usaco1.1.4 Broken Necklace

一. 原题

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 beads
Line 2:	a string of N characters, each of which is r, b, or w

SAMPLE INPUT (file beads.in)

29
wwwbbrwrbrbrrbrbrwrwwrbwrwrrb

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
                             v
wwwbbrwrbrbrrbrbrwrwwrbwrwrrb|wwwbbrwrbrbrrbrbrwrwwrbwrwrrb
                       ******|*****
                       rrrrrb|bbbbb  <-- assignments
                   5xr .....#|#####  6xb

                        5+6 = 11 total

二. 分析：

数据范围只有350，枚举每个位置作为项链断开位置就行了。有个小技巧题目在OUTPUT EXPLAINATION部分也讲的很清楚了。把输入字符串复制一份放在末尾，这样处理题目里项链的环结构比较方便。

三. 代码：

运行结果：

USER: Qi Shen [maxkibb3]
TASK: beads
LANG: C++

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.000 secs, 4180 KB]
   Test 2: TEST OK [0.000 secs, 4180 KB]
   Test 3: TEST OK [0.000 secs, 4180 KB]
   Test 4: TEST OK [0.000 secs, 4180 KB]
   Test 5: TEST OK [0.000 secs, 4180 KB]
   Test 6: TEST OK [0.000 secs, 4180 KB]
   Test 7: TEST OK [0.000 secs, 4180 KB]
   Test 8: TEST OK [0.000 secs, 4180 KB]
   Test 9: TEST OK [0.000 secs, 4180 KB]

All tests OK.

YOUR PROGRAM ('beads') WORKED FIRST TIME! That's fantastic -- and a rare thing. Please accept these special automated congratulations.

AC代码：

/*
ID:maxkibb3
PROG:beads
LANG:C++
*/

#include<cstdio>
#include<cstring>
using namespace std;

int n;
char s[400], ss[800];
int ans = 2;

int forward(int idx, int delta) {
    int flag = 0; // 0: uncertain, 1: red, 2: blue
    int ret = 0;
    for(int i = idx; i > 0 && i < n * 2; i += delta) {
        if(flag == 0) {
            if(ss[i] == 'r') {
                flag = 1;
            }
            else if(ss[i] == 'b') {
                flag = 2;
            }
            ret++;
        }
        else if(flag == 1) {
            if(ss[i] == 'b') {
                return ret;
            } 
            else {
                ret++;
            }
        }
        else {
            if(ss[i] == 'r') {
                return ret;
            }
            else {
                ret++;
            }
        }
    }
    return ret;
}

int main() {
    freopen("beads.in", "r", stdin);
    freopen("beads.out", "w", stdout);
    scanf("%d", &n);
    getchar();
    scanf("%s", s);
    strcpy(ss, s);
    strcpy(ss + n, s);
    for(int i = 0; i < n; i++) {
        int r = forward(i + 1, 1);
        int l = forward(i + n, -1);
        if(r + l >= n) {
            ans = n;
            break;
        }
        else if(r + l > ans) {
            ans = r + l;
        }
    }
    printf("%d\n", ans);
    return 0;
}