• [hdu5164]ac自动机


    中文题目:http://bestcoder.hdu.edu.cn/contests/contest_chineseproblem.php?cid=563&pid=1003

    首先贴一下bc的题解:

    首先我们考虑m=1的情况。给定两个数组A={a1,a2,,an}B={b1,b2,,bk},问BA中出现了几次。令ci=ai+1ai,1i<n,同样令di=bi+1bi,1i<k,那么上述问题可以转化为cidi的模式匹配问题,这个正确性显然,也没有什么好证明的。于是对于m=1的情况只有用个kmp即可搞定。
    
    现在考虑m>1的情况,我们考虑用ac自动机来做。考虑到字符集并不是普通的数字,而是一个分数,我们不放搞个分数类,然后用map存转移边。用m个模式串(Bob的序列)建好自动机之后,把文本串(Alice的序列)在自动机上跑一遍即可统计出答案。
    

     事实上,这个题的精华就在于序列变换,将问题转化为多模板匹配问题。而且由于转化后的序列有二维状态,可以用map映射重新为状态分配一个值(类似离散)。另外由于字符集比较大,所以ac自动机里面需要一点小小的修改,原来的二维数组的第二维需用map,另外需要同时记录所有儿子的字符值。原来的模板只需要小改就可以适应这种情况了。详见代码:

