HDU 2457 (AC自动机 DP)

题目链接:点击这里

题意:给定一个DNA串, 至少改变多少字母才能使得所有的模式串都不出现在这个DNA串里.

先给所有的模式串建立AC自动机,然后DNA串就不能走到自动机上的危险节点, 也就是模式串的结尾节点. 假设dp[i][j]表示在字典树上i节点, DNA串长为j的最小改变个数, 转移就是d[i][j]=min{dp[k][j−1]dp[k][j−1]+1buf[k]=buf[i+1],k是文本串i的后继不是模式串结尾buf[k]≠buf[i+1],k不是文本串i的后继且k不是模式串结尾

#include <bits/stdc++.h>
using namespace std;
#define maxn 1005
#define INF 1111111

int dp[maxn][maxn];//在字典树上i节点 长度为j 最少改变了多少次
int n;
char str[maxn];

void change (char *s) {
int len = strlen (s);
for (int i = 0; i < len; i++) {
if (s[i] == 'A') s[i] = 'a';
else if (s[i] == 'C') s[i] = 'b';
else if (s[i] == 'G') s[i] = 'c';
else s[i] = 'd';
}
}

struct trie {
int next[maxn][4], fail[maxn], end[maxn];
int root, cnt;
int new_node () {
memset (next[cnt], -1, sizeof next[cnt]);
end[cnt++] = 0;
return cnt-1;
}
void init () {
cnt = 0;
root = new_node ();
}
void insert (char *buf) {//字典树插入一个单词
int len = strlen (buf);
int now = root;
for (int i = 0; i < len; i++) {
int id = buf[i]-'a';
if (next[now][id] == -1) {
next[now][id] = new_node ();
}
now = next[now][id];
}
end[now]++;
}
void build () {//构建fail指针
queue <int> q;
fail[root] = root;
for (int i = 0; i < 4; i++) {
if (next[root][i] == -1) {
next[root][i] = root;
}
else {
fail[next[root][i]] = root;
q.push (next[root][i]);
}
}
while (!q.empty ()) {
int now = q.front (); q.pop ();
end[now] += end[fail[now]];
for (int i = 0; i < 4; i++) {
if (next[now][i] == -1) {
next[now][i] = next[fail[now]][i];
}
else {
fail[next[now][i]] = next[fail[now]][i];
q.push (next[now][i]);
}
}
}
}
int query (char *buf) {
int len = strlen (buf);
for (int i = 0; i < cnt; i++) {
for (int j = 0; j <= len; j++) dp[i][j] = INF;
}
dp[0][0] = 0;
for (int j = 0; j < len; j++) {
for (int i = 0; i < cnt; i++) {
if (end[i]) continue;
int id = buf[j]-'a';
int nexti = next[i][id];
if (!end[nexti]) {//可以走到这个点
dp[nexti][j+1] = min (dp[nexti][j+1], dp[i][j]);
}
for (int x = 0; x < 4; x++) if (x != id) {
nexti = next[i][x];
if (!end[nexti]) {
dp[nexti][j+1] = min (dp[nexti][j+1], dp[i][j]+1);
}
}
}
}
int ans = INF;
for (int i = 0; i < cnt; i++) ans = min (ans, dp[i][len]);
if (ans >= INF)
ans = -1;
return ans;
}
}ac;

int main () {
int kase = 0;
while (scanf ("%d", &n) == 1 && n) {
ac.init ();
for (int i = 1; i <= n; i++) {
scanf ("%s", str);
change (str);
ac.insert (str);
}
ac.build ();
scanf ("%s", str);
change (str);
printf ("Case %d: %d\n", ++kase, ac.query (str));
}
return 0;
}