Challenge 3
- Algorithms course
- Expert
- Lesson 39/41
- 4 min
Print the convex hull.
Challenge 3 - Convex hull
The third challenge tests the convex hull algorithm. It computes the hull of a point set using Andrew's monotone chain method.
The count_doublings and kmp_search functions are provided above; you will write convex_hull. Sort points first, then build lower and upper hulls.
This challenge is the third link of the cumulative chain.
Practice convex_hull function
Write convex_hull(points). Return the convex hull of the point list in counterclockwise order. Print [(0, 0), (4, 0), (4, 3), (0, 3)] with print(convex_hull([(0,0), (4,0), (4,3), (0,3), (2,1)])). The count_doublings and kmp_search are provided above.
Starter code
def count_doublings(n):
count = 0
size = 1
last = 0
for i in range(n):
if last == size:
size *= 2
count += 1
last += 1
return count
def kmp_search(text, pattern):
n, m = len(text), len(pattern)
lps = [0] * m
length = 0
i = 1
while i < m:
if pattern[i] == pattern[length]:
length += 1
lps[i] = length
i += 1
elif length != 0:
length = lps[length - 1]
else:
lps[i] = 0
i += 1
i = j = 0
while i < n:
if text[i] == pattern[j]:
i += 1
j += 1
if j == m:
return i - j
elif j != 0:
j = lps[j - 1]
else:
i += 1
return -1
def convex_hull(points):
# Return the convex hullSample solution
def convex_hull(points):
pts = sorted(set(points))
if len(pts) <= 1:
return pts
def cross(o, a, b):
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
lower = []
for p in pts:
while len(lower) >= 2 and cross(lower[-2], lower[-1], p) <= 0:
lower.pop()
lower.append(p)
upper = []
for p in reversed(pts):
while len(upper) >= 2 and cross(upper[-2], upper[-1], p) <= 0:
upper.pop()
upper.append(p)
return lower[:-1] + upper[:-1]
print(convex_hull([(0,0), (4,0), (4,3), (0,3), (2,1)]))Expected output
[(0, 0), (4, 0), (4, 3), (0, 3)]
Questions and answers
Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.
1 Convex hull concepts
| Term | Meaning |
|---|---|
monotone chain |
Andrew's method |
sorting |
First step |
lower hull |
Left to right |
upper hull |
Right to left |
2 cross product
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[____]) * (b[0] - o[0])return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])Explanation: a[1] - o[1] is the y component.
3 Which method builds the convex hull?
- Linear scan
- DFS
- Monotone chain Correct answer
- Greedy
Explanation: The monotone chain (Andrew) method is used.