      1 #pragma comment(linker, "/STACK:10240000,10240000")
      2 
      3 #include <iostream>
      4 #include <cstdio>
      5 #include <algorithm>
      6 #include <cstdlib>
      7 #include <cstring>
      8 #include <map>
      9 #include <queue>
     10 #include <deque>
     11 #include <cmath>
     12 #include <vector>
     13 #include <ctime>
     14 #include <cctype>
     15 #include <set>
     16 #include <bitset>
     17 #include <functional>
     18 #include <numeric>
     19 #include <stdexcept>
     20 #include <utility>
     21 
     22 using namespace std;
     23 
     24 #define mem0(a) memset(a, 0, sizeof(a))
     25 #define mem_1(a) memset(a, -1, sizeof(a))
     26 #define lson l, m, rt << 1
     27 #define rson m + 1, r, rt << 1 | 1
     28 #define define_m int m = (l + r) >> 1
     29 #define rep_up0(a, b) for (int a = 0; a < (b); a++)
     30 #define rep_up1(a, b) for (int a = 1; a <= (b); a++)
     31 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--)
     32 #define rep_down1(a, b) for (int a = b; a > 0; a--)
     33 #define all(a) (a).begin(), (a).end()
     34 #define lowbit(x) ((x) & (-(x)))
     35 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {}
     36 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}
     37 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}
     38 #define pchr(a) putchar(a)
     39 #define pstr(a) printf("%s", a)
     40 #define sstr(a) scanf("%s", a)
     41 #define sint(a) scanf("%d", &a)
     42 #define sint2(a, b) scanf("%d%d", &a, &b)
     43 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c)
     44 #define pint(a) printf("%d
    ", a)
     45 #define test_print1(a) cout << "var1 = " << a << endl
     46 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl
     47 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl
     48 
     49 typedef long long LL;
     50 typedef pair<int, int> pii;
     51 typedef vector<int> vi;
     52 
     53 const int dx[8] = {0, 0, -1, 1, 1, 1, -1, -1};
     54 const int dy[8] = {-1, 1, 0, 0, 1, -1, 1, -1 };
     55 const int maxn = 3e4 + 7;
     56 const int md = 10007;
     57 const int inf = 1e9 + 7;
     58 const LL inf_L = 1e18 + 7;
     59 const double pi = acos(-1.0);
     60 const double eps = 1e-6;
     61 
     62 template<class T>T gcd(T a, T b){return b==0?a:gcd(b,a%b);}
     63 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;}
     64 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;}
     65 template<class T>T condition(bool f, T a, T b){return f?a:b;}
     66 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];}
     67 int make_id(int x, int y, int n) { return x * n + y; }
     68 
     69 LL ans;
     70 
     71 struct AhoCorasickAutoMata {
     72     const static int maxn = 250007;
     73     int cc;
     74     map<int, int> ch[maxn];
     75     vector<int> son[maxn];
     76     int val[maxn], last[maxn], f[maxn];
     77 
     78     void clear() { cc = 0; mem0(val); mem0(ch); mem0(last); mem0(f); rep_up0(i, maxn) { son[i].clear(); ch[i].clear(); } }
     79 
     80     void Insert(int s[], int n) {
     81         int pos = 0;
     82         rep_up0(i, n) {
     83             int id = s[i];
     84             if(!ch[pos][id]) {
     85                 ch[pos][id] = ++ cc;
     86                 son[pos].push_back(id);
     87             }
     88             pos = ch[pos][id];
     89         }
     90         val[pos] ++;
     91     }
     92 
     93     void print(int j) {
     94         if (j) {
     95             ans += val[j];
     96             print(last[j]);
     97         }
     98     }
     99 
    100     void find(int T[], int n) {
    101         int j = 0;
    102         rep_up0(i, n) {
    103             int c = T[i];
    104             while (j && !ch[j][c]) j = f[j];
    105             j = ch[j][c];
    106             if (val[j]) print(j);
    107             else {
    108                 if (last[j]) print(last[j]);
    109             }
    110         }
    111     }
    112 
    113     int getFail() {
    114         queue<int> q;
    115         f[0] = 0;
    116         int SZ = son[0].size();
    117         rep_up0(i, SZ) {
    118             int c = son[0][i];
    119             int u = ch[0][c];
    120             q.push(u);
    121         }
    122         while (!q.empty()) {
    123             int r = q.front(), SZ = son[r].size(); q.pop();
    124             rep_up0(i, SZ) {
    125                 int c = son[r][i];
    126                 int u = ch[r][c];
    127                 q.push(u);
    128                 int v = f[r];
    129                 while (v && !ch[v][c]) v = f[v];
    130                 f[u] = ch[v][c];
    131                 last[u] = val[f[u]]? f[u] : last[f[u]];
    132             }
    133         }
    134     }
    135 };
    136 
    137 AhoCorasickAutoMata ac;
    138 map<pii, int> mp;
    139 int pa[100007], pb[100007];
    140 int a[100007], b[300007];
    141 
    142 int main() {
    143     //freopen("in.txt", "r", stdin);
    144     int T, n, m, tot = 0;
    145     cin >> T;
    146     while (T--) {
    147         ans = 0;
    148         ac.clear();
    149         mp.clear();
    150         cin >> n >> m;
    151         rep_up0(i, n) {
    152             sint(a[i]);
    153         }
    154         rep_up0(i, n - 1) {
    155             int g = gcd(a[i], a[i + 1]);
    156             int ga = a[i] / g, gb = a[i + 1] / g;
    157             int &x = mp[make_pair(ga, gb)];
    158             if (!x) x = ++ tot;
    159             pa[i] = x;
    160         }
    161 
    162         rep_up0(i, m) {
    163             int k;
    164             sint(k);
    165             rep_up0(j, k) {
    166                 sint(b[j]);
    167             }
    168             if (k > n) continue;
    169             if (k == 1) {
    170                 ans += n;
    171                 continue;
    172             }
    173             rep_up0(j, k - 1) {
    174                 int g = gcd(b[j], b[j + 1]);
    175                 int ga = b[j] / g, gb = b[j + 1] / g;
    176                 int &x = mp[make_pair(ga, gb)];
    177                 if (!x) x = ++ tot;
    178                 pb[j] = x;
    179             }
    180             ac.Insert(pb, k - 1);
    181         }
    182         ac.getFail();
    183         ac.find(pa, n - 1);
    184         cout << ans << endl;
    185     }
    186     return 0;
    187 }
    View Code
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  • 原文地址:https://www.cnblogs.com/jklongint/p/4471504.html
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