design LP,HP,B S digital Butterworth and Chebyshev
filter. All array has been specified internally,so user only need to
input f1,f2,f3,f4,fs(in hz), alpha1,alpha2(in db) and iband (to specify
the type of to design). This program output hk(z)=bk(z)/ak(z),k=1,2,...,
ksection and the freq.
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。
1) Write a function reverse(A) which takes a matrix A of arbitrary dimensions as input and returns a matrix B consisting of the columns of A in reverse order. Thus for example, if
A = 1 2 3 then B = 3 2 1
4 5 6 6 5 4
7 8 9 9 8 7
Write a main program to call reverse(A) for the matrix A = magic(5). Print to the screen both A and reverse(A).
2) Write a program which accepts an input k from the keyboard, and which prints out the smallest fibonacci number that is at least as large as k. The program should also print out its position in the fibonacci sequence. Here is a sample of input and output:
Enter k>0: 100
144 is the smallest fibonacci number greater than or equal to 100.
It is the 12th fibonacci number.
