动态规划------最长ZigZag序列问题

题目：http://community.topcoder.com/stat?c=problem_statement&pm=1259&rd=4493

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

 代码实现：

这个问题类似求最长非降子序列，代码有点水。。。主要不知道那里怎么提交测试，就按自己的来了

n = int(input())
a = []
b = []
f = [1]*(n-1)

for i in range(n):
    r = int(input())
    a.append(r)

if n == 1:
    print(1)
elif n == 2:
    print(2)

def sub(a,b):
    if a>=b:
         return 1
    else:
        return -1

for i in range(1,n):
    b.append(sub(a[i],a[i-1]))



for i in range(b.__len__()):
    for j in range(i):
        if f[i] < f[j]:
            f[i] = f[j]
        if (b[i]*b[j])==-1 and f[i] < f[j] + 1:
            f[i] = f[j] + 1

print(f)