East Central North America 2005-2006——Two Ends
East Central North America 2005-2006——Two Ends
题目来源:
题意:
有一组数,你和一个人轮流取数(只能从两端取),问你能取到的最大的数和同时对方取到的数的差值。
题解:
一道裸的区间DP(顺便学了下区间DP,还是得多刷刷专题才好)
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <set>
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
const int maxn = 1e6+10;
int n,dp[1111][1121];
int arr[1111];
int dfs(int l,int r)
{
if(l>r)
return 0;
if(l==r)
return arr[l];
if(dp[l][r]!=-1)
return dp[l][r];
int tl=0,tr=0;
if(arr[r]>arr[l+1])
tl=dfs(l+1,r-1)+arr[l];
else
tl=dfs(l+2,r)+arr[l];
if(arr[r-1]>arr[l])
tr=dfs(l,r-2)+arr[r];
else
tr=dfs(l+1,r-1)+arr[r];
return dp[l][r]=(tl>tr)?tl:tr;
}
int main()
{
#ifndef ONLINE_JUDGE
//freopen("H.in","r",stdin);
//freopen("H.out","w",stdout);
#endif
int cas=0;
while(~scanf("%d",&n) && n)
{
cas++;
int sum=0;
memset(arr,0,sizeof(arr));
memset(dp,-1,sizeof(dp));
for(int i=0;i<n;i++)
{
cin >> arr[i];
sum+=arr[i];
}
int s=dfs(0,n-1);
int s2=sum-s;
printf("In game %d, the greedy strategy might lose by as many as %d points.\n",cas,s-s2);
}
return 0;
}