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/**
* Author: Dean
* License: CC0
* Description: Builds an Ahocorasick Trie, with suffix links.
* Time: O(n + m + z)
* Status: Tested http://www.spoj.com/problems/STRMATCH/, https://codeforces.com/gym/101741/problem/K
* Usage: This is an offline Algorithm, Pass the vector of patterns to Trie.init(v), find function returns the number of times each string appears
*/
const int MaxM = 200005;
struct Trie{
static const int Alpha = 26;
static const int first = 'a';
int lst = 1;
struct node{
int nxt[Alpha] = {}, p = -1;
char c;
vector<int> end; //if all patterns are different, can use flag instead
int SuffixLink = -1;
int cnt = 0;
};
vector<node> V;
int num;
stack<int> reversebfs;
inline int getval(char c) {
return c - first;
}
void CreateSuffixLink() {
queue<int> q;
for(q.push(0); q.size(); q.pop()) {
int pos = q.front();
reversebfs.push(pos);
if(!pos || !V[pos].p) V[pos].SuffixLink = 0;
else {
int val = getval(V[pos].c);
int j = V[V[pos].p].SuffixLink;
V[pos].SuffixLink = V[j].nxt[val];
}
for(int i = 0; i < Alpha; ++i) {
if(V[pos].nxt[i]) q.push(V[pos].nxt[i]);
else if(!pos || !V[pos].p) V[pos].nxt[i] = V[0].nxt[i];
else V[pos].nxt[i] = V[V[pos].SuffixLink].nxt[i];
}
}
}
void init(vector<string> &v) {
V.resize(MaxM);
num = v.size();
int id = 0;
for(auto &s : v) {
int pos = 0;
for(char &c : s) {
int val = getval(c);
if(!V[pos].nxt[val]) {
V[lst].p = pos; V[lst].c = c; V[pos].nxt[val] = lst++;
}
pos = V[pos].nxt[val];
}
V[pos].end.emplace_back(id++);
}
CreateSuffixLink();
}
vector<int> find(string& word) {
int pos = 0;
vector<int> ans(num, 0);
for(auto &c : word) {
int val = getval(c);
pos = V[pos].nxt[val];
V[pos].cnt++; //We count the times we reach each node, and then do a reverse propagation
}
for(;reversebfs.size();reversebfs.pop()) {
int x = reversebfs.top(); //When we process x, we know we have been there V[x].cnt times;
for(int i : V[x].end) ans[i] += V[x].cnt;
if(V[x].SuffixLink != -1) V[V[x].SuffixLink].cnt += V[x].cnt;
}
return ans;
}
};
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