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Competition Arena > IntegerSequence

IntegerSequence

SRM 278 · 2005-12-19 · by Vedensky

SRM 278 · 2005-12-19 · by Vedensky · Dynamic Programming
Class Name: IntegerSequence
Return Type: int
Method Name: maxSubsequence
Arg Types: (vector<int>)
Problem Statement

Problem Statement

You have a sequence of numbers from which you must create the longest subsequence satisfying the following condition: it can be 'cut' into two parts that share exactly one common element (the last element of the first part is the first element of the second part), and the first part is sorted in strictly ascending order while the second part is sorted in strictly descending order. For example, the sequence { 1, 4, 6, 5, 2, 1 } can be 'cut' into { 1, 4, 6 } and { 6, 5, 2, 1 }. The two parts share the 6, and the first sequence is sorted in ascending order while the second sequence is sorted in descending order.

You are given a int[] numbers, a sequence of numbers. Return the minimal number of elements you must throw out from the given sequence such that the remaining subsequence satisfies the condition described above.

Constraints

  • numbers will contain between 1 and 50 elements, inclusive.
  • Each element of numbers will be between 1 and 1000000000, inclusive.
Examples
0)
{1, 4, 6, 5, 2, 1}
Returns: 0

This sequence already satisfies the condition, so the answer is 0.

1)
{1, 2, 1, 2, 3, 2, 1, 2, 1}
Returns: 4

The longest subsequence is { 1, 2, 3, 2, 1 }, so you need to throw out at least 4 elements.

2)
{2, 2, 2, 2, 2}
Returns: 4
3)
{1, 1, 2, 1, 2, 3, 4, 7, 9, 3, 5, 7, 4, 6, 1}
Returns: 6
4)
{4,5,65,34,786,45678,987,543,2,6,98,580,4326,754,54,2,1,3,5,6,8,765,43,3,54}
Returns: 14

Submissions are judged against all 75 archived test cases, of which 5 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class IntegerSequence with a public method int maxSubsequence(vector<int> numbers) · 75 test cases · 2 s / 256 MB per case

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