zoukankan      html  css  js  c++  java
  • CF #355div2 D 宝藏与钥匙 dp 二维数组智商题

    D. Vanya and Treasure
    time limit per test
    1.5 seconds
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    Vanya is in the palace that can be represented as a grid n × m. Each room contains a single chest, an the room located in the i-th row and j-th columns contains the chest of type aij. Each chest of type x ≤ p - 1 contains a key that can open any chest of type x + 1, and all chests of type 1 are not locked. There is exactly one chest of type p and it contains a treasure.

    Vanya starts in cell (1, 1) (top left corner). What is the minimum total distance Vanya has to walk in order to get the treasure? Consider the distance between cell (r1, c1) (the cell in the row r1 and column c1) and (r2, c2) is equal to |r1 - r2| + |c1 - c2|.

    Input

    The first line of the input contains three integers nm and p (1 ≤ n, m ≤ 300, 1 ≤ p ≤ n·m) — the number of rows and columns in the table representing the palace and the number of different types of the chests, respectively.

    Each of the following n lines contains m integers aij (1 ≤ aij ≤ p) — the types of the chests in corresponding rooms. It's guaranteed that for each x from 1 to p there is at least one chest of this type (that is, there exists a pair of r and c, such that arc = x). Also, it's guaranteed that there is exactly one chest of type p.

    Output

    Print one integer — the minimum possible total distance Vanya has to walk in order to get the treasure from the chest of type p.

    Examples
    input
    3 4 3
    2 1 1 1
    1 1 1 1
    2 1 1 3
    output
    5
    input
    3 3 9
    1 3 5
    8 9 7
    4 6 2
    output
    22
    input
    3 4 12
    1 2 3 4
    8 7 6 5
    9 10 11 12
    outpu11
    题意: 给你n*m的个格子,每个格子中都有一个权值(1-p),问你从最左上角的位置开始走,走到
    最终权值为p的格子中(只有一个),只要曾经经过权值为i的格子就能打开权值为i+1的格子中的宝藏,现在要打开权值为p的格子中的宝藏问需要经过的最少步数。
    #include <iostream>
    #include <cstdio>
    #include <cstring>
    #include <cstdlib>
    #include <cmath>
    #include <vector>
    #include <queue>
    #include <stack>
    #include <map>
    #include <algorithm>
    #include <set>
    using namespace std;
    typedef long long ll;
    typedef unsigned long long ull;
    #define MM(a,b) memset(a,b,sizeof(a));
    const double eps = 1e-10;
    const int  inf =0x7f7f7f7f;
    const double pi=acos(-1);
    const int maxn=5+100000;
    const int mod=1e9+7;
    
    int dis[305][305],vis[305][305],ans[305][305];
    struct node{
       int x,y;
    }ne[maxn];
    vector<node> G[maxn];
    
    ll gdis(node u,node v)
    {
        return abs(u.x-v.x)+abs(u.y-v.y);
    }
    
    int main()
    {
        int n,m,p,v,ex,ey;
        while(~scanf("%d %d %d",&n,&m,&p))
        {
            int cnt=0,k1,k2;
            MM(vis,-1);MM(dis,inf);MM(ans,inf);
            for(int i=1;i<=p;i++) G[i].clear();
            for(int i=1;i<=n;i++)
              for(int j=1;j<=m;j++)
              {
                  scanf("%d",&v);
                  G[v].push_back((node){i,j});
                  if(v==p) {ex=i;ey=j;}
              }
            for(int i=1;i<=m;i++)
              {
                 dis[1][i]=i-1;
                 vis[1][i]=0;
              }
            for(int u=1;u<=p;u++)
            {
                for(int k=0;k<G[u].size();k++)
                {
                     int r=G[u][k].x,l=G[u][k].y;
                     for(int i=1;i<=n;i++)
                        if(vis[i][l]==u-1)
                         ans[r][l]=min(ans[r][l],dis[i][l]+abs(i-r));
                }
                for(int k=0;k<G[u].size();k++)
                {
                    int r=G[u][k].x,l=G[u][k].y;
                    for(int j=1;j<=m;j++)
                        if(vis[r][j]!=u)
                        {
                           vis[r][j]=u;
                           dis[r][j]=ans[r][l]+abs(l-j);
                        }
                        else
                          dis[r][j]=min(dis[r][j],ans[r][l]+abs(l-j));
                }
            }
            printf("%d
    ",ans[ex][ey]);
        }
        return 0;
    }
    
    
    

      分析:设置dis和vis以及ans三个数组,假设[i][j]格子中的权值为v,ans[i][j]代表,从最左上角格子开始走,且经过了1-v的格子后到达该格子的最少步数(最终答案就是ans[ex][ey])dis[i][j]代表

    在经过了1-vis[i][j]的权值后,到达该格子的最少步数,vis[i][j]代表该格子所在的行所更新的最大的权值

  • 相关阅读:
    关于oracle的导入数据流程,以及错误解决
    解决 lombok 和 freemarker 下载慢问题 以及安装方法
    解决maven项目没有Maven Dependencies
    将maven仓库改为阿里仓库
    Dos攻击和校网渗透
    KaliLinux切换python版本
    Kali国内更新源
    linux安装jdk(.rpm)
    Centos 关于 mysql 命令
    Linux删除命令
  • 原文地址:https://www.cnblogs.com/smilesundream/p/5559129.html
Copyright © 2011-2022 走看看