HDU 5677 ztr loves substring （dp)

Problem Description

ztr love reserach substring.Today ,he has n string.Now ztr want to konw,can he take out exactly k palindrome from all substring of these n string,and thrn sum of length of these k substring is L.

for example string "yjqqaq"
this string contains plalindromes:"y","j","q","a","q","qq","qaq".
so we can choose "qq" and "qaq".

 

Input

The first line of input contains an positive integer  T(T<=10)  indicating the number of test cases.

For each test case:

First line contains these positive integer  N(1<=N<=100),K(1<=K<=100),L(L<=100) .
The next N line,each line contains a string only contains lowercase.Guarantee even length of string won't more than L.

 

Output

For each test,Output a line.If can output "True",else output "False".

 

Sample Input

   
   
   
   

    
    
    
    3
2 3 7
yjqqaq
claris
2 2 7
popoqqq
fwwf
1 3 3
aaa
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    False
True
True
   
   
   
   
   
   
   
   

    
    
    
    题意：给你n个字符串，然后你可以选k个这n个字符的回文子串，问这k个子串的长度加起来是否可以为l。
   
   
   
   
   
   
   
   

    
    
    
    思路：我们可以事先用manachar求出所以回文子串的长度，然后我们记录长度为i的回文子串的个数，然后我们可以利用背包来判断取k个长度是否可以为l，因为这个是多重背包，我们可以用拆分背包来优化时间。dp[i][j]表示取了i个长度为j可以达到否。不过貌似暴力判断回文和直接多重背包都不会超时。
   
   
   
   
   
   
   
   

    
    
    
    
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<map>
#include<vector>
#include<cstring>
#include<cmath>
using namespace std;
typedef long long ll;
const int inf =0x3f3f3f3f;
const double  pi = acos(-1.0);
const int N = 1e2 + 10;
char str[N][N][N];
int dp[N][N], bag[N*N*N], yes[N][N], cnt[N], cnt1[N*N*N];
void manachar(char *ss)
{
    int l = strlen(ss);
    int len[N*2];
    memset(len, 0, sizeof(len));
    for(int i = l; i>=0; i--)
    {
        ss[i*2+2] = ss[i];
        ss[i*2+1] = '#';
    }
    ss[0] = '*';
    int id = 0;
    for(int i = 1; i<l*2+2; i++)
    {
        if(len[id] + id > i)
            len[i] = min(len[id*2 - i], len[id] + id - i);
        else len[i] = 1;
        while(ss[i + len[i]] == ss[i - len[i]]) len[i]++;
        if(id + len[id] < i + len[i]) id = i;
        if(ss[i] == '#' && len[i] == 1)continue;
        cnt[len[i]-1]++;
    }
}
int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int n, k, l;
        char s[2*N];
        scanf("%d%d%d", &n, &k, &l);
        memset(cnt, 0, sizeof(cnt));
        memset(dp, 0, sizeof(dp));
        for(int i = 0; i<n; i++)
        {
            scanf("%s", s);
            manachar(s);
        }
        int kk = 0;
        for(int i = 1; i<=100; i++)
        {
            int tmp = 1;
            while(cnt[i]>=tmp)
            {
                bag[kk] = tmp*i, cnt1[kk++] = tmp;
                cnt[i] -= tmp;
                tmp*=2;
            }
            if(cnt[i])
                bag[kk] = tmp*i, cnt1[kk++] = tmp;
        }
        dp[0][0] = 1;
        for(int i = 0; i<kk; i++)
        {
            for(int j = l; j>=bag[i]; j--)
            {
                for(int r = cnt1[i]; r<=k; r++)
                {
                    dp[r][j] |= dp[r-cnt1[i]][j - bag[i]];
                }
            }
        }
        if(dp[k][l])
            printf("True\n");
        else printf("False\n");
    }
    return 0;
}

    
    
    
    

    
    
    
    

   
   
   
   

Problem Description

ztr love reserach substring.Today ,he has n string.Now ztr want to konw,can he take out exactly k palindrome from all substring of these n string,and thrn sum of length of these k substring is L.

for example string "yjqqaq"
this string contains plalindromes:"y","j","q","a","q","qq","qaq".
so we can choose "qq" and "qaq".

 

Input

The first line of input contains an positive integer  T(T<=10)  indicating the number of test cases.

For each test case:

First line contains these positive integer  N(1<=N<=100),K(1<=K<=100),L(L<=100) .
The next N line,each line contains a string only contains lowercase.Guarantee even length of string won't more than L.

 

Output

For each test,Output a line.If can output "True",else output "False".

 

Sample Input

    
    
    
    

     
     
     
     3
2 3 7
yjqqaq
claris
2 2 7
popoqqq
fwwf
1 3 3
aaa
    
    
    
    

 

Sample Output

    
    
    
    

     
     
     
     False
True
True