hihocoder #1338 : A Game（区间dp）

http://hihocoder.com/problemset/problem/1338

区间dp。

d[l][r]表示[l,r]区间先手取能得到的最大分数。

#define bug(x) cout<<#x<<" is "<<x<<endl
#define IO std::ios::sync_with_stdio(0)
#include <bits/stdc++.h>
#define iter ::iterator
#define pa pair<int,int>
#define pp pair<int,pa>
using namespace  std;
#define ll long long
#define mk make_pair
#define pb push_back
#define se second
#define fi first
#define ls o<<1
#define rs o<<1|1
const ll mod=1e9+7;
const int N=1e3+10;

int a[N],b[N];
int d[N][N];

int n;

int dfs(int l,int r){
    if(l==r)return a[l];

    if(d[l][r])return d[l][r];

    int ans=-1e9;

    ans=max(ans,b[r]-b[l-1]-dfs(l+1,r));
    ans=max(ans,b[r]-b[l-1]-dfs(l,r-1));
    return d[l][r]=ans;
}
int main(){

    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
        b[i]=b[i-1]+a[i];
    }
    printf("%d
",dfs(1,n));

}

或者d[i][j]表示以i为左端点，j为区间长度的区间先手取能得到的最大分数。

#define bug(x) cout<<#x<<" is "<<x<<endl
#define IO std::ios::sync_with_stdio(0)
#include <bits/stdc++.h>
#define iter ::iterator
#define pa pair<int,int>
#define pp pair<int,pa>
using namespace  std;
#define ll long long
#define mk make_pair
#define pb push_back
#define se second
#define fi first
#define ls o<<1
#define rs o<<1|1
const ll mod=1e9+7;
const int N=1e3+10;

int n;
int a[N],b[N];
int d[N][N];
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
        b[i]=b[i-1]+a[i];
        d[i][1]=a[i];
    }
    for(int j=2;j<=n;j++){
        for(int i=1;i<=n;i++){
            d[i][j]=max(b[i+j-1]-b[i-1]-d[i][j-1],b[i+j-1]-b[i-1]-d[i+1][j-1]);
        }
    }
    printf("%d
",d[1][n]);
}