USACO Broken Necklace

Broken Necklace

You have a necklace of N red, white, or blue beads (3<=N<=350) some of which are red, others blue, and others white, arranged at random. Here are two examples for n=29:

                1 2                               1 2            r b b r                           b r r b          r         b                       b         b         r           r                     b           r        r             r                   w             r       b               r                 w               w      b                 b               r                 r      b                 b               b                 b      b                 b               r                 b       r               r                 b               r        b             r                   r             r         b           r                     r           r           r       r                         r       b             r b r                             r r w            Figure A                         Figure B                        r red bead                        b blue bead                        w white bead

The beads considered first and second in the text that follows have been marked in the picture.

The configuration in Figure A may be represented as a string of b's and r's, where b represents a blue bead and r represents a red one, as follows: brbrrrbbbrrrrrbrrbbrbbbbrrrrb .

Suppose you are to break the necklace at some point, lay it out straight, and then collect beads of the same color from one end until you reach a bead of a different color, and do the same for the other end (which might not be of the same color as the beads collected before this).

Determine the point where the necklace should be broken so that the most number of beads can be collected.

Example

For example, for the necklace in Figure A, 8 beads can be collected, with the breaking point either between bead 9 and bead 10 or else between bead 24 and bead 25.

In some necklaces, white beads had been included as shown in Figure B above. When collecting beads, a white bead that is encountered may be treated as either red or blue and then painted with the desired color. The string that represents this configuration can include any of the three symbols r, b and w.

Write a program to determine the largest number of beads that can be collected from a supplied necklace.

PROGRAM NAME: beads

INPUT FORMAT

Line 1:N, the number of beadsLine 2:a string of N characters, each of which is r, b, or w

SAMPLE INPUT (file beads.in)

29wwwbbrwrbrbrrbrbrwrwwrbwrwrrb

OUTPUT FORMAT

A single line containing the maximum of number of beads that can be collected from the supplied necklace.

SAMPLE OUTPUT (file beads.out)

11

OUTPUT EXPLANATION

Consider two copies of the beads (kind of like being able to runaround the ends). The string of 11 is marked.

                Two necklace copies joined here                             vwwwbbrwrbrbrrbrbrwrwwrbwrwrrb|wwwbbrwrbrbrrbrbrwrwwrbwrwrrb                       ******|*****                       rrrrrb bbbbb  <-- assignments                       rrrrr#bbbbbb                         5 x r  6 x b  <-- 11 total

题解：从网搜的题解

beads这题，比较巧妙的地方就是把字符串复制一份，从而就避免了边界检查。
用left[0][i]来记录从某一点向左可以收集到的最长r色beads数
用left[1][i]来记录从某一点向左可以收集到的最长b色beads数
right数组类推。

显然，如果i为r色，则向左可以收集到的最长r色为left[0][i-1]+1.可以向左收集到的最长b色为0。
如果i为b色，类推。
如果i为w色，i即可做r，也可做b.所以各自加1.

AC code：

/* ID: *****PROG: beads LANG: C++ */ #include <iostream>#include <fstream>#include <string>using namespace std;#define max(a,b) a>b?a:bint lift[2][1000],rigt[2][1000];int main(){freopen("beads.in","r",stdin);      freopen("beads.out","w",stdout); int n,i;    string s;cin>>n;cin>>s;    s+=s;//memset(lift,0,sizeof(lift));//memset(rigt,0,sizeof(rigt));for(i=s.size();i>0;i--){if(s[i-1]=='r'){rigt[0][i]=rigt[0][i+1]+1;rigt[1][i]=0;}else if(s[i-1]=='b'){rigt[0][i]=0;rigt[1][i]=rigt[1][i+1]+1;}else{          rigt[0][i]=rigt[0][i+1]+1;rigt[1][i]=rigt[1][i+1]+1;}}for(i=1;i<=s.size();i++){if(s[i-1]=='r'){lift[0][i]=lift[0][i-1]+1;lift[1][i]=0;}else if(s[i-1]=='b'){lift[0][i]=0;lift[1][i]=lift[1][i-1]+1;}else{lift[0][i]=lift[0][i-1]+1;lift[1][i]=lift[1][i-1]+1;}}int sum=-999999999,t1,t2;for( i=1; i<=n;i++){            t1 = max(rigt[0][i],rigt[1][i]);t2 = max(lift[0][i+n-1],lift[1][i+n-1]);            sum=max(sum,t1+t2);}if(sum>n)cout<<n<<endl;elsecout<<sum<<endl;return 0;}

=====================================================测试数据====================================================================

------- test 1 ----29wwwbbrwrbrbrrbrbrwrwwrbwrwrrb------- test 2 ----3rrr------- test 3 ----77rwrwrwrwrwrwrwrwrwrwrwrwbwrwbwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwrwr------- test 4 ----17wwwwwwwwwwwwwwwww------- test 5 ----50bbrrrbrrrrrrrrbrbbbrbrrbrrrrbbbrbrbbbbbrbrrrbbrbbb------- test 6 ----8rrwwwwbb------- test 7 ----200rrrrrrrrrrrrrrrrrrrrbbbbbbbbbbbbbbbbbbbbrrrrrrrrrrrrrrrrrrrrbbbbbbbbbbbbbbbbbbbbrrrrrrrrrrrrrrrrrrrrbbbbbbbbbbbbbbbbbbbbrrrrrrrrrrrrrrrrrrrrbbbbbbbbbbbbbbbbbbbbrrrrrrrrrrrrrrrrrrrrbbbbbbbbbbbbbbbbbbbb------- test 8 ----350rrbbrbbbwbwwbwbbbbwwrrbbwbrwbrwbbbrbrwrwbrwwwrrbbrrwrbbrwbwrwwwrbrwwwwwrwbwwwrrbrrbbbrbrbbbrbbbrbbwbbbbbrbrrbrwwbrrrrwbwrwrbbwbwrbrbrwwbrrbwbrwwbwwwbrbwrwbwbrbbbwrbwwrrrbwbwbbbbbrrwwwrbrwwrbbwrbbrbbrbwrrwwbrrrbrwbrwwrbwbwrrrbwrwrrbrbbwrwrbrwwwrwbwrrwwwwrrrwrrwbbwrwwrwrbwwbwrrrrbbwrbbrbwwwwwbrbbrbbrbrwbbwbwwbbbbbwwwrbwwbbbwrwwbbrrwrwbwrrwwwrrrwrrwww------- test 9 ----333rwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwbrwb