Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 21366 | Accepted: 9876 |
Description
Each vase has a distinct characteristic (just like flowers do). Hence, putting a bunch of flowers in a vase results in a certain aesthetic value, expressed by an integer. The aesthetic values are presented in a table as shown below. Leaving a vase empty has an aesthetic value of 0.
V A S E S |
||||||
1 |
2 |
3 |
4 |
5 |
||
Bunches |
1 (azaleas) |
7 | 23 | -5 | -24 | 16 |
2 (begonias) |
5 | 21 | -4 | 10 | 23 | |
3 (carnations) |
-21 |
5 | -4 | -20 | 20 |
According to the table, azaleas, for example, would look great in vase 2, but they would look awful in vase 4.
To achieve the most pleasant effect you have to maximize the sum of aesthetic values for the arrangement while keeping the required ordering of the flowers. If more than one arrangement has the maximal sum value, any one of them will be acceptable. You have to produce exactly one arrangement.
Input
- The first line contains two numbers: F, V.
- The following F lines: Each of these lines contains V integers, so that Aij is given as the jth number on the (i+1)st line of the input file.
- 1 <= F <= 100 where F is the number of the bunches of flowers. The bunches are numbered 1 through F.
- F <= V <= 100 where V is the number of vases.
- -50 <= Aij <= 50 where Aij is the aesthetic value obtained by putting the flower bunch i into the vase j.
Output
Sample Input
3 5 7 23 -5 -24 16 5 21 -4 10 23 -21 5 -4 -20 20
Sample Output
53
Source
原題鏈接:http://poj.org/problem?id=1157
題意:給出f朵花,v個花瓶,要把花都插到花瓶裏去,而且花的順序不能改變,編號小的在左邊,每朵花放到花瓶裏都會有一定的價值,問如何放才能產生最大的價值
我們設dp[i][j]表示處理到第i朵花,然後把第i朵花放到第j個花瓶裏時所能獲得的最大價值;
顯然 dp[i][j] = max(dp[i - 1][k]) + val[i][j],其中k< j val[i][j]表示把第i朵花放到第j個花瓶裏產生的價值
本題dp狀態:
i=0 | i=1 | i=2 | i=3 | i=4 | i=5 | |
j=0 | 0 | 0 | 0 | 0 | 0 | 0 |
j=1 | 0 | 7 | 23 | -5 | -24 | 16 |
j=2 | 0 | -INF | 28 | 19 | 33 | 46 |
j=3 | 0 | -INF | -INF | -INF | 24 | 8 |
AC代碼:
/**
* 行有餘力,則來刷題!
* 博客鏈接:http://blog.csdn.net/hurmishine
*
*/
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn=100+5;
const int INF=0x3f3f3f3f;
int a[maxn][maxn];
int dp[maxn][maxn];
int n,m;
int main()
{
//freopen("C:\\Documents and Settings\\Administrator\\桌面\\data.txt","r",stdin);
while(cin>>n>>m)
{
//memset(dp,-INF,sizeof(dp));
for(int i=1; i<=n; i++)
{
for(int j=1; j<=m; j++)
cin>>a[i][j],dp[i][j]=-INF;
}
for(int i=0; i<=m; i++)
dp[0][i]=0;
dp[1][1]=a[1][1];
for(int i=1; i<=n; i++)
{
for(int j=i; j<=m; j++)//j從i開始,小優化
{
for(int k=1; k<j; k++)
{
dp[i][j]=max(dp[i][j],dp[i-1][k]+a[i][j]);
}
}
}
int ans=-INF;
/**
for(int i=0;i<=n;i++)
{
for(int j=0;j<=m;j++)
cout<<dp[i][j]<<"\t";
cout<<endl;
}
*/
for(int i=1; i<=m; i++)
{
ans=max(ans,dp[n][i]);
}
cout<<ans<<endl;
}
return 0;
}
參考博客:http://blog.csdn.net/z309241990/article/details/9268679
http://blog.csdn.net/guard_mine/article/details/40892949
http://blog.csdn.net/wangjian8006/article/details/8964060
http://blog.csdn.net/r1986799047/article/details/48506687