ZigZag

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: vector <int> Returns: int Method signature: int longestZigZag(vector <int> sequence) (be sure your method is public)
Limits
	Time limit (s): 2.000 Memory limit (MB): 64
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

动态规划，最长上升子序列的变形。

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
using namespace std;

class ZigZag
{
public:int longestZigZag(vector <int> sequence )
{
int size=sequence.size();
cout<<"vector size:"<<size<<endl;
int maxsize=1;
int dp[100];
int alt[100];
for(int i=0;i<size;i++)
{
dp[i]=1;
alt[i]=0;
}
if(size==0||size==1)
return size;
else
{
dp[1]=2;
alt[1]=sequence.at(1)-sequence.at(0);
for(int i=2;i<size;i++)
{
int temp=sequence.at(i);
int temp_max=-100000;
for(int j=0;j<i;j++)
{
if(alt[j]<0&&(temp>sequence.at(j))&&dp[j]>=temp_max)
{
temp_max=dp[j]+1;
alt[i]=temp-sequence.at(j);
}
if(alt[j]>0&& (temp<sequence.at(j))&&dp[j]>=temp_max)
{
temp_max=dp[j]+1;
alt[i]=temp-sequence.at(j);
}
}
dp[i]=temp_max;
}
for(int i=0;i<size;i++)
{
if(maxsize<dp[i])
maxsize=dp[i];
}
return maxsize;
}

}
};

代码风格太差了，以后加强这方面的训练。