题意:给定 n 个子串,然后给一个母串,让你对母串重排,然后问你最多含有多少个字串。
析:这个题很容易想到五维DP,这样的话,不但会MLE,而且连数组都不一定开的出来,里面有大量的无用的状态,所以我们把那四个字符出现的次数进行重新编制,假设A出现 a 次,C出现 c 次,G出现 g 次,T出现 t 次,进行压缩的时候,把第A的系数乘以((b+1) + (c+1) + (d+1)),C乘以((c+1) + (d+1)),G乘以(d+1),T乘以1。这样就很简单的dp[i][j] 表示在 i 这个结点 j 状态时,最多有多少个。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <cmath> #include <stack> #include <sstream> #include <list> #include <assert.h> #include <bitset> #define debug() puts("++++"); #define gcd(a, b) __gcd(a, b) #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define fi first #define se second #define pb push_back #define sqr(x) ((x)*(x)) #define ms(a,b) memset(a, b, sizeof a) //#define sz size() #define pu push_up #define pd push_down #define cl clear() #define all 1,n,1 #define FOR(i,x,n) for(int i = (x); i < (n); ++i) #define freopenr freopen("in.txt", "r", stdin) #define freopenw freopen("out.txt", "w", stdout) using namespace std; typedef long long LL; typedef unsigned long long ULL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const double inf = 1e20; const double PI = acos(-1.0); const double eps = 1e-8; const int maxn = 11*11*11*11 + 10; const int maxm = 1e5 + 10; const int mod = 50007; const int dr[] = {-1, 0, 1, 0}; const int dc[] = {0, -1, 0, 1}; const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"}; int n, m; const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; inline bool is_in(int r, int c) { return r >= 0 && r < n && c >= 0 && c < m; } const int maxnode = 50 * 10 + 10; const int sigma = 4; int dp[maxnode][maxn]; struct Aho{ int ch[maxnode][sigma]; int f[maxnode]; int val[maxnode]; int sz; void clear(){ sz = 1; ms(ch[0], 0); } inline int idx(char ch){ if(ch == 'A') return 0; if(ch == 'C') return 1; if(ch == 'G') return 2; return 3; } void insert(const char *s){ int u = 0; for(int i = 0; s[i]; ++i){ int c = idx(s[i]); if(!ch[u][c]){ ms(ch[sz], 0); val[sz] = 0; ch[u][c] = sz++; } u = ch[u][c]; } ++val[u]; } void getFail(){ queue<int> q; f[0] = 0; for(int i = 0; i < sigma; ++i){ int u = ch[0][i]; if(u){ f[u] = 0; q.push(u); } } while(!q.empty()){ int r = q.front(); q.pop(); for(int c = 0; c < sigma; ++c){ int u = ch[r][c]; if(!u){ ch[r][c] = ch[f[r]][c]; continue; } q.push(u); int v = f[r]; while(v && !ch[v][c]) v = f[v]; f[u] = ch[v][c]; val[u] += val[f[u]]; } } } int solve(int s1, int s2, int s3, int s4){ ms(dp, -1); dp[0][0] = 0; int cnt1 = s2 * s3 * s4; int cnt2 = s3 * s4; int cnt3 = s4; int ans = 0; FOR(j, 0, s1) FOR(k, 0, s2) FOR(l, 0, s3) FOR(y, 0, s4) FOR(i, 0, sz){ int pre = j * cnt1 + k * cnt2 + l * cnt3 + y; if(dp[i][pre] < 0) continue; if(j + 1 < s1){ int nxt = ch[i][0]; int st = pre + cnt1; dp[nxt][st] = max(dp[nxt][st], dp[i][pre] + val[nxt]); ans = max(ans, dp[nxt][st]); } if(k + 1 < s2){ int nxt = ch[i][1]; int st = pre + cnt2; dp[nxt][st] = max(dp[nxt][st], dp[i][pre] + val[nxt]); ans = max(ans, dp[nxt][st]); } if(l + 1 < s3){ int nxt = ch[i][2]; int st = pre + cnt3; dp[nxt][st] = max(dp[nxt][st], dp[i][pre] + val[nxt]); ans = max(ans, dp[nxt][st]); } if(y + 1 < s4){ int nxt = ch[i][3]; int st = pre + 1; dp[nxt][st] = max(dp[nxt][st], dp[i][pre] + val[nxt]); ans = max(ans, dp[nxt][st]); } } return ans; } }; Aho aho; char s[50]; int main(){ int kase = 0; while(scanf("%d", &n) == 1 && n){ aho.cl; for(int i = 0; i < n; ++i){ scanf("%s", s); aho.insert(s); } aho.getFail(); scanf("%s", s); int cnt[4] = {1, 1, 1, 1}; for(int i = 0; s[i]; ++i) ++cnt[aho.idx(s[i])]; printf("Case %d: %d\n", ++kase, aho.solve(cnt[0], cnt[1], cnt[2], cnt[3])); } return 0; }