[LibreOJ NOIP Round #1] 旅游路线

[题目链接]

https://loj.ac/problem/539

[算法]

首先 ， 我们用f[u][k]表示现在在景点u ，还有k元钱 ， 最多能够走多少路

不难发现f[u][k] = max{ f[v][k - P[u]] + Dist(u,v,min(C,ci)) } ( dist(u,v,w)表示从u走到v ， 最多经过w条路 ， 最多能走多少路 ）

用倍增弗洛伊德求dist， 然后进行上述dp ， 即可

时间复杂度 : O(N^4 + N^3logN + TlogQ)

[代码]

#include<bits/stdc++.h>
using namespace std;
const int inf = 1e9;
#define MAXN 110
#define MAXLOG 20
 
int n,m,C,T,tot;
int head[MAXN];
int a[MAXN],b[MAXN],p[MAXN],c[MAXN];
int dis[MAXN][MAXN],f[MAXN][MAXN * MAXN];
int mat[MAXLOG][MAXN][MAXN];
 
template <typename T> inline void read(T &x)
{
    T f = ; x = ;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
    for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
    x *= f;
}
 
int main()
{
 
        read(n); read(m); read(C); read(T);
        for (int i = ; i <= n; i++)
        {
                read(p[i]);
                read(c[i]);
                c[i] = min(c[i],C);
        }
        for (int i = ; i <= n; i++)
        {
                for (int j = ; j <= n; j++)
                {
                        if (i != j)
                                mat[][i][j] = -inf;
                }
        }
        for (int i = ; i <= m; i++)
        {
                int u,v,w;
                read(u); read(v); read(w);
                mat[][u][v] = max(mat[][u][v],w);
        }
        for (int i = ; i < MAXLOG; i++)
        {
                memcpy(mat[i],mat[i - ],sizeof(mat[i]));
                for (int k = ; k <= n; k++)
                {
                        for (int x = ; x <= n; x++)
                        {
                                for (int y = ; y <= n; y++)
                                {
                                        if (mat[i - ][x][k] != -inf && mat[i - ][k][y] != -inf)
                                                mat[i][x][y] = max(mat[i][x][y],mat[i - ][x][k] + mat[i - ][k][y]);
                                }
                        }
                }
        }
        for (int i = ; i <= n; i++)
        {
                for (int x = ; x <= n; x++) a[x] = -inf;
                a[i] = ;
                for (int k = ; k < MAXLOG; k++)
                {
                        if (c[i] & ( << k))
                        {
                                for (int x = ; x <= n; x++) b[x] = -inf;
                                for (int x = ; x <= n; x++)
                                {
                                        for (int y = ; y <= n; y++)
                                        {
                                                b[y] = max(b[y],a[x] + mat[k][x][y]);
                                        }
                                }
                                memcpy(a,b,sizeof(a));
                        }
                }
                for (int j = ; j <= n; j++) dis[i][j] = a[j];
        }
        for (int i = ; i <= n * n; i++)
        {
                for (int j = ; j <= n; j++)
                {
                        if (i < p[j])
                        {
                                f[j][i] = ;
                                continue;
                        }
                        for (int k = ; k <= n; k++) f[j][i] = max(f[j][i],f[k][i - p[j]] + dis[j][k]);
                }
        }
        while (T--)
        {
                int s,q,d;
                read(s); read(q); read(d);
                if (f[s][q] < d)
                {
                        printf("-1\n");
                        continue;
                }
                int l =  , r = q , mid , ans;
                while (l <= r)
                {
                        mid = (l + r) >> ;
                        if (f[s][mid] >= d)
                        {
                                ans = mid;
                                r = mid - ;
                        } else l = mid + ;
                }
                printf("%d\n",q - ans);
        }
 
        return ;
 
}