因为数的总和一定，所以用一个人得分越高，那么另一个人的得分越低。
用$dp[i][j]$表示从$[i, j]$开始游戏，先手能够取得的最高分。
转移通过枚举取的数的个数$k$来转移。因为你希望先手得分尽量高，所以另一个人的最高得分应尽量少。
$dp[i][j] = sum[i][j] - min {dp[i + k][j],dp[i][j - k]}$
但是发现计算$dp[i + k][j],dp[i][j - k]$的最小值的地方很重复，所以用一个$f[i][j]$储存前者的最优值，$g[i][j]$储存后者的最优值。
这样就将代码的时间复杂度优化到O(n2)
Code
1 /** 2 * uva 3 * Problem#10891 4 * Accepted 5 * Time:0ms 6 */ 7 #include<iostream> 8 #include<cstdio> 9 #include<cctype> 10 #include<cstring> 11 #include<cstdlib> 12 #include<cmath> 13 #include<sstream> 14 #include<algorithm> 15 #include<map> 16 #include<set> 17 #include<queue> 18 #include<vector> 19 #include<stack> 20 using namespace std; 21 typedef bool boolean; 22 #define INF 0xfffffff 23 #define smin(a, b) a = min(a, b) 24 #define smax(a, b) a = max(a, b) 25 template<typename T> 26 inline void readInteger(T& u){ 27 char x; 28 long long aFlag = 1; 29 while(!isdigit((x = getchar())) && x != '-'); 30 if(x == '-'){ 31 x = getchar(); 32 aFlag = -1; 33 } 34 for(u = x - '0'; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - '0'); 35 ungetc(x, stdin); 36 u *= aFlag; 37 } 38 39 int n; 40 int *list; 41 int f[101][101]; 42 int g[101][101]; 43 int dp[101][101]; 44 45 inline boolean init(){ 46 readInteger(n); 47 if(n == 0) return false; 48 list = new int[(const int)(n + 1)]; 49 for(int i = 1; i <= n; i++){ 50 readInteger(list[i]); 51 } 52 return true; 53 } 54 55 int *sum; 56 inline void getSum(){ 57 sum = new int[(const int)(n + 1)]; 58 sum[0] = 0; 59 for(int i = 1; i <= n; i++) 60 sum[i] = sum[i - 1] + list[i]; 61 } 62 63 inline void solve(){ 64 memset(f, 0x7f, sizeof(f)); 65 memset(g, 0x7f, sizeof(g)); 66 for(int i = 1; i <= n; i++) f[i][i] = g[i][i] = dp[i][i] = list[i]; 67 for(int k = 1; k < n; k++){ 68 for(int i = 1; i + k <= n; i++){ 69 int j = i + k; 70 int m = 0; 71 smin(m, f[i + 1][j]); 72 smin(m, g[i][j - 1]); 73 dp[i][j] = sum[j] - sum[i - 1] - m; 74 f[i][j] = min(f[i + 1][j], dp[i][j]); 75 g[i][j] = min(g[i][j - 1], dp[i][j]); 76 } 77 } 78 printf("%d ", dp[1][n] * 2 - sum[n]); 79 delete[] list; 80 delete[] sum; 81 } 82 83 int main(){ 84 while(init()){ 85 getSum(); 86 solve(); 87 } 88 return 0; 89 }