TopCoder problem "ZigZag" used in TCCC '03 Semifinals 3 (Division I Level One)



Problem Statement

    

A sequence of numbers is called a zig-zag sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two elements is trivially a zig-zag sequence.

For example, 1,7,4,9,2,5 is a zig-zag sequence because the differences (6,-3,5,-7,3) are alternately positive and negative. In contrast, 1,4,7,2,5 and 1,7,4,5,5 are not zig-zag sequences, the first because its first two differences are positive and the second because its last difference is zero.

Given a sequence of integers, sequence, return the length of the longest subsequence of sequence that is a zig-zag sequence. A subsequence is obtained by deleting some number of elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.

 

Definition

    
Class:ZigZag
Method:longestZigZag
Parameters:int[]
Returns:int
Method signature:int longestZigZag(int[] sequence)
(be sure your method is public)
    
 

Constraints

-sequence contains between 1 and 50 elements, inclusive.
-Each element of sequence is between 1 and 1000, inclusive.
 

Examples

0)
    
{ 1, 7, 4, 9, 2, 5 }
Returns: 6
The entire sequence is a zig-zag sequence.
1)
    
{ 1, 17, 5, 10, 13, 15, 10, 5, 16, 8 }
Returns: 7
There are several subsequences that achieve this length. One is 1,17,10,13,10,16,8.
2)
    
{ 44 }
Returns: 1
3)
    
{ 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Returns: 2
4)
    
{ 70, 55, 13, 2, 99, 2, 80, 80, 80, 80, 100, 19, 7, 5, 5, 5, 1000, 32, 32 }
Returns: 8
5)
    
{ 374, 40, 854, 203, 203, 156, 362, 279, 812, 955, 
600, 947, 978, 46, 100, 953, 670, 862, 568, 188, 
67, 669, 810, 704, 52, 861, 49, 640, 370, 908, 
477, 245, 413, 109, 659, 401, 483, 308, 609, 120, 
249, 22, 176, 279, 23, 22, 617, 462, 459, 244 }

Returns: 36

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1259

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4493&pm=1259

Writer:

vorthys

Testers:

Logan , lbackstrom , brett1479 , schveiguy

Problem categories:

Dynamic Programming