Hyper Strings
Problem Statement :
String A is called a Super String if and only if: A contains only letters a,b,c,d,e,f,g,h,i,j; For any i and j, A[i] has lower ascii code than A[j], where 0 < i < j < length(A) Given a set of Super Strings H, a Hyper String is a string that can be constructed by concatenation of some Super Strings of the set H. We can use each Super String as many times as we want. Given set H, you have to compute the number of Hyper Strings with length no greater than M. Input Format The first line of input contains two integers, N(the number of Super Strings in H) and M. The next N lines describe the Super Strings in set H. Constraints N and M are not greater than 100. Output Format Output an integer which is the number of possible Hyper Strings that can be derived. Since it may not fit in 32 bit integer, print the output module 1000000007. (i.e. answer = answer % 1000000007)
Solution :
Solution in C :
In C++ :
#include <algorithm>
#include <functional>
#include <iterator>
#include <numeric>
#include <limits>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <cassert>
using namespace std;
#define REP(i, n) for (int (i) = 0, __n = (int)(n); (i) < __n; ++(i))
#define REPS(i, s, n) for (int (i) = (s), __n = (int)(n); (i) < __n; ++(i))
#define REPD(i, n) for (int (i) = (n); (i) >= 0; --(i))
#define FOREACH(i, x) for (auto i = (x).begin(); i != (x).end(); ++i)
#define SIZE(x) (int)((x).size())
const int MOD = 1000000007;
const int MAXL = (1<<10);
const int MAXN = 100;
const int MAXM = 100;
string S[MAXN];
int64_t memo[MAXM+1][MAXL];
int ways[MAXL], A[MAXN], lo[MAXN], len[MAXN];
int N, M;
inline int lobit(int x) {
for (int p = 0; x > 0; x >>= 1, ++p)
if (x & 1) return p;
return -1;
}
inline int hibit(int x) {
int res = -1;
for (int p = 0; x > 0; x >>= 1, ++p)
if (x & 1) res = p;
return res;
}
int count_ways(int s) {
string X;
for (int i = 0; s > 0; s >>= 1, ++i)
if (s & 1) X += 'a' + i;
int L = X.length();
vector<int> dp(L+1, 0);
dp[0] = 1;
REPS(i, 1, L+1) {
REP(j, N) {
if ((int)S[j].length() > i) continue;
if (X.substr(i - S[j].length(), S[j].length()) != S[j]) continue;
dp[i] += dp[i - S[j].length()];
}
}
return dp[L];
}
int64_t solve(int m, int last) {
if (m > M) return 0;
int64_t& res = memo[m][last];
if (res != -1) return ways[last] > 1 ? 0 : res;
int hi = hibit(last); res = 1;
REP(i, N) {
int64_t val = 0;
if (ways[A[i]] > 1) continue;
if (lo[i] <= hi) val = solve(m + len[i], A[i]);
else val = solve(m + len[i], A[i] | last);
res = (res + val) % MOD;
}
return res;
}
int main() {
ios_base::sync_with_stdio(false);
cin >> N >> M;
REP(i, N) {
cin >> S[i]; int x = 0;
FOREACH(it, S[i]) x |= (1 << (*it - 'a'));
A[i] = x; lo[i] = lobit(x); len[i] = S[i].length();
}
REPS(s, 1, MAXL) ways[s] = count_ways(s);
memset(memo, -1, sizeof(memo));
cout << solve(0, 0) << "\n";
return EXIT_SUCCESS;
}
In Java :
import java.util.*;
public class Solution
{
int N,M;
boolean[] source=new boolean[1 << 10];
int[] bin=new int[20];
long[][] dp=new long[110][12];
int[][][] ok=new int[10][10][11];
boolean[] state=new boolean[1 << 10];
boolean[] vis=new boolean[1 << 10];
final int mod=1000000007;
boolean State(int s)
{
//if (s==0) return true;
if (vis[s]) return state[s];
vis[s]=true;
if (source[s])
{
state[s]=source[s];
}
else
{
state[s]=false;
int tmp=0;
for (int i=0;i<10;i++)
{
if ((bin[i] & s)!=0)
{
tmp+=bin[i];
if (source[tmp] && State(s-tmp))
{
