Find 100 closest points to the origin in a Cartesian plane?

Question

Given a million points in a Cartesian plane, design an algorithm to find 100 closest points to the origin.

Answer 1

Create max heap of size 100

calculate distance of first 100 points add it to the max heap, Now from here calculate distance from one by one and check weather we have to add it to the max heap or not we can do it by comparing top element with the current distance

if current distance < top element in max heap then remove top element in max heap and add current distance
else do nothing

loop the above if else condition for each of the million elements

Order:
Assuming there are n elements and we have to find top m elements then O(m+(n-m)logm) since m << n
Net order is O(nlogm)