Find the N Smallest - Discussion
Edge Cases​
- Empty Collection: If the collection is empty, the function should return an empty array.
2.z
**N Greater than Collection Size**: If
N` is greater than the number of elements in the collection, the function should return all elements sorted in ascending order. - N is Zero: If
N
is zero, the function should return an empty array. - Collection with Duplicate Elements: The function should correctly handle collections with duplicate elements.
Complexity​
- Time Complexity:
- Sorting Approach: O(n log n) where n is the number of elements in the collection.
- Min-Heap Approach: O(n log k) where n is the number of elements and k is the number of smallest elements to find.
- Space Complexity:
- Sorting Approach: O(n) due to the need to store the sorted array.
- Min-Heap Approach: O(k) for storing the k smallest elements in the heap.
Proposed Solutions​
Solution 1: Using sorted()
and prefix()
​
Description​
This approach leverages Swift's built-in sorted()
method to sort the elements of the collection in ascending order and then uses the prefix()
method to retrieve the first n
elements. This combination ensures that the function returns the smallest n
elements sorted in ascending order.
Implementation​
import Foundation
extension Collection where Element: Comparable {
func challenge38(count n: Int) -> [Element] {
return Array(self.sorted().prefix(n))
}
}
Pros​
- Simple and easy to understand.
- Utilizes Swift's powerful standard library functions for sorting and slicing collections.
Cons​
- The
sorted()
method has a time complexity of O(n log n), which might not be efficient for very large collections. - The entire collection is sorted even if only a few smallest elements are needed.
Solution 2: Using a Min-Heap (Priority Queue)​
Description​
This approach uses a Min-Heap (Priority Queue) to efficiently keep track of the N smallest elements in the collection. A Min-Heap allows us to insert elements and extract the minimum element in O(log k) time, making it more efficient than sorting the entire array when N is much smaller than the size of the collection.
Implementation​
import Foundation
// MARK: - MinHeap Implementation
struct MinHeap<Element: Comparable> {
private var heap = [Element]()
var count: Int {
return heap.count
}
mutating func insert(_ element: Element) {
heap.append(element)
siftUp(heap.count - 1)
}
mutating func extractMin() -> Element? {
guard !heap.isEmpty else { return nil }
heap.swapAt(0, heap.count - 1)
let min = heap.removeLast()
siftDown(0)
return min
}
private mutating func siftUp(_ index: Int) {
var child = index
var parent = (child - 1) / 2
while child > 0 && heap[child] < heap[parent] {
heap.swapAt(child, parent)
child = parent
parent = (child - 1) / 2
}
}
private mutating func siftDown(_ index: Int) {
var parent = index
while true {
let leftChild = 2 * parent + 1
let rightChild = 2 * parent + 2
var candidate = parent
if leftChild < heap.count && heap[leftChild] < heap[candidate] {
candidate = leftChild
}
if rightChild < heap.count && heap[rightChild] < heap[candidate] {
candidate = rightChild
}
if candidate == parent {
return
}
heap.swapAt(parent, candidate)
parent = candidate
}
}
}
// MARK: - Extension for Collection
extension Collection where Element: Comparable {
func challenge38(count n: Int) -> [Element] {
var minHeap = MinHeap<Element>()
for element in self {
minHeap.insert(element)
}
var result = [Element]()
for _ in 0..<min(n, minHeap.count) {
if let min = minHeap.extractMin() {
result.append(min)
}
}
return result
}
}
Pros​
- More efficient for large collections when N is much smaller than the size of the collection.
- Avoids sorting the entire collection, reducing unnecessary computations.
Cons​
- Slightly more complex to implement compared to the simple sorting approach.
- Requires understanding of heap data structures and their operations.
Conclusion​
Using a Min-Heap (Priority Queue) to find the N smallest elements in a collection is an efficient approach, especially when N is much smaller than the size of the collection. This method avoids sorting the entire collection, reducing unnecessary computations. While the implementation is slightly more complex, it offers significant performance benefits for large collections. The sorting approach, while simpler, is suitable for smaller collections or cases where the simplicity of implementation is preferred.