Outpost must so possible.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Outpost must so possible.
![1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
"""Given a list of points, find the k closest to the origin.
Idea: Maintain a max heap of k elements.
We can iterate through all points.
If a point p has a smaller distance to the origin than the top element of a
heap, we add point p to the heap and remove the top element.
After iterating through all points, our heap contains the k closest points to
the origin.
111111
from heapq import heapify, heappushpop
def k_closest(points, k, origin=(0, 0)):
# Time: 0(k+(n-k)logk)
# Space: 0(k)
"""Initialize max heap with first k points.
Python does not support a max heap; thus we can use the default min heap
where the keys (distance) are negated.
heap = [(-distance (p, origin), p) for p in points[:k]]
heapify(heap)
11 11 11
For every point p in points [k:],
check if p is smaller than the root of the max heap;
if it is, add p to heap and remove root. Reheapify.
11 11 11
for point in points [k:]:
dist = distance (point, origin)
heappushpop (heap, (-dist, point)) #heappushpop does conditional check
"""Same as:
if d < -heap [0][0]:
heappush(heap, (-d,p))
heappop (heap)
Note: heappushpop is more efficient than separate push and pop calls.
Each heappushpop call takes 0(logk) time.
return [point for nd, point in heap] # return points in heap
def distance (point, origin=(0, 0)):
""" Calculates the distance for a point from origo"""
return (point [0] - origin[0])**2 + (point [1] - origin[1]) **2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a48f55f-d319-4fa0-a1c3-0d0c662e6918%2Faed67b2d-9ce4-46ed-9f49-b59c1042ee06%2F5l0sdac_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
"""Given a list of points, find the k closest to the origin.
Idea: Maintain a max heap of k elements.
We can iterate through all points.
If a point p has a smaller distance to the origin than the top element of a
heap, we add point p to the heap and remove the top element.
After iterating through all points, our heap contains the k closest points to
the origin.
111111
from heapq import heapify, heappushpop
def k_closest(points, k, origin=(0, 0)):
# Time: 0(k+(n-k)logk)
# Space: 0(k)
"""Initialize max heap with first k points.
Python does not support a max heap; thus we can use the default min heap
where the keys (distance) are negated.
heap = [(-distance (p, origin), p) for p in points[:k]]
heapify(heap)
11 11 11
For every point p in points [k:],
check if p is smaller than the root of the max heap;
if it is, add p to heap and remove root. Reheapify.
11 11 11
for point in points [k:]:
dist = distance (point, origin)
heappushpop (heap, (-dist, point)) #heappushpop does conditional check
"""Same as:
if d < -heap [0][0]:
heappush(heap, (-d,p))
heappop (heap)
Note: heappushpop is more efficient than separate push and pop calls.
Each heappushpop call takes 0(logk) time.
return [point for nd, point in heap] # return points in heap
def distance (point, origin=(0, 0)):
""" Calculates the distance for a point from origo"""
return (point [0] - origin[0])**2 + (point [1] - origin[1]) **2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education