51nod - 1022【四边形不等式优化DP】

 1 #include <iostream>
 2 #include <algorithm>
 3 #include <cstring>
 4 #include <cstdio>
 5 #include <bitset>
 6 #include <vector>
 7 #include <queue>
 8 #include <stack>
 9 #include <cmath>
10 #include <list>
11 #include <set>
12 #include <map>
13 #define rep(i,a,b) for(int i = a;i <= b;++ i)
14 #define per(i,a,b) for(int i = a;i >= b;-- i)
15 #define mem(a,b) memset((a),(b),sizeof((a)))
16 #define FIN freopen("in.txt","r",stdin)
17 #define FOUT freopen("out.txt","w",stdout)
18 #define IO ios_base::sync_with_stdio(0),cin.tie(0)
19 #define mid ((l+r)>>1)
20 #define ls (id<<1)
21 #define rs ((id<<1)|1)
22 #define N 2010
23 #define INF 0x3f3f3f3f
24 #define INFF ((1LL<<62)-1)
25 typedef long long LL;
26 using namespace std;
27 
28 int n, m, T, c[N], s[N][N], sum[N], dp[N][N];
29 int main()
30 {IO;
31     //FIN;
32     while(cin >> n){
33         sum[0] = 0;
34         rep(i, 1, n){ 
35             cin >> c[i]; 
36             sum[i] = sum[i-1] + c[i]; 
37         }
38         rep(i, 1, n){
39             c[i+n] = c[i];
40             sum[i+n] = sum[i+n-1]+c[i+n];
41         }
42 
43         mem(dp, 0);
44         per(i, n*2, 1){
45             rep(j, i, n*2){
46                 if(i == j)    { s[i][j] = i; continue; }
47                 dp[i][j] = INF;
48                 LL res = sum[j]-sum[i-1];
49                 rep(k, s[i][j-1], s[i+1][j]){
50                     if(dp[i][k]+dp[k+1][j]+res < dp[i][j]){
51                         dp[i][j] = dp[i][k]+dp[k+1][j]+res;
52                         s[i][j] = k;
53                     }
54                 }
55             }
56         }
57         int ans = INF;
58         rep(i, 1, n)    ans = min(ans, dp[i][i+n-1]);
59         cout << ans << endl;
60     }
61     return 0;
62 }