HDU 1087 Super Jumping! Jumping! Jumping! DP
2014-08-22 18:00
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题目大意:给定一段长度为N(N<=1000)序列,在a[i]<a[j]的条件下我们可以从i走到j,可以获得a[j]的分数,问获得的最大分数是多少。
题目分析:可以考虑N^2的DP,类似于LIS问题,把LIS转化为分数即可。
其中DP方程:
dp[i]=max(a[i],dp[j]+a[i]),其中j<i并且a[j]<a[i].
如下代码:
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define INF 9999999
const int MAXN=1001;
using namespace std;
int dp[MAXN],a[MAXN],n;
int main()
{
while(scanf("%d",&n)!=EOF)
{
if(!n)
break;
for(int i=1;i<=n;i++)
cin>>a[i];
dp[1]=a[1];
int ans=-INF;
for(int i=1;i<=n;i++)
{
dp[i]=a[i];
for(int j=1;j<i;j++)
{
if(a[j]<a[i])
dp[i]=max(dp[i],dp[j]+a[i]);
}
ans=max(ans,dp[i]);
}
cout<<ans<<endl;
}
// while(1);
return 0;
}
题目分析:可以考虑N^2的DP,类似于LIS问题,把LIS转化为分数即可。
其中DP方程:
dp[i]=max(a[i],dp[j]+a[i]),其中j<i并且a[j]<a[i].
如下代码:
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define INF 9999999
const int MAXN=1001;
using namespace std;
int dp[MAXN],a[MAXN],n;
int main()
{
while(scanf("%d",&n)!=EOF)
{
if(!n)
break;
for(int i=1;i<=n;i++)
cin>>a[i];
dp[1]=a[1];
int ans=-INF;
for(int i=1;i<=n;i++)
{
dp[i]=a[i];
for(int j=1;j<i;j++)
{
if(a[j]<a[i])
dp[i]=max(dp[i],dp[j]+a[i]);
}
ans=max(ans,dp[i]);
}
cout<<ans<<endl;
}
// while(1);
return 0;
}
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