zoukankan      html  css  js  c++  java
  • HDU 2391 Filthy Rich (dp)

    题目连接

    Problem Description
    They say that in Phrygia, the streets are paved with gold. You’re currently on vacation in Phrygia, and to your astonishment you discover that this is to be taken literally: small heaps of gold are distributed throughout the city. On a certain day, the Phrygians even allow all the tourists to collect as much gold as they can in a limited rectangular area. As it happens, this day is tomorrow, and you decide to become filthy rich on this day. All the other tourists decided the same however, so it’s going to get crowded. Thus, you only have one chance to cross the field. What is the best way to do so?

    Given a rectangular map and amounts of gold on every field, determine the maximum amount of gold you can collect when starting in the upper left corner of the map and moving to the adjacent field in the east, south, or south-east in each step, until you end up in the lower right corner.

    Input
    The input starts with a line containing a single integer, the number of test cases.
    Each test case starts with a line, containing the two integers r and c, separated by a space (1 <= r, c <= 1000). This line is followed by r rows, each containing c many integers, separated by a space. These integers tell you how much gold is on each field. The amount of gold never negative.
    The maximum amount of gold will always fit in an int.

    Output
    For each test case, write a line containing “Scenario #i:”, where i is the number of the test case, followed by a line containing the maximum amount of gold you can collect in this test case. Finish each test case with an empty line.

    Sample Input
    1
    3 4
    1 10 8 8
    0 0 1 8
    0 27 0 4

    Sample Output
    Scenario #1:
    42

    分析:
    首行给出T,代表有T组数据。每组数据第一行给出n,m代表接着有n行m列的数据。起点在左上角,终点在右下角,每一步可以向下向右向右下走,输出途中最大数字和。

    思路:动态规划,dp[i][j]代表到达(i,j)能获取的最大数字和
    状态转移方程
    dp[i][j]=max(dp[i][j],dpi][j-1]+tu[i][j]),j-1>=0;
    dp[i][j]=max(dp[i][j],dp[i-1][j]+tu[i][j]),i-1>=0;
    dp[i][j]=max(dp[i][j],dp[i-1][j-1]+tu[i][j]),i-1>=0,j-1>=0;

    代码:

    #include<stdio.h>
    #include<iostream>
    #include<string.h>
    using namespace std;
    int tu[1010][1010];
    int dp[1010][1010];
    int main()
    {
        int T;
        scanf("%d",&T);
        for(int t=1;t<=T;t++)
        {
            int n,m;
            scanf("%d%d",&n,&m);
            for(int i=0; i<n; i++)
            {
                for(int j=0; j<m; j++)
                    scanf("%d",&tu[i][j]);
            }
            memset(dp,0,sizeof(dp));
            dp[0][0]=tu[0][0];
            for(int i=0; i<n; i++)
                for(int j=0; j<m; j++)
                {
                    if(j-1>=0&&dp[i][j]<dp[i][j-1]+tu[i][j])
                        dp[i][j]=dp[i][j-1]+tu[i][j];
                    if(i-1>=0&&dp[i][j]<dp[i-1][j]+tu[i][j])
                        dp[i][j]=dp[i-1][j]+tu[i][j];
                    if(j-1>=0&&i-1>=0&&dp[i][j]<dp[i-1][j-1]+tu[i][j])
                        dp[i][j]=dp[i-1][j-1]+tu[i][j];
                }
                printf("Scenario #%d:
    ",t);
                printf("%d
    
    ",dp[n-1][m-1]);
        }
        return 0;
    }
    
  • 相关阅读:
    Mysql大量插入随机数据方法--存储过程
    Linux永久修改系统时间和时区方法
    python反转字符串(简单方法)及简单的文件操作示例
    sql怎么批量替换字段里的字符串的
    varchar和Nvarchar区别
    VS改大小写的快捷键
    SQL中PIVOT 行列转换
    [转]VS中展开和折叠代码
    Bootstrap 标签页(Tab)插件
    C# DataTable 和List之间相互转换的方法
  • 原文地址:https://www.cnblogs.com/cmmdc/p/7862180.html
Copyright © 2011-2022 走看看