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:
class Solution { public int solution(int K, int M, int[] 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 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Java 21
Time spent on task 73 minutes
Notes
not defined yet
Code: 08:12:31 UTC,
java,
autosave
Code: 09:25:03 UTC,
swift4,
autosave
import Foundation
import Glibc
// you can write to stdout for debugging purposes, e.g.
// print("this is a debug message")
public func solution(_ K : Int, _ M : Int, _ A : inout [Int]) -> Int {
var low = A.max()!
var high = A.reduce(0, +)
if K == 1 { return high }
if K >= A.count { return low }
while low <= high {
let mid = (low + high) / 2
if isValid(A: A, maxBlockCount: K, maxBlockSize: mid) {
high = mid - 1
} else {
low = mid + 1
}
}
return low
}
func isValid(A: [Int], maxBlockCount: Int, maxBlockSize: Int) -> Bool {
var blockSum = 0
var blockCount = 0
for a in A {
if blockSum + a > maxBlockSize {
blockSum = a
blockCount += 1
} else {
blockSum += a
}
if blockCount >= maxBlockCount {
return false
}
}
return true
}
Code: 09:25:03 UTC,
swift4,
verify,
result: Passed
import Foundation
import Glibc
// you can write to stdout for debugging purposes, e.g.
// print("this is a debug message")
public func solution(_ K : Int, _ M : Int, _ A : inout [Int]) -> Int {
var low = A.max()!
var high = A.reduce(0, +)
if K == 1 { return high }
if K >= A.count { return low }
while low <= high {
let mid = (low + high) / 2
if isValid(A: A, maxBlockCount: K, maxBlockSize: mid) {
high = mid - 1
} else {
low = mid + 1
}
}
return low
}
func isValid(A: [Int], maxBlockCount: Int, maxBlockSize: Int) -> Bool {
var blockSum = 0
var blockCount = 0
for a in A {
if blockSum + a > maxBlockSize {
blockSum = a
blockCount += 1
} else {
blockSum += a
}
if blockCount >= maxBlockCount {
return false
}
}
return true
}
Analysis
Code: 09:25:11 UTC,
swift4,
verify,
result: Passed
import Foundation
import Glibc
// you can write to stdout for debugging purposes, e.g.
// print("this is a debug message")
public func solution(_ K : Int, _ M : Int, _ A : inout [Int]) -> Int {
var low = A.max()!
var high = A.reduce(0, +)
if K == 1 { return high }
if K >= A.count { return low }
while low <= high {
let mid = (low + high) / 2
if isValid(A: A, maxBlockCount: K, maxBlockSize: mid) {
high = mid - 1
} else {
low = mid + 1
}
}
return low
}
func isValid(A: [Int], maxBlockCount: Int, maxBlockSize: Int) -> Bool {
var blockSum = 0
var blockCount = 0
for a in A {
if blockSum + a > maxBlockSize {
blockSum = a
blockCount += 1
} else {
blockSum += a
}
if blockCount >= maxBlockCount {
return false
}
}
return true
}
Analysis
Code: 09:25:17 UTC,
swift4,
final,
score:
100
import Foundation
import Glibc
// you can write to stdout for debugging purposes, e.g.
// print("this is a debug message")
public func solution(_ K : Int, _ M : Int, _ A : inout [Int]) -> Int {
var low = A.max()!
var high = A.reduce(0, +)
if K == 1 { return high }
if K >= A.count { return low }
while low <= high {
let mid = (low + high) / 2
if isValid(A: A, maxBlockCount: K, maxBlockSize: mid) {
high = mid - 1
} else {
low = mid + 1
}
}
return low
}
func isValid(A: [Int], maxBlockCount: Int, maxBlockSize: Int) -> Bool {
var blockSum = 0
var blockCount = 0
for a in A {
if blockSum + a > maxBlockSize {
blockSum = a
blockCount += 1
} else {
blockSum += a
}
if blockCount >= maxBlockCount {
return false
}
}
return true
}Analysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N*log(N+M))
expand all
Correctness tests
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
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4.
0.008 s
OK
5.
0.008 s
OK
6.
0.004 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.004 s
OK
1.
0.004 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
expand all
Performance tests
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 s
OK
1.
0.016 s
OK
2.
0.016 s
OK
3.
0.016 s
OK
4.
0.016 s
OK
1.
0.008 s
OK
2.
0.012 s
OK
3.
0.012 s
OK
4.
0.012 s
OK
1.
0.012 s
OK
2.
0.016 s
OK
3.
0.016 s
OK
4.
0.012 s
OK