Uva 11552 Fewest Flops 字符串dp

Problem F

FEWEST FLOPS

A common way to uniquely encode a string is by replacing its consecutive repeating characters (or “chunks”) by the number of times the character occurs followed by the character itself. For example, the string “aabbbaabaaaa” may be encoded as “2a3b2a1b4a”. (Note for this problem even a single character “b” is replaced by “1b”.)

Suppose we have a string S and a number k such that k divides the length of S. Let S1 be the substring of S from 1 to k, S2 be the substring of S from k + 1 to 2k, and so on. We wish to rearrange the characters of each block Si independently so that the concatenation of those permutations S’ has as few chunks of the same character as possible. Output the fewest number of chunks.

For example, let S be “uuvuwwuv” and k be 4. Then S1 is “uuvu” and has three chunks, but may be rearranged to “uuuv” which has two chunks. Similarly, S2 may be rearranged to “vuww”. Then S’, or S1S2, is “uuuvvuww” which is 4 chunks, indeed the minimum number of chunks.

Program Input

The input begins with a line containing t (1 ≤ t ≤ 100), the number of test cases. The following t lines contain an integer k and a string S made of no more than 1000 lowercase English alphabet letters. It is guaranteed that k will divide the length of S.

Program Output

For each test case, output a single line containing the minimum number of chunks after we rearrange S as described above.

INPUT

2
5 helloworld
7 thefewestflops

OUTPUT

8
10

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Calgary Collegiate Programming Contest 2008

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注释流题解

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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int INF=1e9;
const int maxn=1111;
const int maxc=33;

int f[maxn][maxc][maxc];
char s[maxn][maxn];

//将第h组字符串中的重复字母删除并存入数组s[h]中
void judge(int h,int i,int j,char* str)
{
    bool hash[maxc]={0};
    int ln=0;
    for (int k=i;k<j;k++)
        if (!hash[str[k]-'a']){
            hash[str[k]-'a']=true;
            s[h][ln++]=str[k];
        }
    s[h][ln]='\0';
}

//查找l-1组字符中l组的第i个字符的位置，若不含有则返回-1
int fin(int l,int i)
{
    for (int j=0;j<strlen(s[l-1]);j++)
        if (s[l][i]==s[l-1][j]) return j;
    return -1;
}

int main()
{
    int T,k,n;
    char str[maxn];
    scanf("%d",&T);
    while (T--)
    {
        scanf("%d%s",&k,str);
        n=strlen(str)/k;//计算组数
        for (int i=0;i<n;i++) judge(i,i*k,(i+1)*k,str);//分组并消除重复字符
        //DP  f[l][i][j]表示第l组以第i个字符开头以第j个字符结尾时前l组的最小块数
        for (int l=0;l<n;l++)
            for (int i=0;i<strlen(s[l]);i++)
                for (int j=0;j<strlen(s[l]);j++)
                {
                    f[l][i][j]=INF;//初始化f[l][i][j]
                    if (i!=j||strlen(s[l])==1)//开头字符i不能等于结尾字符j除非l组只有一个块
                    {
                        if (l==0) f[l][i][j]=strlen(s[l]);//若l为第一组，则字符数即为最小块数
                        else
                        {
                            int tmp,ret;
                            ret=fin(l,i);//找到l-1组中与s[l][i]相同的字符位置
                            if (ret>=0)//找到的情况下
                            {
                                tmp=INF;
                                for (int g=0;g<strlen(s[l-1]);g++)//寻找以s[l-1][g]为首字母
                                    tmp=min(tmp,f[l-1][g][ret]);//s[l-1][ret]为尾字母时前l-1组的最小块数
                                f[l][i][j]=tmp+strlen(s[l])-1;//前l-1组的最小块数+l组的块数-重复的块数1
                            }
                            tmp=INF;
                            for (int p=0;p<strlen(s[l-1]);p++)//枚举l-1组首字母
                                for (int q=0;q<strlen(s[l-1]);q++)//枚举尾字母
                                    tmp=min(tmp,f[l-1][p][q]);//寻找最小值
                            f[l][i][j]=min(f[l][i][j],tmp+(int)strlen(s[l]));//前l-1组的最小块数+l组的块数
                        }
                    }
                }
        int ans=INF;
        for (int i=0;i<strlen(s[n-1]);i++)
            for (int j=0;j<strlen(s[n-1]);j++)
                ans=min(ans,f[n-1][i][j]);//寻找最佳答案
        printf("%d\n",ans);
    }
    return 0;
}