python - Points in the circle - performance

Question

I'm learning python by solving CodeWars Katas. The exercise is: "Write a function that calculates the number of points in the circle". My code:

from math import sqrt
import time
start = time.time()

def points(n):
    count=0
    for i in range (-n,n+1):
        for j in range(-n,n+1):
          if abs(i)+abs(j)<=n:
            count=count+1
            continue
          if (sqrt(i**2+j**2))<=n:
             count=count+1
    return count

print (points(1000))
end = time.time()
print(end - start)

It's look like execution time for this is too long (7 second for points(1000), 21 seconds for points(2000)). How to make this more efficient (get rid of loops?).

标签： pythonperformanceloopsmath

Answer 1

怎么样：

def points(n):
    return n * n * PI

或者这还不够“精确”。我们是否正在查看圆点，正方形像素 - 在线内部（以及该线到底在什么像素上？），..？（也许使用n-1？）。