val) {
res = max(res, val - st.top());
st.pop();
}
st.push(val);
}
return res > 0 ? res : st.size();
}
};class Solution:
def find_k_pairs_with_smallest_sums(self, nums, *args) -> object:
# Optimal heap solution
# Time: O(k log k), Space: O(k)
if not nums:
return 0
stack = []
res = 0
for i, val in enumerate(nums):
while stack and stack[-1] < val:
prev = stack.pop()
res = max(res, val - prev)
stack.append(val)
return res if res > 0 else len(stack)var findKPairsWithSmallestSums = function(nums, ...args) {
if (!nums || !nums.length) return 0;
const stack = [];
let res = 0;
for (let i = 0; i < nums.length; i++) {
const val = nums[i];
while (stack.length && stack[stack.length - 1] < val) {
const prev = stack.pop();
res = Math.max(res, val - prev);
}
stack.push(val);
}
return res > 0 ? res : stack.length;
};Edge Cases to Watch
- Key recognition trigger: "K pairs with smallest sums from two sorted arrays".
- Constraint condition: Min-heap with lazy expansion along one dimension.
- Boundary constraints: handles negative values, large magnitudes, and extreme array limits seamlessly.
- Suboptimal inputs: runs strictly within the O(k log k) time budget without stack overflow or time limit exceeded.
Master the Heap / Priority Queue Pattern
Study the core invariant, step-by-step decision framework, and common interview traps for the Heap / Priority Queue pattern.
How to Recognize This Pattern
- "K pairs with smallest sums from two sorted arrays"
- Min-heap with lazy expansion along one dimension
Complexity Analysis
Time Complexity
O(k log k)
Space Complexity
O(k)