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K Closest Points to Origin - Heap / Priority Queue - Leetcode 973

Disclaimer: This is a personal summary and interpretation based on a YouTube video. It is not official material and not endorsed by the original creator. All rights remain with the respective creators.

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This document summarizes the key takeaways from the video. I highly recommend watching the full video for visual context and coding demonstrations.

Before You Get Started

  • I summarize key points to help you learn and review quickly.
  • Simply click on Ask AI links to dive into any topic you want.

Problem Introduction

  • Summary: The problem involves finding the K closest points to the origin (0, 0) on a plane from a list of points, using Euclidean distance. It's a common interview question, especially at companies like Amazon, and tests knowledge of efficient data structures.
  • Key Takeaway/Example: Euclidean distance for a point (x, y) is sqrt(x² + y²), but you can skip the square root for comparisons since it preserves order.
  • Link for More Details: Ask AI: K Closest Points to Origin

Brute Force Approach

  • Summary: Calculate the Euclidean distance for each point, store them in a list, sort the list, and return the first K points. This works but is inefficient due to sorting the entire list.
  • Key Takeaway/Example: For points like [[1,3], [-2,2]] and K=1, distances are sqrt(10) and sqrt(8); after sorting, pick the smallest.
  • Link for More Details: Ask AI: Brute Force for K Closest Points

Heap Data Structure Basics

  • Summary: Heaps are tree-like structures that maintain order: min-heaps keep the smallest element at the root, max-heaps the largest. They're useful for efficiently tracking extremes in a dataset.
  • Key Takeaway/Example: Inserting or removing from a heap is O(log k) where k is the heap size, making it great for problems needing the top K elements.
  • Link for More Details: Ask AI: Heap Data Structure

Optimal Solution Using Heap

  • Summary: Use a heap of size K to track the closest points. Calculate distances as you iterate through points, adding to the heap and popping the farthest if it exceeds K.
  • Key Takeaway/Example: For points with distances 10, 8, 2 and K=2, the heap ensures you end up with 2 and 8 after processing.
  • Link for More Details: Ask AI: Heap Solution for K Closest Points

Python-Specific Heap Implementation

  • Summary: Python's heapq provides a min-heap, so negate distances to simulate a max-heap for popping the largest (farthest) when the heap reaches size K.
  • Key Takeaway/Example: Push tuples like (-distance, x, y) to the heap; this keeps the largest negative (smallest actual distance) at the root for correct popping.
  • Link for More Details: Ask AI: Python Heapq for K Closest

Time and Space Complexity

  • Summary: The heap approach runs in O(n log k) time since each insertion/pop is log k, and space is O(k) for the heap.
  • Key Takeaway/Example: Better than sorting's O(n log n) when k is much smaller than n.
  • Link for More Details: Ask AI: Complexity of Heap Solution

Code Walkthrough

  • Summary: Implement using heapq: initialize an empty list as heap, iterate points calculating negative distance, push to heap, and pop if size exceeds K. Finally, extract coordinates.
  • Key Takeaway/Example:
import heapq

class Solution:
    def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
        heap = []
        for x, y in points:
            dist = -(x * x + y * y)
            if len(heap) == k:
                heapq.heappushpop(heap, (dist, x, y))
            else:
                heapq.heappush(heap, (dist, x, y))
        return [[x, y] for _, x, y in heap]

About the summarizer

I'm Ali Sol, a Backend Developer. Learn more: