Tasks Details
medium
Divide array A into K blocks and minimize the largest sum of any block.
Task Score
100%
Correctness
100%
Performance
100%
You are given integers K, M and a non-empty array A consisting of N integers. Every element of the array is not greater than M.
You should divide this array into K blocks of consecutive elements. The size of the block is any integer between 0 and N. Every element of the array should belong to some block.
The sum of the block from X to Y equals A[X] + A[X + 1] + ... + A[Y]. The sum of empty block equals 0.
The large sum is the maximal sum of any block.
For example, you are given integers K = 3, M = 5 and array A such that:
A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2 A[6] = 2The array can be divided, for example, into the following blocks:
- [2, 1, 5, 1, 2, 2, 2], [], [] with a large sum of 15;
- [2], [1, 5, 1, 2], [2, 2] with a large sum of 9;
- [2, 1, 5], [], [1, 2, 2, 2] with a large sum of 8;
- [2, 1], [5, 1], [2, 2, 2] with a large sum of 6.
The goal is to minimize the large sum. In the above example, 6 is the minimal large sum.
Write a function:
def solution(K, M, A)
that, given integers K, M and a non-empty array A consisting of N integers, returns the minimal large sum.
For example, given K = 3, M = 5 and array A such that:
A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2 A[6] = 2the function should return 6, as explained above.
Write an efficient algorithm for the following assumptions:
- N and K are integers within the range [1..100,000];
- M is an integer within the range [0..10,000];
- each element of array A is an integer within the range [0..M].
Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Python
Total time used 1 minutes
Effective time used 1 minutes
Notes
not defined yet
Task timeline
Code: 14:27:01 UTC,
py,
verify,
result: Passed
def blockSizeIsValid(A, max_block_cnt, max_block_size):
block_sum = 0
block_cnt = 0
for element in A:
if block_sum + element > max_block_size:
block_sum = element
block_cnt += 1
else:
block_sum += element
if block_cnt >= max_block_cnt:
return False
return True
def binarySearch(A, max_block_cnt, using_M_will_give_you_wrong_results):
lower_bound = max(A)
upper_bound = sum(A)
if max_block_cnt == 1: return upper_bound
if max_block_cnt >= len(A): return lower_bound
while lower_bound <= upper_bound:
candidate_mid = int((lower_bound + upper_bound) / 2)
if blockSizeIsValid(A, max_block_cnt, candidate_mid):
upper_bound = candidate_mid - 1
else:
lower_bound = candidate_mid + 1
return lower_bound
def solution(K, M, A):
return binarySearch(A,K,M)
Analysis
Code: 14:27:18 UTC,
py,
verify,
result: Passed
def blockSizeIsValid(A, max_block_cnt, max_block_size):
block_sum = 0
block_cnt = 0
for element in A:
if block_sum + element > max_block_size:
block_sum = element
block_cnt += 1
else:
block_sum += element
if block_cnt >= max_block_cnt:
return False
return True
def binarySearch(A, max_block_cnt, using_M_will_give_you_wrong_results):
lower_bound = max(A)
upper_bound = sum(A)
if max_block_cnt == 1: return upper_bound
if max_block_cnt >= len(A): return lower_bound
while lower_bound <= upper_bound:
candidate_mid = (lower_bound + upper_bound) // 2
if blockSizeIsValid(A, max_block_cnt, candidate_mid):
upper_bound = candidate_mid - 1
else:
lower_bound = candidate_mid + 1
return lower_bound
def solution(K, M, A):
return binarySearch(A,K,M)
Analysis
Code: 14:27:24 UTC,
py,
verify,
result: Passed
def blockSizeIsValid(A, max_block_cnt, max_block_size):
block_sum = 0
block_cnt = 0
for element in A:
if block_sum + element > max_block_size:
block_sum = element
block_cnt += 1
else:
block_sum += element
if block_cnt >= max_block_cnt:
return False
return True
def binarySearch(A, max_block_cnt, using_M_will_give_you_wrong_results):
lower_bound = max(A)
upper_bound = sum(A)
if max_block_cnt == 1: return upper_bound
if max_block_cnt >= len(A): return lower_bound
while lower_bound <= upper_bound:
candidate_mid = (lower_bound + upper_bound) // 2
if blockSizeIsValid(A, max_block_cnt, candidate_mid):
upper_bound = candidate_mid - 1
else:
lower_bound = candidate_mid + 1
return lower_bound
def solution(K, M, A):
return binarySearch(A,K,M)
Analysis
Code: 14:27:26 UTC,
py,
final,
score:
100
def blockSizeIsValid(A, max_block_cnt, max_block_size):
block_sum = 0
block_cnt = 0
for element in A:
if block_sum + element > max_block_size:
block_sum = element
block_cnt += 1
else:
block_sum += element
if block_cnt >= max_block_cnt:
return False
return True
def binarySearch(A, max_block_cnt, using_M_will_give_you_wrong_results):
lower_bound = max(A)
upper_bound = sum(A)
if max_block_cnt == 1: return upper_bound
if max_block_cnt >= len(A): return lower_bound
while lower_bound <= upper_bound:
candidate_mid = (lower_bound + upper_bound) // 2
if blockSizeIsValid(A, max_block_cnt, candidate_mid):
upper_bound = candidate_mid - 1
else:
lower_bound = candidate_mid + 1
return lower_bound
def solution(K, M, A):
return binarySearch(A,K,M)Analysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N*log(N+M))
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Correctness tests
1.
0.028 s
OK
2.
0.028 s
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3.
0.028 s
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4.
0.028 s
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1.
0.028 s
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2.
0.028 s
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3.
0.028 s
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0.028 s
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5.
0.028 s
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6.
0.028 s
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1.
0.028 s
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2.
0.028 s
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3.
0.028 s
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4.
0.028 s
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1.
0.028 s
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2.
0.028 s
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3.
0.028 s
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1.
0.028 s
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2.
0.028 s
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3.
0.028 s
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1.
0.028 s
OK
2.
0.028 s
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3.
0.028 s
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4.
0.028 s
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expand all
Performance tests
1.
0.028 s
OK
2.
0.028 s
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3.
0.028 s
OK
4.
0.028 s
OK
1.
0.044 s
OK
2.
0.068 s
OK
3.
0.072 s
OK
4.
0.072 s
OK
1.
0.088 s
OK
2.
0.092 s
OK
3.
0.088 s
OK
4.
0.088 s
OK
1.
0.428 s
OK
2.
0.440 s
OK
3.
0.436 s
OK
4.
0.448 s
OK
1.
0.128 s
OK
2.
0.292 s
OK
3.
0.300 s
OK
4.
0.300 s
OK
1.
0.124 s
OK
2.
0.428 s
OK
3.
0.432 s
OK
4.
0.124 s
OK