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();

}