POJ 3691 DNA repair AC自動機DP，poj3691

POJ 3691 DNA repair AC自動機DP，poj3691

題目大意：給出一些病毒串，和一個串，問至少修改多少個使得原串中不含病毒串。

思路：AC自動機+DP，比較裸的題。先按照病毒串建立AC自動機（Trie圖當然也可以），然後設出狀態：f[i][j]表示匹配到原串第i個字元時，在AC自動機的j號節點時沒有病毒串的最小花費。轉移的時候有三種情況：1.轉移出病毒串，這個時候直接continue。2.轉移與原串相符，這個時候直接將數值轉移過去。3.轉移與原串不符，這個時候轉移數值之後還要+1。

在建立AC自動機的時候千萬不要忘記，一個串的自串中有病毒，那麼這個串也有病毒。

CODE：

#include <queue>#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define MAX 1010#define INF 0x3f3f3f3fusing namespace std;int cnt;struct Trie *tree[MAX];struct Trie{Trie *son[4],*fail;int id;bool end;Trie() {memset(son,NULL,sizeof(son));fail = NULL;end = false;id = ++cnt;tree[cnt] = this;}}*root = new Trie();int cases;char s[MAX];int f[MAX][MAX];inline void Initialize(){cnt = 0;root = new Trie();memset(f,0x3f,sizeof(f));}inline int P(char c){if(c == 'A')return 0;if(c == 'G')return 1;if(c == 'C')return 2;return 3;}inline void Insert(char *s){Trie *now = root;while(*s != '\0') {if(now->son[P(*s)] == NULL)now->son[P(*s)] = new Trie();now = now->son[P(*s)];++s;}now->end = true;}void MakeTrieGraph(){static queue<Trie *> q;while(!q.empty())q.pop();for(int i = 0; i < 4; ++i)if(root->son[i] != NULL)root->son[i]->fail = root,q.push(root->son[i]);while(!q.empty()) {Trie *now = q.front(); q.pop();for(int i = 0; i < 4; ++i)if(now->son[i] != NULL) {Trie *temp = now->fail;while(temp != root && temp->son[i] == NULL)temp = temp->fail;if(temp->son[i] != NULL)temp = temp->son[i];now->son[i]->fail = temp;now->son[i]->end |= temp->end;q.push(now->son[i]);}elsenow->son[i] = now->fail->son[i] ? now->fail->son[i]:root;}}void AC_Automaton_DP(){f[0][1] = 0;for(int i = 0; i < 4; ++i)if(root->son[i] == NULL)root->son[i] = root;int length = strlen(s);for(int i = 1; i <= length; ++i)for(int j = 1; j <= cnt; ++j)for(int k = 0; k < 4; ++k) {Trie *aim = tree[j]->son[k];if(aim->end)continue;f[i][aim->id] = min(f[i][aim->id],f[i - 1][j] + (P(s[i - 1]) != k));}}int main(){while(scanf("%d",&cases),cases) {Initialize();for(int i = 1; i <= cases; ++i) {scanf("%s",s);Insert(s);}MakeTrieGraph();scanf("%s",s);AC_Automaton_DP();int ans = INF,length = strlen(s);for(int i = 1; i <= cnt; ++i)ans = min(ans,f[length][i]);if(ans == INF)ans = -1;static int T = 0;printf("Case %d: %d\n",++T,ans);}return 0;}