Answer
code
Work Step by Step
# 11.50 (Geometry: find nearest points) When a new point is added to the plane, Listing
# 11.5 finds the pair of two nearest points by examining the distance between every
# pair of two points. This approach is correct, but not efficient. A more efficient algorithm
# can be described as follows:
# Let d be the current shortest distance between two
# nearest points p1 and p2
# Let p be the new point added to the plane
# For each existing point t:
# if distance(p, t) < d:
# d = distance(p, t)
# p1, p2 = p, t
# Rewrite Listing 11.5 using this new approach.
def distance(x1, y1, x2, y2):
return ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)) ** 0.5
def nearestPoints(points):
# p1 and p2 are the indices in the points list
p1, p2 = 0, 1 # Initial two points
shortestDistance = distance(points[p1][0], points[p1][1],
points[p2][0], points[p2][1]) # Initialize shortestDistance
# Compute distance for every two points
for i in range(len(points)):
for j in range(i + 1, len(points)):
d = distance(points[i][0], points[i][1],
points[j][0], points[j][1]) # Find distance
if shortestDistance > d:
p1, p2 = i, j # Update p1, p2
shortestDistance = d # New shortestDistance
return p1, p2
def main():
numberOfPoints = eval(input("Enter the number of points: "))
# Create a list to store points
points = []
print("Enter", numberOfPoints, "points:", end='')
for i in range(numberOfPoints):
point = 2 * [0]
point[0], point[1] = \
eval(input("Enter coordinates separated by a comma: "))
points.append(point)
# p1 and p2 are the indices in the points list
p1, p2 = nearestPoints(points)
# Display result
print("The closest two points are (" +
str(points[p1][0]) + ", " + str(points[p1][1]) + ") and (" +
str(points[p2][0]) + ", " + str(points[p2][1]) + ")")
main() # Call the main function