state[s]=true;
break;
}
}
}
}
return state[s];
}
void build()
{
bin[0]=1;
for (int i=1;i<=12;i++) bin[i]=bin[i-1] << 1;
}
void init()
{
Scanner scan=new Scanner(System.in);
N=scan.nextInt();
M=scan.nextInt();
for (int i=1;i<=N;i++)
{
String str=scan.next();
int tmp=0;
for (int j=0;j<str.length();j++)
{
tmp+=bin[str.charAt(j)-'a'];
}
source[tmp]=true;
}
for (int i=0;i<10;i++) dp[0][i]=0;
dp[0][9]=1;
for (int i=0;i<(1 << 10);i++)
{
if (!State(i)) continue;
int from=11;
int to=-1;
int cnt=0;
for (int j=0;j<10;j++)
{
if ((bin[j] & i)!=0)
{
cnt++;
from=Math.min(from, j);
to=Math.max(to,j);
}
}
ok[from][to][cnt]++;
}
}
void work()
{
for (int i=1;i<=M;i++)
{
for (int j=0;j<10;j++)
{
dp[i][j]=0;
for (int k=1;k<=10;k++)
{
if (i-k<0) break;
for (int l=0;l<10;l++)
{
for (int m=0;m<=l;m++)
{
//if (ok[m][j][k])
{
dp[i][j]+=dp[i-k][l]*ok[m][j][k];
dp[i][j]%=mod;
}
}
}
}
}
}
int result=0;
for (int i=0;i<=M;i++)
{
for (int j=0;j<10;j++)
{
result+=dp[i][j];
result%=mod;
}
}
System.out.println(result);
}
void run()
{
build();
init();
work();
}
public static void main(String[] args)
{
new Solution().run();
}
}
In C :
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define XXX 1
#define MOD (1000000007)
#define NMAX 100
#define MMAX 100
#define SMAX 11
char s[NMAX][SMAX];
int lens[NMAX];
int count[SMAX];
unsigned long long nways[MMAX+1];
// Return 1 if str is a concatenation of other strings in the list
int match(char *str, int n, int N)
{
int i = 0;
int ns;
if (n==0)
return 1; // This string is composite
for (i=0; i<N; i++) {
if (str!=s[i]
&& (ns = lens[i]) <= n
&& ns != 0
&& strncmp(str, s[i], ns)==0
&& match(str+ns, n-ns, N)) {
return 1;
}
}
return 0;
}
// Count the ways of generating string length m (fills cache, nways[])
unsigned long long countways(int m)
{
int i;
unsigned long long ways=0;
if (nways[m]!=0)
return nways[m];
for (i=1; i<SMAX && i<=m; i++)
ways = (ways + count[i]*countways(m-i))%MOD;
nways[m] = ways;
return ways;
}
int main(void)
{
int N, M;
int i;
unsigned long long total;
scanf("%d %d\n", &N, &M);
// Read input super strings
for (i=0; i<N; i++) {
scanf("%s", s[i]);
lens[i] = strlen(s[i]);
}
// Eliminate strings that are composites of shorter strings
for (i=0; i<N; i++)
if (match(s[i], lens[i], N))
lens[i] = 0;
// Count strings of each length
for (i=0; i<SMAX; i++)
count[i] = 0;
for (i=0; i<N; i++)
++count[lens[i]];
// Initialise the cache
nways[0] = 1;
for (i=1; i<=M; i++)
nways[i] = 0;
// Fill the cache
(void)countways(M);
total = 0;
for (i=0; i<=M; i++)
total += nways[i];
printf("%llu\n", total%MOD);
return 0;
}
In Python3 :
from collections import Counter
j,k = map(int, input().split())
supers_list = []
for i in range(j):
supers_list.append(input())
def check_concat(Str_, Sub_Str_):
if Sub_Str_ == "":
return False
for i in supers_list:
if i == Sub_Str_ and Str_ != Sub_Str_:
return True
x = Sub_Str_.startswith(i)
if x == True:
if check_concat(Str_, Sub_Str_[len(i):]) == True:
return True
return False
def filter_():
tmp = []
global supers_list
for i in supers_list:
if check_concat(i,i) == False:
tmp.append(i)
supers_list = tmp
filter_()
y = Counter(len(i) for i in supers_list)
saved = {}
def f(x):
if x in saved: return saved[x]
if x<1: return 0
k = y[x] if x in y else 0
for i in y:
k += y[i]*f(x-i)
saved[x] = k
return k
x = 0
for i in range(1,k+1):
x+=f(i)
print((x+1)%1000000007)
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