POJ 2533 Longest Ordered Subsequence C++版

OJ题解 6583浏览

Description

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1, a2, ..., aN) be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8). Your program, when given the numeric sequence, must find the length of its longest ordered subsequence. Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

7
1 7 3 5 9 4 8

Sample Output

4

Slyar:属于简单的经典的DP，求最长上升子序列(LIS)。先研究了O(n^2)的思路。

DP状态转移方程:

D[i] = max{1, D[j] + 1} (j = 1, 2, 3, ..., i-1 且 A[j] < A[i])

网友最新评论 (2)

1. 我错了，没想到博主已经给出解答了。
shilong13年前（2011-09-07）回复
2. 博主，非O(n^2)的思路是什么啊？
shilong13年前（2011-09-07）回复