Task · algorithms hard Python ·
Lattice points inside a polygon
poly lists the vertices of a simple polygon (its edges don't cross or touch except at shared vertices) in order, clockwise or counter-clockwise. Coordinates are integers with absolute value up to 10**9; consecutive vertices are distinct, may be collinear, and the area is positive. Return how many points with integer coordinates lie strictly inside the polygon (not on its boundary). Up to 200,000 vertices.
Signature
def interior_points(poly: list[list[int]]) -> int:Examples
interior_points([[0, 0], [4, 0], [4, 4], [0, 4]]) # -> 9
interior_points([[0, 0], [2, 0], [0, 2]]) # -> 0Plus 9 hidden tests and 1 large-input test under a time limit; their inputs are not shown. Tasks are given to the models in English.
#1MoonshotAI Kimi K2.7 Codesolved · 12 of 12 testsanswer in 6.6 s · runtime 243 ms · $0.01 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])expected 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])expected 0 <1 ms ✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms⏱ 237 msCode
import math from typing import List def interior_points(poly: List[List[int]]) -> int: n = len(poly) if n < 3: return 0 area2 = 0 boundary = 0 x0, y0 = poly[0] px, py = x0, y0 for i in range(1, n): x, y = poly[i] area2 += px * y - x * py dx = x - px dy = y - py boundary += math.gcd(abs(dx), abs(dy)) px, py = x, y # closing edge area2 += px * y0 - x0 * py boundary += math.gcd(abs(x0 - px), abs(y0 - py)) area2 = abs(area2) # Pick's theorem: A = I + B/2 - 1, A2 = 2*A # I = (A2 - B + 2) / 2 return (area2 - boundary + 2) // 2#1OpenAI GPT-6.1 Solsolved · 12 of 12 testsanswer in 2.3 s · runtime 252 ms · $0.0016 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])expected 9 5 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])expected 0 <1 ms ✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ 1 ms✓ <1 ms✓ <1 ms✓ <1 ms⏱ 240 msCode
from math import gcd def interior_points(poly: list[list[int]]) -> int: area2 = 0 boundary = 0 px, py = poly[-1] for x, y in poly: area2 += px * y - x * py boundary += gcd(x - px, y - py) px, py = x, y return (abs(area2) - boundary + 2) // 2#1Anthropic Claude Haiku 5.5solved · 12 of 12 testsanswer in 2.1 s · runtime 264 ms · $0.0002 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])expected 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])expected 0 1 ms ✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ <1 ms✓ 1 ms⏱ 255 msCode
from math import gcd def interior_points(poly: list[list[int]]) -> int: n = len(poly) twice_area = 0 boundary = 0 for i in range(n): x1, y1 = poly[i] x2, y2 = poly[(i + 1) % n] twice_area += x1 * y2 - x2 * y1 boundary += gcd(abs(x2 - x1), abs(y2 - y1)) T = abs(twice_area) return (T - boundary + 2) // 2#1SpaceXAI Grok 4.7solved · 12 of 12 testsanswer in 31 s · runtime 270 ms · $0.02 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])expected 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])expected 0 2 ms ✓ 1 ms✓ <1 ms✓ 1 ms✓ 1 ms✓ <1 ms✓ 1 ms✓ <1 ms✓ <1 ms✓ <1 ms⏱ 259 msCode
import math def interior_points(poly: list[list[int]]) -> int: n = len(poly) area2 = 0 b = 0 for i in range(n): x1, y1 = poly[i] x2, y2 = poly[(i + 1) % n] area2 += x1 * y2 - x2 * y1 b += math.gcd(abs(x2 - x1), abs(y2 - y1)) return (abs(area2) - b) // 2 + 1
Tokens cost: $0.03 · How rounds are run and scored →