Given an array of positive integers nums, return the smallest k values, in any order you want.
Example:
Input: nums = [5, 9, 3, 6, 2, 1, 3, 2, 7, 5], k = 4 Output: [1, 2, 2, 3] Explanation: Smallest number is 1, 2nd smallest is 2, 3rd smallest is 2, 4th smallest is 3
The result can be in any order, [2, 1, 3, 2] is also a correct answer.
Your algorithm should run in O(n) time and use O(log n) extra space.
The task is to find the smallest k integers from a given array of positive integers nums. The result can be in any order.
Input: nums = [5, 9, 3, 6, 2, 1, 3, 2, 7, 5], k = 4 Output: [1, 2, 2, 3]
The core challenge is to efficiently find the smallest k integers from the array without sorting the entire array, which would take O(n log n) time. This problem is significant in scenarios where we need to quickly find the top or bottom k elements, such as in streaming data or large datasets.
To solve this problem efficiently, we can use a Min-Heap data structure. A Min-Heap allows us to efficiently extract the smallest elements. Here’s how we can approach the problem:
A naive solution would be to sort the array and then return the first k elements. However, this approach has a time complexity of O(n log n), which is not optimal for large arrays.
We can use a Min-Heap to keep track of the smallest k elements. The steps are as follows:
Here is a step-by-step breakdown of the algorithm:
import java.util.PriorityQueue;
public class SmallestKIntegers {
public static int[] findSmallestK(int[] nums, int k) {
// Min-Heap to store the smallest k elements
PriorityQueue<Integer> minHeap = new PriorityQueue<>();
// Iterate through the array
for (int num : nums) {
// Add the current number to the Min-Heap
minHeap.add(num);
// If the size of the Min-Heap exceeds k, remove the largest element
if (minHeap.size() > k) {
minHeap.poll();
}
}
// Extract the smallest k elements from the Min-Heap
int[] result = new int[k];
for (int i = 0; i < k; i++) {
result[i] = minHeap.poll();
}
return result;
}
public static void main(String[] args) {
int[] nums = {5, 9, 3, 6, 2, 1, 3, 2, 7, 5};
int k = 4;
int[] smallestK = findSmallestK(nums, k);
// Print the result
for (int num : smallestK) {
System.out.print(num + " ");
}
}
}
The time complexity of this approach is O(n log k) because we perform O(log k) operations for each of the n elements. The space complexity is O(k) for storing the k smallest elements in the Min-Heap.
Consider the following edge cases:
To test the solution comprehensively, consider the following test cases:
When approaching such problems, consider the following tips:
In this blog post, we discussed how to find the smallest k integers from an array using a Min-Heap. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for improving problem-solving skills and preparing for coding interviews.
For further reading and practice, consider the following resources: