116 lines
3.0 KiB
C++
116 lines
3.0 KiB
C++
#include <algorithm>
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#include <cmath>
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#include <cstdio>
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#include <cstring>
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#include <queue>
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using namespace std;
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typedef long long LL;
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const int kMaxN = 2000;
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const double kEps = 1e-6;
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const double kInf = 1e100;
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int n, m;
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char T[kMaxN], S[kMaxN];
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int fail[kMaxN], trans[kMaxN][10], tot[kMaxN], node_cnt = 0;
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double val[kMaxN];
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void AddString(const char *s, double V) {
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int p = 0;
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while (*s) {
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if (trans[p][*s - '0'] == 0) trans[p][*s - '0'] = ++node_cnt;
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p = trans[p][*s - '0'];
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s++;
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}
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tot[p]++;
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val[p] += V;
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}
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void BuildAutomaton() {
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int L = 0, R = 0;
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int *Q = new int[kMaxN + 10]();
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fail[0] = -1;
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while (L <= R) {
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int u = Q[L++];
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for (int i = 0; i < 10; i++) {
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if (trans[u][i] != 0) {
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int v = fail[u];
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while (v != -1 && trans[v][i] == 0) v = fail[v];
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// 反复沿着失配边跳转
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if (v != -1) fail[trans[u][i]] = trans[v][i];
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// 子节点的内容在父节点就处理好
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Q[++R] = trans[u][i];
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} else if (fail[u] != -1)
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trans[u][i] = trans[fail[u]][i];
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// 其余情况置0，回到初始状态
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}
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}
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for (int i = 1; i <= R; i++) {
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tot[Q[i]] += tot[fail[Q[i]]];
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val[Q[i]] += val[fail[Q[i]]];
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// 叠加，从贪心匹配变成匹配所有
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}
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delete[] Q;
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}
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double dp[kMaxN][kMaxN];
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int pre_node[kMaxN][kMaxN];
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char pre_char[kMaxN][kMaxN];
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char last_ans[kMaxN];
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double calc(double v_guess) {
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for (int i = 0; i <= node_cnt; i++) val[i] -= tot[i] * v_guess;
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for (int i = 0; i <= n; i++)
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for (int j = 0; j <= node_cnt; j++) dp[i][j] = -kInf;
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dp[0][0] = 0;
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for (int i = 0; i < n; i++)
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for (int j = 0; j <= node_cnt; j++) {
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if (dp[i][j] == -kInf) continue;
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if (T[i] != '.') {
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int v = trans[j][T[i] - '0'];
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if (dp[i][j] + val[v] > dp[i + 1][v]) {
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dp[i + 1][v] = dp[i][j] + val[v];
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pre_node[i + 1][v] = j;
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pre_char[i + 1][v] = T[i];
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}
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} else {
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for (int k = 0; k < 10; k++) {
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int v = trans[j][k];
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if (dp[i][j] + val[v] > dp[i + 1][v]) {
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dp[i + 1][v] = dp[i][j] + val[v];
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pre_node[i + 1][v] = j;
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pre_char[i + 1][v] = '0' + k;
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}
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}
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}
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}
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for (int i = 0; i <= node_cnt; i++) val[i] += tot[i] * v_guess;
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int res_pos = 0;
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for (int i = 1; i <= node_cnt; i++)
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if (dp[n][i] > dp[n][res_pos]) res_pos = i;
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for (int str_p = n, node_p = res_pos; str_p >= 1; str_p--) {
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last_ans[str_p - 1] = pre_char[str_p][node_p];
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node_p = pre_node[str_p][node_p];
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}
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last_ans[n] = 0;
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return dp[n][res_pos];
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}
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int main() {
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#ifdef local
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freopen("pro.in", "r", stdin);
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#endif
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scanf("%d%d", &n, &m);
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scanf("%s", T);
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for (int i = 0; i < m; i++) {
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int V;
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scanf("%s%d", S, &V);
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AddString(S, log(V));
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}
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BuildAutomaton();
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double L = 0, R = log(1e9), M, res = 0;
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while (R - L > kEps) {
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M = (L + R) / 2;
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if (calc(M) > 0) {
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res = M;
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L = M;
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} else
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R = M;
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}
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calc(res);
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puts(last_ans);
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return 0;
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} |