bzoj 1003: [ZJOI2006]物流运输trans

最新推荐文章于 2019-11-30 17:30:13 发布

原创最新推荐文章于 2019-11-30 17:30:13 发布 · 902 阅读

1 ·

CC 4.0 BY-SA版权

刷题记录专栏收录该内容

7 篇文章

订阅专栏

本文介绍了一种利用SPFA算法预处理最短路径，并结合动态规划解决问题的方法。通过实例展示了如何优化计算过程，降低时间复杂度。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

这道题还算比较水。。

spfa预处理从第i天到第j天的可行最短路存为t[i][j]，

然后直接dp。

f[i] 代表到第i天的最小费用

f[i] = min(f[i],min(t[1][i]*i,f[j]+k+t[j+1][i]*(i-j)))

/*
ID:zsy99021
PROB:bzoj1003 
LANG:C++
*/
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <iostream>
#include <fstream>
#include <ctime>
#define N 108
#define M 28
#define mid(l,r) ((l+r) >> 1)
#define INF 0x7ffffff
using namespace std;
  
long long n,t[N][N],m,k,e,head[M];
long long f[N]; 
bool flag[N][M];
  
struct wulala
{
    int node,next,dist;
}h[M*M];
  
int spfa(int a,int b)
{
    bool block[M],inq[M];
    int dis[M];
    int tail = 0,headd = 1,q[M*M];
    memset(block,0,sizeof(block));
    memset(inq,0,sizeof(inq));
    memset(q,0,sizeof(q));
    for (int i = 1;i <= m;i++) dis[i] = INF;
    for (int i = a;i <= b;i++)
        for (int j = 1;j <= m;j++) if (flag[i][j]) block[j] = true;
    q[1] = 1; inq[1] = true; dis[1] = 0;
    while(tail < headd)
    {
        int u = q[++tail];
        int c = head[u];
        while(c)
        {
            if (block[h[c].node]||dis[h[c].node] < dis[u] + h[c].dist)
            {
                c = h[c].next;
                continue;
            }
            if (!inq[h[c].node]) q[++headd] = h[c].node;
            dis[h[c].node] = dis[u] + h[c].dist;
            inq[h[c].node] = true;
            c = h[c].next; 
        }
        inq[u] = false;
    }
    return(dis[m]);
}
  
void init()
{
    memset(flag,0,sizeof(flag));
    scanf("%d%d%d%d",&n,&m,&k,&e);
    for (int i = 1;i <= e;i++)
    {
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        h[2*i-1].node = y;
        h[2*i].node = x;
        h[2*i-1].dist = h[2*i].dist = z;
        h[2*i-1].next = head[x];
        head[x] = 2 * i - 1;
        h[2*i].next = head[y];
        head[y] = 2 * i;
    }
    int d;
    scanf("%d",&d);
    for (int i = 1;i <= d;i++)
    {
        int a,b,p;
        scanf("%d%d%d",&p,&a,&b);
        for (int j = a;j <= b;j++) flag[j][p] = true; 
    } 
    for (int i = 1;i <= n;i++)
        for (int j = i;j <= n;j++)
            t[i][j] = spfa(i,j);
}
  
void work()
{
    memset(f,127,sizeof(f)); 
    for (int i = 1;i <= n;i++) f[0] = 0;
    for (int i = 1;i <= n;i++)
        for (int j = 0;j < i;j++)
            f[i] = min(f[i],min(t[1][i]*i,f[j]+k+t[j+1][i]*(i-j)));
}
  
void debug()
{
    for (int i = 1;i <= n;i++)
    {
        for (int j = 1;j <= n;j++) printf("%d ",t[i][j]);
        printf("\n");
    }
}
  
int main()
{
    init();
//  debug();
    work();
    printf("%d\n",f[n]);
    return 0;
}