h1.py

# import cv2
# import numpy as np
# from sklearn.cluster import DBSCAN
# import matplotlib.pyplot as plt
#
# img = cv2.imread("../assets/pic1.jpg")
# h, w = img.shape[:2]
# # canvas = np.zeros((5*h, 5*w, 3), dtype=np.uint8)
# # canvas[:] = 0
# # canvas[2*h:3*h, 2*w:3*w] = img
# # img = canvas
#
# bbox = (int(h / 3), int(h - h // 8.5), int(w // 5.3), int(w - w // 7.5))
# copy = img[bbox[0]: bbox[1], bbox[2]: bbox[3]].copy()
# img[:, :] = 0
# img[bbox[0]: bbox[1], bbox[2]: bbox[3]] = copy
# # h, w = img.shape[:2]
# canvas = np.zeros((3*h, 3*w, 3), dtype=np.uint8)
# canvas[:] = 0
# canvas[h:2*h, w:2*w] = img
# img = canvas
# img_draw = img.copy()
#
# gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# gray = np.power(gray / 255.0, 5) * 255
# gray = gray.astype(np.uint8)
#
# plt.hist(gray.ravel(), bins=256, range=(0, 256))
# plt.show()
#
# cv2.imshow("gamma", gray)
#
# edges = cv2.Canny(gray, 160, 240)  # edge detection
# # lines = cv2.HoughLinesP(edges, rho=1, theta=np.pi / 180, threshold=160,
# #                         minLineLength=128, maxLineGap=16)  # line detection
# cv2.imshow("edge", edges)
# cv2.waitKey()
#
# lines = cv2.HoughLinesP(edges, rho=1, theta=np.pi / 180, threshold=64,
#                         minLineLength=48, maxLineGap=16)  # line detection
#
# line_eq = []
# for line in lines:
#     x1, y1, x2, y2 = line[0]
#     cv2.line(img_draw, (x1, y1), (x2, y2), (0, 255, 0), 1)
#     a, b = y2 - y1, x1 - x2
#     c = x2 * y1 - x1 * y2
#     line_eq.append(np.array([a, b, c]))
#
# intersections = []
# for i in range(len(line_eq)):
#     for j in range(i + 1, len(line_eq)):
#         l1, l2 = line_eq[i], line_eq[j]
#         v = np.cross(l1, l2)
#         if abs(v[2]) > 1e-6:
#             v = v / v[2]
#             intersections.append(v[:2])  # compute intersection
# print(f"{len(intersections)} intersections in total.")
#
# for i, vp in enumerate(intersections):
#     x, y = int(vp[0]), int(vp[1])
#     cv2.circle(img_draw, (x, y), 2, (0, 0, 255), -1)
#     cv2.putText(img_draw, f"Int{i}", (x + 10, y),
#                 cv2.FONT_HERSHEY_SIMPLEX, 0.6, (0, 0, 255), 1)
#
# # intersections = np.array(intersections)
# # clustering = DBSCAN(eps=60, min_samples=6).fit(intersections)  # select vanishing points from intersection
# # labels = clustering.labels_
#
# # vanishing_points = []
# # for label in set(labels):
# #     if label == -1:
# #         continue
# #
# #     cluster = intersections[labels == label]
# #     vp = cluster.mean(axis=0)
# #     vanishing_points.append(vp)
# # print(f"{len(vanishing_points)} vp in total:", vanishing_points)
# #
# # for i, vp in enumerate(vanishing_points):
# #     x, y = int(vp[0]), int(vp[1])
# #     cv2.circle(img_draw, (x, y), 3, (0, 0, 255), -1)
# #     cv2.putText(img_draw, f"VP{i}", (x + 10, y),
# #                 cv2.FONT_HERSHEY_SIMPLEX, 0.8, (0, 0, 255), 2)
#
#
# # if len(vanishing_points) >= 2:
# #     v1, v2 = np.array([*vanishing_points[0], 1]), np.array([*vanishing_points[1], 1])
# #     line = np.cross(v1, v2)
# #     a, b, c = line  # compute vanishing lines based on vanishing points
# #     h, w = img.shape[:2]
# #
# #     x1, x2 = 0, w
# #     y1, y2 = int((-c - a * x1) / b), int((-c - a * w) / b)
# #     cv2.line(img_draw, (x1, y1), (x2, y2), (255, 0, 0), 1)
# #     cv2.putText(img_draw, "Vanishing Line", (50, 50),
# #                 cv2.FONT_HERSHEY_SIMPLEX, 1, (255, 0, 0), 2)
# #
# # # contours, _ = cv2.findContours(edges, cv2.RETR_LIST, cv2.CHAIN_APPROX_NONE)  # contour detection
# # # ellipse_count = 0
# # # for cnt in contours:
# # #     if len(cnt) < 100:
# # #         continue
# # #
# # #     area = cv2.contourArea(cnt)
# # #     if area < 500:
# # #         continue
# # #
# # #     try:
# # #         ellipse = cv2.fitEllipse(cnt)
# # #         cv2.ellipse(img_draw, ellipse, (255, 255, 0), 3)
# # #         ellipse_count += 1
# # #         if ellipse_count >= 2:
# # #             break
# # #     except:
# # #         pass
#
# plt.figure(figsize=(10, 8))
# plt.imshow(cv2.cvtColor(img_draw, cv2.COLOR_BGR2RGB))
# plt.axis("off")
# plt.show()


from math import *


def valid_number(x, x_pred, n):
    """
    abs(x - x_pred) <= (1 / 2) * (10 ^ n - p)
    """
    diff = abs(x - x_pred)
    res = log(2 * diff, 10)
    return floor(n - res)


def factorial(n):
    if n == 0:
        return 1

    res = 1
    for i in range(1, n + 1):
        res *= i
    return res


if __name__ == '__main__':
    print(valid_number(x=pi, x_pred=3.141, n=1))
    print(valid_number(x=pi, x_pred=3.15, n=1))
    print(valid_number(x=pi, x_pred=22 / 7, n=2))

    x1 = 0.0
    for i in range(9):
        x1 += (-1) ** i * 5 ** i / factorial(i)
    print(x1)

    x2 = 0.0
    for i in range(9):
        x2 += 5 ** i / factorial(i)
    print(1 / x2)

    print(e ** -5)