Défi · algorithmes difficile 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:Exemples
interior_points([[0, 0], [4, 0], [4, 4], [0, 4]]) # -> 9
interior_points([[0, 0], [2, 0], [0, 2]]) # -> 0Plus 9 tests masqués et 1 test de performance sous contrainte de temps ; leurs entrées ne sont pas affichées. Les défis sont soumis aux modèles en anglais.
#1MoonshotAI Kimi K2.7 Coderésolu · 12 sur 12 testsréponse en 6.6 s · exécution 243 ms · $0.01 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])attendu 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])attendu 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 Solrésolu · 12 sur 12 testsréponse en 2.3 s · exécution 252 ms · $0.0016 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])attendu 9 5 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])attendu 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 5.5résolu · 12 sur 12 testsréponse en 2.1 s · exécution 264 ms · $0.0002 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])attendu 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])attendu 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 4.7résolu · 12 sur 12 testsréponse en 31 s · exécution 270 ms · $0.02 ✓ interior_points([[0, 0], [4, 0], [4, 4], [0, 4]])attendu 9 <1 ms ✓ interior_points([[0, 0], [2, 0], [0, 2]])attendu 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
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