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 8
Time spent on task 2 minutes
Notes
not defined yet
Code: 07:28:00 UTC,
java,
autosave
Code: 07:28:10 UTC,
java,
autosave
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a : A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
}
Code: 07:28:32 UTC,
java,
autosave
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
}
Code: 07:28:42 UTC,
java,
verify,
result: Failed
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
Analysis
Compile error
Solution.java:5: error: illegal start of expression
public int solution(int K, int M, int[] A) {
^
Solution.java:5: error: ';' expected
public int solution(int K, int M, int[] A) {
^
Solution.java:5: error: <identifier> expected
public int solution(int K, int M, int[] A) {
^
Solution.java:5: error: not a statement
public int solution(int K, int M, int[] A) {
^
Solution.java:5: error: ';' expected
public int solution(int K, int M, int[] A) {
^
Solution.java:5: error: ';' expected
public int solution(int K, int M, int[] A) {
^
Solution.java:23: error: illegal start of expression
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:23: error: ';' expected
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:23: error: <identifier> expected
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:23: error: not a statement
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:23: error: ';' expected
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:23: error: ';' expected
private boolean isDivision(int K, int target, int[] A) {
^
Solution.java:38: error: reached end of file while parsing
}
^
13 errors
Code: 07:29:02 UTC,
java,
autosave
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
Code: 07:29:27 UTC,
java,
verify,
result: Passed
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
Analysis
Code: 07:29:32 UTC,
java,
verify,
result: Passed
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) return false;
}
return true;
}
}
Analysis
Code: 07:29:36 UTC,
java,
final,
score:
100
import java.util.*;
class Solution {
public int solution(int K, int M, int[] A) {
int low = Arrays.stream(A).max().getAsInt();
int up = Arrays.stream(A).sum();
int res = up;
while (low <= up) {
int mid = (low + up) / 2;
if (isDivision(K, mid, A)) {
res = mid;
up = mid - 1;
} else {
low = mid + 1;
}
}
return res;
}
private boolean isDivision(int K, int target, int[] A) {
int sum = 0;
int count = 1;
for (int a: A) {
sum += a;
if (sum > target) {
sum = a;
count++;
}
if (count > K) 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.
0.088 s
OK
2.
0.088 s
OK
3.
0.088 s
OK
4.
0.088 s
OK
1.
0.088 s
OK
2.
0.088 s
OK
3.
0.088 s
OK
4.
0.088 s
OK
5.
0.088 s
OK
6.
0.088 s
OK
1.
0.088 s
OK
2.
0.092 s
OK
3.
0.088 s
OK
4.
0.092 s
OK
1.
0.088 s
OK
2.
0.088 s
OK
3.
0.088 s
OK
1.
0.088 s
OK
2.
0.088 s
OK
3.
0.088 s
OK
1.
0.088 s
OK
2.
0.092 s
OK
3.
0.096 s
OK
4.
0.088 s
OK
expand all
Performance tests
1.
0.088 s
OK
2.
0.088 s
OK
3.
0.092 s
OK
4.
0.088 s
OK
1.
0.124 s
OK
2.
0.124 s
OK
3.
0.124 s
OK
4.
0.128 s
OK
1.
0.140 s
OK
2.
0.136 s
OK
3.
0.140 s
OK
4.
0.140 s
OK
1.
0.416 s
OK
2.
0.416 s
OK
3.
0.416 s
OK
4.
0.420 s
OK
1.
0.320 s
OK
2.
0.316 s
OK
3.
0.320 s
OK
4.
0.316 s
OK
1.
0.444 s
OK
2.
0.440 s
OK
3.
0.440 s
OK
4.
0.444 s
OK