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December 2010

PrefixSet edition (2010-10)

Spoken language:

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

You are going on a trip to a range of mountains whose relative heights are represented by array A, as shown in a figure below. You have to choose how many flags you should take with you. The goal is to set the maximum number of flags on the peaks, according to certain rules.

Flags can only be set on peaks. What's more, if you take K flags, then the distance between any two flags should be greater than or equal to K. The distance between indices P and Q is the absolute value |P − Q|.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

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

that, given a non-empty array A of N integers, returns the maximum number of flags that can be set on the peaks of the array.

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

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

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

You are going on a trip to a range of mountains whose relative heights are represented by array A, as shown in a figure below. You have to choose how many flags you should take with you. The goal is to set the maximum number of flags on the peaks, according to certain rules.

Flags can only be set on peaks. What's more, if you take K flags, then the distance between any two flags should be greater than or equal to K. The distance between indices P and Q is the absolute value |P − Q|.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

int solution(vector<int> &A);

that, given a non-empty array A of N integers, returns the maximum number of flags that can be set on the peaks of the array.

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

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

A non-empty array A consisting of N integers is given.

A *peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

You are going on a trip to a range of mountains whose relative heights are represented by array A, as shown in a figure below. You have to choose how many flags you should take with you. The goal is to set the maximum number of flags on the peaks, according to certain rules.

Flags can only be set on peaks. What's more, if you take K flags, then the distance between any two flags should be greater than or equal to K. The distance between indices P and Q is the absolute value |P − Q|.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

int solution(vector<int> &A);

that, given a non-empty array A of N integers, returns the maximum number of flags that can be set on the peaks of the array.

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

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

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

class Solution { public int solution(int[] A); }

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

int solution(List<int> A);

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

func Solution(A []int) int

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

class Solution { public int solution(int[] A); }

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

class Solution { public int solution(int[] A); }

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

function solution(A);

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

fun solution(A: IntArray): Int

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

function solution(A)

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

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.

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

int solution(NSMutableArray *A);

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

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

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

function solution($A);

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

sub solution { my (@A) = @_; ... }

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

def solution(A)

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

def solution(a)

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

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

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

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

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

function solution(A: number[]): number;

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].

A non-empty array A consisting of N integers is given.

*peak* is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A:

has exactly four peaks: elements 1, 3, 5 and 10.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

Private Function solution(A As Integer()) As Integer

For example, the following array A:

the function should return 3, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].