【LOJ】#3089. 「BJOI2019」奥术神杖

LOJ#3089. 「BJOI2019」奥术神杖

看见乘积就取log，开根号就是除法，很容易发现这就是一道01分数规划。。

然后建出AC自动机直接dp就行，判断条件要设成>0，因为起点的值是1，取完ln后是0

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('\n')
#define eps 1e-10
#define MAXN 2005
#define ba 47
//#define ivorysi
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;T f = 1;char c = getchar();
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 +c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}

int N,M,cur;
int nxt[MAXN][10],pre[MAXN],Ncnt;
char T[MAXN],s[MAXN],ans[MAXN];
db val[MAXN];
vector<db> ed[MAXN];
db dp[2][MAXN];
int from[MAXN][MAXN];
char c[MAXN][MAXN];
void Insert(db v) {
    int l = strlen(s + 1);int p = 1;
    for(int i = 1 ; i <= l ; ++i) {
	if(!nxt[p][s[i] - '0']) nxt[p][s[i] - '0'] = ++Ncnt;
	p = nxt[p][s[i] - '0'];
    }
    ed[p].pb(v);
}
queue<int> Q;
void build_ACAM() {
    for(int i = 0 ; i <= 9 ; ++i) nxt[0][i] = 1;
    pre[1] = 0;
    Q.push(1);
    while(!Q.empty()) {
	int u = Q.front();Q.pop();
	ed[u].insert(ed[u].end(),ed[pre[u]].begin(),ed[pre[u]].end());
	for(int i = 0 ; i <= 9 ; ++i) {
	    int v = nxt[u][i];
	    if(v) {
		pre[v] = nxt[pre[u]][i];
		Q.push(v);
	    }
	    else nxt[u][i] = nxt[pre[u]][i];
	}
    }
}

bool Calc(db mid) {
    memset(val,0,sizeof(val));
    for(int i = 1 ; i <= Ncnt ; ++i) {
	for(auto v : ed[i]) val[i] += v - mid;
    }
    for(int i = 1 ; i <= Ncnt ; ++i) dp[0][i] = dp[1][i] = -1e9;
    dp[0][1] = 0;cur = 0;
    from[0][1] = 0;
    for(int i = 1 ; i <= N ; ++i) {
	for(int j = 1 ; j <= Ncnt ; ++j) dp[cur ^ 1][j] = -1e9;
	for(int j = 1 ; j <= Ncnt ; ++j) {
	    if(dp[cur][j] <= -1e9) continue;
	    if(T[i] == '.') {
		for(int h = 0 ; h <= 9 ; ++h) {
		    if(dp[cur ^ 1][nxt[j][h]] < dp[cur][j] + val[nxt[j][h]]) {
			dp[cur ^ 1][nxt[j][h]] = dp[cur][j] + val[nxt[j][h]];
			from[i][nxt[j][h]] = j;
			c[i][nxt[j][h]] = h + '0';
		    }
		}
	    }
	    else {
		int h = T[i] - '0';
		if(dp[cur ^ 1][nxt[j][h]] < dp[cur][j] + val[nxt[j][h]]) {
		    dp[cur ^ 1][nxt[j][h]] = dp[cur][j] + val[nxt[j][h]];
		    from[i][nxt[j][h]] = j;
		    c[i][nxt[j][h]] = h + '0';
		}
	    }
	}
	cur ^= 1;
    }
    for(int i = 1 ; i <= Ncnt ; ++i) {
	if(dp[cur][i] > 0) return true;
    }
    return false;
}
void Solve() {
    read(N);read(M);
    scanf("%s",T + 1);
    Ncnt = 1;
    int v;
    for(int i = 1 ; i <= M ; ++i) {
	scanf("%s",s + 1);read(v);
	Insert(log(v));
    }
    build_ACAM();
    int cnt = 50;
    db l = 0,r = 21;
    while(cnt--) {
	db mid = (l + r) / 2;

	if(Calc(mid)) l = mid;
	else r = mid;
    }
    Calc(l);
    int st = 0;
    for(int i = 1 ; i <= Ncnt ; ++i) {
	if(dp[cur][i] > 0) st = i;
    }
    for(int i = N ; i >= 1 ; --i) {
	int pre = from[i][st];
	ans[i] = c[i][st];
	st = pre;
    }
    for(int i = 1 ; i <= N ; ++i) {
	putchar(ans[i]);
    }
    enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
}