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AVAILABLE LESSONS:

Lesson 1

Iterations

Lesson 2

Arrays

Lesson 3

Time Complexity

Lesson 4

Counting Elements

Lesson 5

Prefix Sums

Lesson 6

Sorting

Lesson 7

Stacks and Queues

Lesson 8

Leader

Lesson 9

Maximum slice problem

Lesson 10

Prime and composite numbers

Lesson 11

Sieve of Eratosthenes

Lesson 12

Euclidean algorithm

Lesson 13

Fibonacci numbers

Lesson 14

Binary search algorithm

Lesson 15

Caterpillar method

Lesson 16

Greedy algorithms

Lesson 17

Dynamic programming

Lesson 99

Future training

Divide array A into K blocks and minimize the largest sum of any block.

Spoken language:

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:

The 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:

int solution(int K, int M, int A[], int N);

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:

the 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 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

The 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:

int solution(int K, int M, vector<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:

the 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 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

The 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:

int solution(int K, int M, vector<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:

the 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 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

The 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); }

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

int solution(int K, int M, List<int> A);

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

func Solution(K int, M int, A []int) int

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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); }

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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); }

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

function solution(K, M, A);

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

fun solution(K: Int, M: Int, A: IntArray): Int

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

function solution(K, M, A)

For example, given K = 3, M = 5 and array A such that:

the 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].

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

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:

The 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:

int solution(int K, int M, NSMutableArray *A);

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

function solution(K: longint; M: longint; A: array of longint; N: longint): longint;

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

function solution($K, $M, $A);

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

sub solution { my ($K, $M, @A) = @_; ... }

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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)

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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)

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

object Solution { def solution(k: Int, m: Int, a: Array[Int]): Int }

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

public func solution(_ K : Int, _ M : Int, _ A : inout [Int]) -> Int

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

function solution(K: number, M: number, A: number[]): number;

For example, given K = 3, M = 5 and array A such that:

the 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].

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:

The 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:

Private Function solution(K As Integer, M As Integer, A As Integer()) As Integer

For example, given K = 3, M = 5 and array A such that:

the 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].