HDU 3341 Lost's revenge （AC自动机 + DP + 变进制/hash）题解
题意：给你些分数串，给你一个主串，主串每出现一个分数串加一分，要你重新排列主串，最多几分
思路：显然这里开$40^4$去状压内存不够。但是我们自己想想会发现根本不用开那么大，因为很多状态是废状压，不是不存在的，那么可以考虑想办法简化状态。
一个是hash，直接打表所有子情况，用ha[][][][]表示出所有情况，那么直接dp[status][size]去dp。
还有一种用变进制：
假设ACGT的总数分别为num[0],num[1],num[2],num[3]
那么对于ACGT的数量分别为ABCD的状态可以记录为：
A*(num[1]+1)*(num[2]+1)*(num[3]+1) + B*(num[2]+1)*(num[3]+1)+ C*(num[3]+1) +D
显然末尾D基数为1，次末尾C基数(num[3]+1)，那么D不管怎么变（最多变num[3]）永远影响不到C那个级数（（num[3] + 1 ）* k），那么就能区分变得是哪一位。
代码：
/*变进制*/ #include<set> #include<map> #include<queue> #include<cmath> #include<string> #include<cstdio> #include<vector> #include<cstring> #include <iostream> #include<algorithm> using namespace std; typedef long long ll; typedef unsigned long long ull; const int maxn = 500 + 5; const int M = 50 + 5; const ull seed = 131; const int INF = 0x3f3f3f3f; const int MOD = 20090717; int n, m; int dp[15000][maxn]; int getid(char s){ if(s == 'A') return 0; if(s == 'C') return 1; if(s == 'G') return 2; return 3; } struct Aho{ struct state{ int next[4]; int fail, cnt; }node[maxn]; int size; queue<int> q; void init(){ size = 0; newtrie(); while(!q.empty()) q.pop(); } int newtrie(){ memset(node[size].next, 0, sizeof(node[size].next)); node[size].cnt = node[size].fail = 0; return size++; } void insert(char *s){ int len = strlen(s); int now = 0; for(int i = 0; i < len; i++){ int c = getid(s[i]); if(node[now].next[c] == 0){ node[now].next[c] = newtrie(); } now = node[now].next[c]; } node[now].cnt++; } void build(){ node[0].fail = -1; q.push(0); while(!q.empty()){ int u = q.front(); q.pop(); if(node[node[u].fail].cnt && u) node[u].cnt += node[node[u].fail].cnt; for(int i = 0; i < 4; i++){ if(!node[u].next[i]){ if(u == 0) node[u].next[i] = 0; else node[u].next[i] = node[node[u].fail].next[i]; } else{ if(u == 0) node[node[u].next[i]].fail = 0; else{ int v = node[u].fail; while(v != -1){ if(node[v].next[i]){ node[node[u].next[i]].fail = node[v].next[i]; break; } v = node[v].fail; } if(v == -1) node[node[u].next[i]].fail = 0; } q.push(node[u].next[i]); } } } } void query(char *s){ int ans = 0; int len = strlen(s); int num[4] = {0}; for(int i = 0; i < len; i++){ num[getid(s[i])]++; } memset(dp, -1, sizeof(dp)); dp[0][0] = 0; int fac[4]; fac[0] = (num[1] + 1) * (num[2] + 1) * (num[3] + 1); fac[1] = (num[2] + 1) * (num[3] + 1); fac[2] = (num[3] + 1); fac[3] = 1; for(int i = 0; i <= num[0]; i++){ for(int j = 0; j <= num[1]; j++){ for(int k = 0; k <= num[2]; k++){ for(int l = 0; l <= num[3]; l++){ int id = i * fac[0] + j * fac[1] + k * fac[2] + l; for(int g = 0; g < size; g++){ if(dp[id][g] == -1) continue; for(int h = 0; h < 4; h++){ int nex; if(h == 0 && i == num[0]) continue; if(h == 1 && j == num[1]) continue; if(h == 2 && k == num[2]) continue; if(h == 3 && l == num[3]) continue; nex = id + fac[h]; int add = node[node[g].next[h]].cnt; if(dp[nex][node[g].next[h]] < dp[id][g] + add){ dp[nex][node[g].next[h]] = dp[id][g] + add; if(i + j + k + l + 1 == len) ans = max(ans , dp[nex][node[g].next[h]]); } } } } } } } printf("%d\n", ans); } }ac; char s[45]; int main(){ int ca = 1; while(~scanf("%d", &n) && n){ ac.init(); for(int i = 0; i < n; i++){ scanf("%s", s); ac.insert(s); } ac.build(); scanf("%s", s); printf("Case %d: ", ca++); ac.query(s); } return 0; }
