Problem B:Longest Ordered Subsequence
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).
* "Copyright (c) 2006 Robert B. Reese ("AUTHOR")"
* All rights reserved.
* (R. Reese, reese@ece.msstate.edu, Mississippi State University)
* IN NO EVENT SHALL THE "AUTHOR" BE LIABLE TO ANY PARTY FOR
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT
* OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF THE "AUTHOR"
* HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About:
hamsterdb is a database engine written in ANSI C. It supports a B+Tree index structure, uses memory mapped I/O (if available), supports cursors, and can create in-memory databases.
Release focus: Major feature enhancements
Changes:
This release comes with many changes and new features. It can manage multiple databases in one file. A new flag (HAM_LOCK_EXCLUSIVE) places an exclusive lock on the file. hamsterdb was ported to Windows CE, and the Solution file for Visual Studio 2005 now supports builds for x64. Several minor bugs were fixed, performance was improved, and small API changes occurred. Pre-built libraries for Windows (32-bit and 64-bit) are available for download.
Author:
cruppstahl
Floyd-Warshall算法描述
1)適用范圍：
a)APSP(All Pairs Shortest Paths)
b)稠密圖效果最佳
c)邊權可正可負
2)算法描述：
a)初始化：dis[u,v]=w[u,v]
b)For k:=1 to n
For i:=1 to n
For j:=1 to n
If dis[i,j]>dis[i,k]+dis[k,j] Then
Dis[I,j]:=dis[I,k]+dis[k,j]
c)算法結束：dis即為所有點對的最短路徑矩陣
3)算法小結：此算法簡單有效，由于三重循環結構緊湊，對于稠密圖，效率要高于執行|V|次Dijkstra算法。時間復雜度O(n^3)。
考慮下列變形：如(I,j)∈E則dis[I,j]初始為1,else初始為0，這樣的Floyd算法最后的最短路徑矩陣即成為一個判斷I,j是否有通路的矩陣。更簡單的，我們可以把dis設成boolean類型，則每次可以用“dis[I,j]:=dis[I,j]or(dis[I,k]and dis[k,j])”來代替算法描述中的藍色部分，可以更直觀地得到I,j的連通情況。
