关于维护AC自动机fail树的三道题目

由易到难

e-Government CF 163E

http://blog.youkuaiyun.com/gyarenas/article/details/9315319

GRE Words hdu 4117 

http://acm.hdu.edu.cn/showproblem.php?pid=4117

这题本来的做法是ac自动机优化dp，然而hdu加入了新的数据，估计构造了一些会导致fail链很长的数据，以前的做法会TLE，这就又需要我们维护fail树，用线段树维护fail树的dfs序列，支持单点修改区间求最值。需要注意的是当fail链比较短时(比如这题的原始数据)，用线段树维护做法反而耗时更长。

一开始交上去各种优化各种MLE，后来发现原来是AC自动机初始化一下把整个数组置空了，特意找了篇oj判MLE的方法http://blog.youkuaiyun.com/a775700879/article/details/12521915，从这种情况来看，hdu用的方法应该和bnuoj一样

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <algorithm>
#include <vector>
#include <cstring>
#include <stack>
#include <cctype>
#include <utility>   
#include <map>
#include <string>  
#include <climits> 
#include <set>
#include <string>    
#include <sstream> 
#include <ctime>
#include <bitset>
#include <iomanip>
#pragma comment(linker, "/STACK:102400000,102400000")

using std::priority_queue;
using std::vector;
using std::swap;
using std::stack;
using std::sort;
using std::max;
using std::min;
using std::pair;
using std::map;
using std::string;
using std::cin;
using std::cout;
using std::set;
using std::queue;
using std::string;
using std::stringstream;
using std::make_pair;
using std::getline;
using std::greater;
using std::endl;
using std::multimap;
using std::deque;
using std::unique;
using std::lower_bound;
using std::random_shuffle;
using std::bitset;
using std::upper_bound;
using std::multiset;
using std::ios;
using std::make_heap;
using std::push_heap;
using std::pop_heap;

typedef long long LL;
typedef unsigned long long ULL;
typedef unsigned UN;
typedef pair<int, int> PAIR;
typedef multimap<int, int> MMAP;
typedef long double LF;

const int MAXN(300010);
const int MAXM(20010);
const int MAXE(2100010);
const int MAXK(6);
const int HSIZE(1313131);
const int SIGMA_SIZE(26);
const int MAXH(18);
const int INFI((INT_MAX-1) >> 1);
const ULL BASE(31);
const LL LIM(1e13);
const int INV(-10000);
const int MOD(1000000007);
const double EPS(1e-7);
const LF PI(acos(-1.0));

template<typename T> inline bool checkmax(T &a, T b){if(b > a) { a = b; return true;} return false;}
template<typename T> inline bool checkmin(T &a, T b){if(b < a) { a = b; return true;} return false;}
template<typename T> inline T ABS(T a){return a < 0? -a: a;}
template<typename T> inline bool EZ(T a){return ABS(a) < EPS;}

struct SGT{
	int val[MAXN << 2];
	inline int ls(int rt){return rt << 1;}
	inline int rs(int rt){return (rt << 1)|1;}
	inline void push_up(int rt){val[rt] = max(val[ls(rt)], val[rs(rt)]);}
	void build(int l, int r, int rt){
		val[rt] = -INFI;
		if(l == r) return;
		int m = (l+r) >> 1;
		build(l, m, ls(rt));
		build(m+1, r, rs(rt));
	}
	void update(int l, int r, int rt, int qi, int qv){
		if(l == r){
			checkmax(val[rt], qv);
			return;
		}
//		push_down(rt);
		int m = (l+r) >> 1;
		if(qi <= m) update(l, m, ls(rt), qi, qv);
		else update(m+1, r, rs(rt), qi, qv);
		push_up(rt);
	}
	int query(int l, int r, int rt, int ql, int qr){
		if(ql <= l && qr >= r) return val[rt];
//		push_down(rt);
		int m = (l+r) >> 1;
		int ret = -INFI;
		if(ql <= m) checkmax(ret, query(l, m, ls(rt), ql, qr));
		if(qr > m) checkmax(ret, query(m+1, r, rs(rt), ql, qr));
		return ret;
	}
} sgt;

int left[MAXN], right[MAXN], ind;

struct TREE{
	int *first, *v, *next;  //内存优化，先借用线段树的内存
	int rear;
	void init(int n){
		first = sgt.val;
		v = sgt.val+MAXN;
		next = sgt.val+2*MAXN;
		memset(first, -1, sizeof(first[0])*n);
		rear = 0;
	}
	void insert(int tu, int tv){
		v[rear] = tv;
		next[rear] = first[tu];
		first[tu] = rear++;
	}
	void dfs(int u){
		left[u] = ++ind;
		for(int i = first[u]; ~i; i = next[i])
			dfs(v[i]);
		right[u] = ind;
	}
} tree;

int po[MAXM], sco[MAXM];
int front, back;
struct AC{
	int f[MAXN], ch[MAXN][SIGMA_SIZE], size;
	void init(){
		memset(ch[0], 0, sizeof(ch[0])); // !!!memset(ch[0], 0, sizeof(ch));
		size = 1;
	}
	void insert(char *sp, int i){
		int rt = 0;
		for(; *sp; ++sp){
			int id = *sp-'a';
			if(!ch[rt][id]){
				memset(ch[size], 0, sizeof(ch[size]));
				ch[rt][id] = size++;
			}
			rt = ch[rt][id];
		}
		po[i] = rt;
	}
	void construct(){
		front = back = 0;
		tree.init(size);
		for(int i = 0; i < SIGMA_SIZE; ++i)
			if(ch[0][i]){
				f[ch[0][i]] = 0;
				tree.insert(0, ch[0][i]);
				left[back++] = ch[0][i]; 
			}
		while(front < back){
			int cur = left[front++];	
			for(int i = 0; i < SIGMA_SIZE; ++i){
				int u = ch[cur][i];
				if(u){
					f[u] = ch[f[cur]][i];
					tree.insert(f[u], u);
					left[back++] = u;
				} 
				else
					ch[cur][i] = ch[f[cur]][i];
			}
		}
		ind = 0;
		tree.dfs(0);
	}
} ac;

char str[MAXN+MAXM];
char *tst[MAXM];

int main(){
//	freopen("d:\\in.txt", "r", stdin);
//    freopen("d:\\out.txt", "w", stdout);
	int TC, n_case(0);
	scanf("%d", &TC);
	while(TC--){
		ac.init();
		int n;
		scanf("%d", &n);
		tst[0] = str;
		for(int i = 0; i < n; ++i){
			scanf("%s%d", tst[i], sco+i);
			tst[i+1] = tst[i]+strlen(tst[i])+1;
			ac.insert(tst[i], i);
		}
		ac.construct();
		sgt.build(1, ind, 1);
		int ans = 0;
		for(int i = n-1; i >= 0; --i){
			int temp = sgt.query(1, ind, 1, left[po[i]], right[po[i]]);
			checkmax(temp, 0);
			temp += sco[i];
			int rt = 0;
			for(char *sp = tst[i]; *sp; ++sp){
				int id = *sp-'a';
				rt = ac.ch[rt][id];
				sgt.update(1, ind, 1, left[rt], temp);
			}
			checkmax(ans, temp);
		}
		printf("Case #%d: %d\n", ++n_case, ans);
	}
	return 0;
}

阿狸的打字机

http://blog.youkuaiyun.com/gyarenas/article/details/9260235