/*Hash*/ #include<set> #include<map> #include<queue> #include<cmath> #include<string> #include<cstdio> #include<vector> #include<cstring> #include <iostream> #include<algorithm> using namespace std; typedef long long ll; typedef unsigned long long ull; const int maxn = 500 + 5; const int M = 50 + 5; const ull seed = 131; const int INF = 0x3f3f3f3f; const int MOD = 20090717; int n, m; int dp[15000][maxn]; int ha[42][42][42][42]; int getid(char s){ if(s == 'A') return 0; if(s == 'C') return 1; if(s == 'G') return 2; return 3; } struct Aho{ struct state{ int next[4]; int fail, cnt; }node[maxn]; int size; queue<int> q; void init(){ size = 0; newtrie(); while(!q.empty()) q.pop(); } int newtrie(){ memset(node[size].next, 0, sizeof(node[size].next)); node[size].cnt = node[size].fail = 0; return size++; } void insert(char *s){ int len = strlen(s); int now = 0; for(int i = 0; i < len; i++){ int c = getid(s[i]); if(node[now].next[c] == 0){ node[now].next[c] = newtrie(); } now = node[now].next[c]; } node[now].cnt++; } void build(){ node[0].fail = -1; q.push(0); while(!q.empty()){ int u = q.front(); q.pop(); if(node[node[u].fail].cnt && u) node[u].cnt += node[node[u].fail].cnt; //attention for(int i = 0; i < 4; i++){ if(!node[u].next[i]){ if(u == 0) node[u].next[i] = 0; else node[u].next[i] = node[node[u].fail].next[i]; } else{ if(u == 0) node[node[u].next[i]].fail = 0; else{ int v = node[u].fail; while(v != -1){ if(node[v].next[i]){ node[node[u].next[i]].fail = node[v].next[i]; break; } v = node[v].fail; } if(v == -1) node[node[u].next[i]].fail = 0; } q.push(node[u].next[i]); } } } } void query(char *s){ int ans = 0; int len = strlen(s); int tot = 0; int num[4] = {0}; for(int i = 0; i < len; i++){ num[getid(s[i])]++; } for(int i = 0; i <= num[0]; i++){ for(int j = 0; j <= num[1]; j++){ for(int k = 0; k <= num[2]; k++){ for(int l = 0; l <= num[3]; l++){ ha[i][j][k][l] = tot; for(int g = 0; g < size; g++){ dp[tot][g] = -1; } tot++; } } } } for(int i = 0; i <= num[0]; i++){ for(int j = 0; j <= num[1]; j++){ for(int k = 0; k <= num[2]; k++){ for(int l = 0; l <= num[3]; l++){ } } } } dp[0][0] = 0; for(int i = 0; i <= num[0]; i++){ for(int j = 0; j <= num[1]; j++){ for(int k = 0; k <= num[2]; k++){ for(int l = 0; l <= num[3]; l++){ int id = ha[i][j][k][l]; for(int g = 0; g < size; g++){ if(dp[id][g] == -1) continue; for(int h = 0; h < 4; h++){ int nex; if(h == 0 && i == num[0]) continue; if(h == 1 && j == num[1]) continue; if(h == 2 && k == num[2]) continue; if(h == 3 && l == num[3]) continue; if(h == 0) nex = ha[i + 1][j][k][l]; if(h == 1) nex = ha[i][j + 1][k][l]; if(h == 2) nex = ha[i][j][k + 1][l]; if(h == 3) nex = ha[i][j][k][l + 1]; int add = node[node[g].next[h]].cnt; if(dp[nex][node[g].next[h]] < dp[id][g] + add){ dp[nex][node[g].next[h]] = dp[id][g] + add; if(i + j + k + l + 1 == len) ans = max(ans , dp[nex][node[g].next[h]]); } } } } } } } printf("%d\n", ans); } }ac; char s[45]; int main(){ int ca = 1; while(~scanf("%d", &n) && n){ ac.init(); for(int i = 0; i < n; i++){ scanf("%s", s); ac.insert(s); } ac.build(); scanf("%s", s); printf("Case %d: ", ca++); ac.query(s); } return 0; }
