Tasks Details
medium
Find the maximal sum of any double slice.
Task Score
100%
Correctness
100%
Performance
100%
A non-empty array A consisting of N integers is given.
A triplet (X, Y, Z), such that 0 ≤ X < Y < Z < N, is called a double slice.
The sum of double slice (X, Y, Z) is the total of A[X + 1] + A[X + 2] + ... + A[Y − 1] + A[Y + 1] + A[Y + 2] + ... + A[Z − 1].
For example, array A such that:
A[0] = 3 A[1] = 2 A[2] = 6 A[3] = -1 A[4] = 4 A[5] = 5 A[6] = -1 A[7] = 2contains the following example double slices:
- double slice (0, 3, 6), sum is 2 + 6 + 4 + 5 = 17,
- double slice (0, 3, 7), sum is 2 + 6 + 4 + 5 − 1 = 16,
- double slice (3, 4, 5), sum is 0.
The goal is to find the maximal sum of any double slice.
Write a function:
def solution(A)
that, given a non-empty array A consisting of N integers, returns the maximal sum of any double slice.
For example, given:
A[0] = 3 A[1] = 2 A[2] = 6 A[3] = -1 A[4] = 4 A[5] = 5 A[6] = -1 A[7] = 2the function should return 17, because no double slice of array A has a sum of greater than 17.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [3..100,000];
- each element of array A is an integer within the range [−10,000..10,000].
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Python
Time spent on task 25 minutes
Notes
not defined yet
Code: 15:58:27 UTC,
java,
autosave
Code: 15:58:45 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 15:59:05 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 15:59:15 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print()
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 15:59:29 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
print()
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 15:59:34 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
expand all
Example tests
1.
0.036 s
OK
stdout:
2 8 8 12 17 17 0 5 9 9 15 17
Code: 16:00:14 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
expand all
Example tests
1.
0.036 s
OK
stdout:
2 8 8 12 17 17 0 5 9 9 15 17
User test case 1:
[1, -2, 3, -4, -5]
Code: 16:01:12 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(fromEndMaxEnding[i+1], fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
expand all
Example tests
1.
0.052 s
OK
stdout:
2 8 8 12 17 17 0 5 9 9 15 17
User test case 1:
[-1, -2, -3, -4, -5]
Code: 16:04:42 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(fromStartMaxEnding[i-1], fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 16:04:48 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
expand all
Example tests
1.
0.036 s
OK
stdout:
2 8 7 11 16 15 0 5 9 8 14 16
User test case 1:
[-1, -2, -3, -4, -5]
Code: 16:05:53 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
print(fromEndMaxEnding[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
expand all
Example tests
1.
0.036 s
OK
stdout:
2 8 7 11 16 15 0 5 9 8 14 16
User test case 1:
[-1, -2, -3, -4, -5]
Code: 16:05:59 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
print(fromStartMaxEnding[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 16:06:10 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Code: 16:22:27 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ans
Analysis
User test case 1:
[-1, -2, -3, -4, -5]
Code: 16:22:29 UTC,
py,
final,
score:
100
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(A):
fromStartMaxEnding = [0] * len(A)
for i in range(1, len(A)-1):
fromStartMaxEnding[i] = max(0, fromStartMaxEnding[i-1]+A[i])
fromEndMaxEnding = [0] * len(A)
for i in range(len(A)-2, 0, -1):
fromEndMaxEnding[i] = max(0, fromEndMaxEnding[i+1]+A[i])
ans = -1 * 2**23
for i in range(1, len(A)-1):
ans = max(ans, fromStartMaxEnding[i-1] + fromEndMaxEnding[i+1])
return ansAnalysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N)
expand all
Correctness tests
1.
0.036 s
OK
2.
0.036 s
OK
3.
0.036 s
OK
1.
0.036 s
OK
2.
0.036 s
OK
1.
0.036 s
OK
1.
0.036 s
OK
1.
0.036 s
OK
1.
0.036 s
OK
expand all
Performance tests
1.
0.036 s
OK
1.
0.036 s
OK
1.
0.040 s
OK
1.
0.236 s
OK
1.
0.248 s
OK
1.
0.264 s
OK
1.
0.248 s
OK
2.
0.236 s
OK