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ambitious

Find the longest path down the Cartesian tree.

Programming language:
Spoken language:

A non-empty array A consisting of N different integers is given. We are looking for the longest possible sequence built from elements of A, A[B[0]], A[B[1]], ..., A[B[K]], satisfying the following conditions:

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].
- For any two consecutive elements of the sequence, A[B[I]] and A[B[I+1]], all the elements of A between them must be smaller than them; that is, for any J = MIN(B[I], B[I+1]) + 1, ..., MAX(B[I], B[I+1]) − 1, we have A[J] < A[B[I+1]].

Write a function:

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

that, given an array A containing N different integers, computes the maximum length of a sequence satisfying the above conditions.

For example, for the following array A:

the function should return 6.

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A non-empty array A consisting of N different integers is given. We are looking for the longest possible sequence built from elements of A, A[B[0]], A[B[1]], ..., A[B[K]], satisfying the following conditions:

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].
- For any two consecutive elements of the sequence, A[B[I]] and A[B[I+1]], all the elements of A between them must be smaller than them; that is, for any J = MIN(B[I], B[I+1]) + 1, ..., MAX(B[I], B[I+1]) − 1, we have A[J] < A[B[I+1]].

Write a function:

int solution(vector<int> &A);

that, given an array A containing N different integers, computes the maximum length of a sequence satisfying the above conditions.

For example, for the following array A:

the function should return 6.

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A non-empty array A consisting of N different integers is given. We are looking for the longest possible sequence built from elements of A, A[B[0]], A[B[1]], ..., A[B[K]], satisfying the following conditions:

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].
- For any two consecutive elements of the sequence, A[B[I]] and A[B[I+1]], all the elements of A between them must be smaller than them; that is, for any J = MIN(B[I], B[I+1]) + 1, ..., MAX(B[I], B[I+1]) − 1, we have A[J] < A[B[I+1]].

Write a function:

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

that, given an array A containing N different integers, computes the maximum length of a sequence satisfying the above conditions.

For example, for the following array A:

the function should return 6.

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

func Solution(A []int) int

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

function solution(A);

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

function solution(A)

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

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 sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

int solution(NSMutableArray *A);

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

function solution($A);

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

def solution(A)

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

def solution(a)

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

- The sequence must be decreasing; that is, A[B[0]] > A[B[1]] > ... > A[B[K]].

Write a function:

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

For example, for the following array A:

A sequence of length 6 satisfying the given conditions can be as follows:

Assume that:

- the elements of A are all distinct;
- N is an integer within the range [1..100,000];
- each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].

Complexity:

- expected worst-case time complexity is O(N);

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