The government of a small but important country has decided that the alphabet needs to be streamlined and reordered. Uppercase letters will be eliminated. They will issue a royal decree in the form of a String of B and A characters. The first character in the decree specifies whether a must come ( B )Before b in the new alphabet or ( A )After b . The second character determines the relative placement of b and c , etc. So, for example, "BAA" means that a must come Before b , b must come After c , and c must come After d .
Any letters beyond these requirements are to be excluded, so if the decree specifies k comparisons then the new alphabet will contain the first k+1 lowercase letters of the current alphabet.
Create a class Alphabet that contains the method choices that takes the decree as input and returns the number of possible new alphabets that conform to the decree. If more than 1,000,000,000 are possible, return -1.
Definition
平均因子分解法，適用于正定矩陣First, let s recall the Definition of the Cholesky decomposition: Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U U, where U is the square root matrix of X, and satisfies:
(1) U U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal).
It seems that the assumption of positive definiteness is necessary. Actually, it is "positive definite" which guarantees the existence of such kind of decomposition.
Problem Statement
You are given a string input. You are to find the longest substring of input such that the reversal of the substring is also a substring of input. In case of a tie, return the string that occurs earliest in input.
Definition
Class: ReverseSubstring
Method: findReversed
Parameters: string
Returns: string
Method signature: string findReversed(string input)
(be sure your method is public)
Notes
The substring and its reversal may overlap partially or completely.
The entire original string is itself a valid substring (see example 4).
Constraints
input will contain between 1 and 50 characters, inclusive.
Each character of input will be an uppercase letter ( A - Z ).
Examples
0)
"XBCDEFYWFEDCBZ"
Returns: "BCDEF"
We see that the reverse of BCDEF is FEDCB, which appears later in the string.
1)
CHAPT12\Chapt12.cpp Part of the 32-bit test progrma for the Win32Port class.
CHAPT12\Chapt12.dsp The Visual C++ project file for the program.
CHAPT12\Chapt12.dsw The Visual C++ workspace file for the program.
CHAPT12\Chapt12.h The header file for the app s application class
CHAPT12\Chapt12.ico The icon used in Chapt12.exe
CHAPT12\Chapt12.rc The resource file use in the test program.
CHAPT12\Chapt12Dlg.cpp The implementation of the dialog class
CHAPT12\Chapt12Dlg.h The declarations of the dialog class
CHAPT12\MyWin32Port.h Definition for a class derived from Win32Port.
CHAPT12\resource.h The resource IDs
CHAPT13\AnsiWinTerm.cpp Class used in Win32 terminal emulation
CHAPT13\AnsiWinTerm.h Header file for the AnsiWinTerm class
CHAPT13\Chapt13.cpp 32-bit test program of terminal emulation
CHAPT13\Chapt13.dsp Visual C++ project file
CHAPT13\Chapt13.dsw Visual C++ workspace file
CHAPT13\Chapt13.rc The resource file used in the test program
CHAPT13\resource.h IDs defined in the resource file
CHAPT13\Win32Term.cpp The Win32 general purpose terminal class
CHAPT13\Win32Term.h Definition of the class
CHAPT13\Debug\Chapt13.exe 32-bit executable of the test program.
Session 1: common and useful built-in Mathematica functions variable assignment and function Definition
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