# # AC自动机

## # 练习题

### #CF1400F - x-prime Substrings (opens new window)

#include <cstring>
#include <iostream>
#include <queue>
#include <set>
#include <vector>

using namespace std;
const int INF = 0x3f3f3f3f;

struct Node {
int fail = 0, children[9]{};
bool match = false;
};

string s, t;
int x, dp[5005][5005];
set<string> xprime;
vector<int> suffix = {0};
vector<Node> nodes;

void generate_xprime() {
if (suffix[0] == x) {
xprime.insert(t);
return;
}
for (int i = 1; i <= 9 && i + suffix[0] <= x; ++i) {
t.push_back(i + '0');
for (int &j : suffix)
j += i;
suffix.emplace_back(i);
bool ok = true;
for (int &j : suffix)
if (j != x && x % j == 0) {
ok = false;
break;
}
if (ok)
generate_xprime();
suffix.pop_back();
for (int &j : suffix)
j -= i;
t.pop_back();
}
}

void build_aca() {
nodes.emplace_back(Node{});
for (const string &str : xprime) {
int curr = 0;
for (const char &c : str) {
if (!nodes[curr].children[c - '1']) {
nodes[curr].children[c - '1'] = nodes.size();
nodes.emplace_back(Node{});
}
curr = nodes[curr].children[c - '1'];
}
nodes[curr].match = true;
}
queue<int> q;
for (const int &u : nodes[0].children)
if (u)
q.push(u);

while (!q.empty()) {
int u = q.front();
q.pop();
for (int i = 0; i < 9; ++i) {
int &v = nodes[u].children[i];
if (v) {
nodes[v].fail = nodes[nodes[u].fail].children[i];
q.push(v);
} else
v = nodes[nodes[u].fail].children[i];
}
}
}

int main() {
cin >> s >> x;

// Step 1: Enumerate all x-prime strings
generate_xprime();

// Step 2: Build Aho-Corasick automaton with x-prime strings
build_aca();

// Step 3: Dynamic programming
memset(dp, 0x3f, sizeof(dp));
int n = s.size(), m = nodes.size(), ans = INF;
dp[0][0] = 0;
for (int i = 0; i < n; ++i)
for (int j = 0; j < m; ++j) {
if (dp[i][j] == INF)
continue;
dp[i + 1][j] = min(dp[i + 1][j], dp[i][j] + 1);
int nxt = nodes[j].children[s[i] - '1'];
if (!nodes[nxt].match)
dp[i + 1][nxt] = min(dp[i + 1][nxt], dp[i][j]);
}
for (int j = 0; j < m; ++j)
ans = min(ans, dp[n][j]);
cout << ans;
}

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### #SPOJ - Ada and Jobs (opens new window)

#include <iostream>
#include <queue>
#include <vector>
#define INF 0x3f3f3f3f

using namespace std;

struct Node {
int occur = INF, fail = 0, children[26]{};
};

int main() {
int q;
cin >> q;
vector<string> dict;
vector<pair<int, string>> query;
while (q--) {
int t;
string s;
cin >> t >> s;
if (t == 0)
dict.emplace_back(s);
else
query.emplace_back(dict.size(), s);
}
int m = dict.size();
vector<Node> nodes(1);
for (int i = 1; i <= m; ++i) {
int current = 0;
for (char c : dict[i - 1]) {
if (!nodes[current].children[c - 'a']) {
nodes[current].children[c - 'a'] = nodes.size();
nodes.emplace_back(Node{});
}
current = nodes[current].children[c - 'a'];
}
nodes[current].occur = min(nodes[current].occur, i);
}
queue<int> que;
for (const int &u : nodes[0].children)
if (u)
que.push(u);
while (!que.empty()) {
int u = que.front();

// Push down the timestamp. This is critical.
nodes[u].occur = min(nodes[u].occur, nodes[nodes[u].fail].occur);
que.pop();
for (int i = 0; i < 26; ++i) {
int &v = nodes[u].children[i];
if (v) {
nodes[v].fail = nodes[nodes[u].fail].children[i];
que.push(v);
} else
v = nodes[nodes[u].fail].children[i];
}
}
string ans;
for (auto &[ts, s] : query) {
int current = 0;
bool found = false;
int idx = 0;
while (idx < s.size()) {
char c = s[idx];
if (nodes[current].children[c - 'a']) {
current = nodes[current].children[c - 'a'];
if (nodes[current].occur <= ts) {
ans += "YES\n";
found = true;
break;
}
idx++;
} else {
current = nodes[current].fail;
if (!current)
idx++;
}
}
if (!found)
ans += "NO\n";
}
cout << ans;
}

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