hdu5375 Gray Code

Problem DescriptionThe reflected binary code, also known as gray code after Frank Gray, is a binary numeral system where t Wo successive values differ in only onebit (binary digit). The reflected binary code is originally designed to prevent spurious output from electromechanical switches. Today, Gray codes is widely used to facilitate error correction in digital communications such as digital terrestrial tel Evision and some cable TV systems.



Now, is given a binary number of length n including ' 0 ', ' 1 ' and '? ' (? means that can use the either 0 or 1 to the fill this position) and n integers (a1,a2,...., an). A certain binary number corresponds to a gray code only. If the ith bit of this gray code was 1,you can get the point AI.
Can you tell me how many points can get to most?

For instance, the binary number "00?0" could be "0000" or "0010", and the corresponding gray code is "0000" or "0011". You can choose ' 0000 ' getting nothing or ' 0011 ' getting the point A3 and A4.

Inputthe first line of the input contains the number of test cases T.

Each test case is begins with a string with ' 0 ', ' 1 ' and '? '.

The next line contains n (1<=n<=200000) integers (n is the length of the string).

A1 A2 A3 ... an (1<=ai<=1000)

Outputfor each test case, output "case #x: ans", in which X are the case number counted from one, ' ans ' are the points you ca n Get at most
Sample Input

200?01 2 4 8???? 1 2 4 8

Sample Output

Case #1:12
Case #2:15
The operation of Gray Code is i^ (i>>1), give you each bit corresponding value and this number (including 0,1,? ），？ can be 0, or can be 1, to find the maximum value, is a DP problem.
DP[I][1] Indicates the maximum value that can be generated when I is 1, anddp[i][0] represents the maximum value that can be generated by the first. 
#include <iostream> #include <stdio.h> #include <stdlib.h> #include <string.h> #include < math.h> #include <vector> #include <map> #include <set> #include <queue> #include <stack > #include <string> #include <algorithm>using namespace std, #define INF 88888888#define MAXN 200050char s[ Maxn];int Dp[maxn][2],a[maxn];int Main () {int n,m,i,j,t,len,num1=0;scanf ("%d", &t), while (t--) {scanf ("%s", s+1); Len=strlen (s+1); for (i=1;i<=len;i++) {scanf ("%d", &a[i]);} Dp[1][0]=dp[1][1]=-inf;if (s[1]== ' 1 ') {dp[1][1]=a[1];} if (s[1]== ' 0 ') {dp[1][0]=0;} if (s[1]== '? ') {dp[1][0]=0;dp[1][1]=a[1];} for (i=2;i<=len;i++) {dp[i][0]=dp[i][1]=-inf;if (s[i]== ' 1 ' | | s[i]== '? ') {Dp[i][1]=max (dp[i-1][0]+a[i],dp[i-1][1]);} if (s[i]== ' 0 ' | | | s[i]== '? ') {Dp[i][0]=max (dp[i-1][0],dp[i-1][1]+a[i]);}} num1++;p rintf ("Case #%d:%d\n", Num1,max (Dp[len][0],dp[len][1]));} return 0;}

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hdu5375 Gray Code