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。
This book describes a collection of standards, conventions,
and guidelines for creating effective UML diagrams. They are
based on sound, proven principles that will lead to diagrams
that are easier to understand and work with.
Probabilistic Principal Components Analysis. [VAR, U, LAMBDA] = PPCA(X, PPCA_DIM) computes the principal
％ component subspace U of dimension PPCA_DIM using a centred covariance
matrix X. The variable VAR contains the off-subspace variance (which
is assumed to be spherical), while the vector LAMBDA contains the
variances of each of the principal components. This is computed
using the eigenvalue and eigenvector decomposition of X.
實現最優二叉樹的構造；在此基礎上完成哈夫曼編碼器與譯碼器。 假設報文中只會出現如下表所示的字符：
字符 A B C D E F G H I J K L M N
頻度 186 64 13 22 32 103 21 15 47 57 1 5 32 20 57
字符 O P Q R S T U V W X Y Z ， ．
頻度 63 15 1 48 51 80 23 8 18 1 16 1 6 2
要求完成的系統應具備如下的功能：
1．初始化。從終端（文件）讀入字符集的數據信息，。建立哈夫曼樹。
2．編碼：利用已建好的哈夫曼樹對明文文件進行編碼，并存入目標文件（哈夫曼碼文件）。
3．譯碼：利用已建好的哈夫曼樹對目標文件（哈夫曼碼文件）進行編碼，并存入指定的明文文件。
4．輸出哈夫曼編碼文件：輸出每一個字符的哈夫曼編碼。
Abstract
A new intelligent milometer base on a microcontroller can count the sum. By taking full use of the processor 89s51 and E² PROM (AT24C02) and sensor of magnetism, it can count the sum of fully distance and the course of development.
function [U,center,result,w,obj_fcn]= fenlei(data)
[data_n,in_n] = size(data)
m= 2 ％ Exponent for U
max_iter = 100 ％ Max. iteration
min_impro =1e-5 ％ Min. improvement
c=3
[center, U, obj_fcn] = fcm(data, c)
for i=1:max_iter
if F(U)>0.98
break
else
w_new=eye(in_n,in_n)
center1=sum(center)/c
a=center1(1)./center1
deta=center-center1(ones(c,1),:)
w=sqrt(sum(deta.^2)).*a
for j=1:in_n
w_new(j,j)=w(j)
end
data1=data*w_new
[center, U, obj_fcn] = fcm(data1, c)
center=center./w(ones(c,1),:)
obj_fcn=obj_fcn/sum(w.^2)
end
end
display(i)
result=zeros(1,data_n) U_=max(U)
for i=1:data_n
for j=1:c
if U(j,i)==U_(i)
result(i)=j continue
end
end
end
function [U,V,num_it]=fcm(U0,X)
％ MATLAB (Version 4.1) Source Code (Routine fcm was written by Richard J.
％ Hathaway on June 21, 1994.) The fuzzification constant
％ m = 2, and the stopping criterion for successive partitions is epsilon =??????.
％*******Modified 9/15/04 to have epsilon = 0.00001 and fix univariate bug********
％ Purpose:The function fcm attempts to find a useful clustering of the
％ objects represented by the object data in X using the initial partition in U0.
