44. Decode Ways & Gray Code

Decode ways

A message containing letters fromA-ZIs being encoded to numbers using the following mapping:

 
'A'-> 1 'B'-> 2... 'Z'-> 26
 

Given an encoded message containing digits, determine the total number of ways to decode it.

For example, given encoded message"12", It cocould be decoded"AB"(1 2) or"L"(12 ).

The number of ways Decoding"12"Is 2.

Thoughts: dynamic planning, analysis:

12121212: the front is 1 or (the front is 2 and the current value <7): F (n) = f (n-1) + f (n-2 );

1202: The current value is 0, followed by 1 or 2, F (n) = f (n-2). Otherwise, return 0.

In other cases, F (n) = f (n-1 );

 
Class solution {public: int numdecodings (string s) {int n = S. size (); If (n = 0 | s [0] = '0') return 0; vector <int> F (n + 1 ); f [0] = f [1] = 1; for (INT Index = 2; index <= N; ++ index) {If ('0' = s [index-1]) {If ('1' = s [index-2] | '2' = s [index-2]) f [Index] = f [index-2]; else return 0 ;} else if ('1' = s [index-2] | ('2' = s [index-2] & S [index-1] <'7' )) f [Index] = f [index-1] + F [index-2]; else f [Index] = f [index-1];} return f [N] ;}};
 

 

Gray Code

The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integerNRepresenting the total number of BITs in the code, print the sequence of Gray code. A gray code sequence must begin with 0.

For example, givenN= 2, return[0, 1, 3, 2]. Its Gray code sequence is:

 
00-001-111-310-2
 

Note:For a givenN, A gray code sequence is not uniquely defined.

For example,[0, 2, 3, 1]Is also a valid Gray code sequence according to the above definition.

For now, the judge is able to judge based on one instance of Gray code sequence. Sorry about that.

Thought: The method is clever. Each time a loop is changed, only the highest bit 0-> 1 is changed.

Class solution {public: vector <int> graycode (int n) {vector <int> VEC (1, 0); For (INT I = 0; I <N; ++ I) {int v = 1 <I; for (Int J = Vec. size ()-1; j> = 0; -- j) Vec. push_back (VEC [J] + V);} return VEC ;}};
 

 

44. Decode Ways & Gray Code