UVa12589 Learning Vector

Posted 2020-11-08 俺是小程

大家都是用优雅的记忆化搜索做的，我最笨，懒得写记忆化，直接递推暴力转移了。

这题的难点在贪心上。自己想出来了

大概明天会写详细证明吧。。

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <cstring>
 4 #include <algorithm>
 5 using namespace std;
 6 typedef pair<int, int> P;
 7 #define x first
 8 #define y second
 9 const int MAXN = 50 + 2;
10 
11 P v[MAXN];
12 int N, K;
13 
14 inline bool cmp(const P &lhs, const P &rhs)
15 {
16     return (double) ((double)lhs.y / (double)lhs.x) > 
17     (double) ((double)rhs.y / (double)rhs.x);
18 }
19 
20 int f[MAXN][MAXN][MAXN * MAXN];
21 
22 int main()
23 {
24     //freopen("12589.in", "r", stdin);
25     int T;
26     cin>>T;
27     int cnt = 0;
28     while(T--)
29     {
30         cnt++;
31         cin>>N>>K;
32         register int a, b;
33         for(int i = 1; i <= N; i++)
34         {
35             scanf(" %d %d", &a, &b);
36             v[i] = P(a, b);
37         }
38         
39         sort(v + 1, v + N + 1, cmp);
40         
41         memset(f, -0x3f, sizeof(f));
42         for(int i = 0; i <= N; i++)
43             for(int j = 0; j <= K; j++)
44                 f[i][j][0] = 0;
45 
46         register int mxh[2] = {0}, d = 0;
47         for(int i = 1; i <= N; i++)
48         {
49             d ^= 1;
50             for(int j = 0; j <= min(i, K); j++)
51                 for(int h = 0; h <= mxh[d]; h++)
52                 {
53                     f[i + 1][j + 1][h + v[i].y] = max(f[i + 1][j + 1][h + v[i].y], 
54                     f[i][j][h] + (v[i].x * v[i].y) + 2 * (v[i].x * h));
55                     f[i + 1][j][h] = max(f[i + 1][j][h], f[i][j][h]);
56                     mxh[d ^ 1] = max(mxh[d ^ 1], h + v[i].y);
57                 }
58         }
59 
60         int ans = 0;
61         for(int i = 1; i <= max(mxh[0], mxh[1]); i++)
62             ans = max(ans, f[N + 1][K][i]);
63         printf("Case %d: %d\n", cnt, ans);
64     }
65     return 0;
66 }