Cow Exhibition

Posted 2020-10-03 山杉三

"Fat and docile, big and dumb, they look so stupid, they aren‘t much 
fun..." 
- Cows with Guns by Dana Lyons 

The cows want to prove to the public that they are both smart and fun. In order to do this, Bessie has organized an exhibition that will be put on by the cows. She has given each of the N (1 <= N <= 100) cows a thorough interview and determined two values for each cow: the smartness Si (-1000 <= Si <= 1000) of the cow and the funness Fi (-1000 <= Fi <= 1000) of the cow. 

Bessie must choose which cows she wants to bring to her exhibition. She believes that the total smartness TS of the group is the sum of the Si‘s and, likewise, the total funness TF of the group is the sum of the Fi‘s. Bessie wants to maximize the sum of TS and TF, but she also wants both of these values to be non-negative (since she must also show that the cows are well-rounded; a negative TS or TF would ruin this). Help Bessie maximize the sum of TS and TF without letting either of these values become negative. 

Input

* Line 1: A single integer N, the number of cows 

* Lines 2..N+1: Two space-separated integers Si and Fi, respectively the smartness and funness for each cow. 

Output

* Line 1: One integer: the optimal sum of TS and TF such that both TS and TF are non-negative. If no subset of the cows has non-negative TS and non- negative TF, print 0. 

Sample Input

5
-5 7
8 -6
6 -3
2 1
-8 -5

Sample Output

8

Hint

OUTPUT DETAILS: 

Bessie chooses cows 1, 3, and 4, giving values of TS = -5+6+2 = 3 and TF 
= 7-3+1 = 5, so 3+5 = 8. Note that adding cow 2 would improve the value 
of TS+TF to 10, but the new value of TF would be negative, so it is not 
allowed. 

 

题目意思:多组数据取其中几组,使其和最大,还要求前面的数之和与后面的数之和都大于0;

解题思路:0/1背包的问题

 1 #include <stdio.h>
 2 #include <string.h>
 3 #include <algorithm>
 4 #include <iostream>
 5 
 6 using namespace std;
 7 long long INF = 1e12;
 8 const int MAX = 200009;
 9 long long dp[MAX];
10 int N;
11 
12 int main()
13 {
14     while(cin>>N)
15     {
16         int s[105],t[105];
17         for(int i = 0;i <MAX;i++)
18             dp[i] = -INF;
19             dp[100000] = 0;
20         for(int i = 1;i <= N;i++)
21             scanf("%d %d",&s[i],&t[i]);
22 
23         for(int i =1;i <=N;i++)
24         {
25             if(s[i]< 0&&t[i] < 0)
26                 continue;
27             if(s[i]>0)
28             {
29                 for(int j = 200000;j>=s[i];j--)
30                     if(dp[j-s[i]]>-INF)
31                     {
32                         dp[j] = max(dp[j],dp[j-s[i]]+t[i]);
33                     }
34 
35             }
36             else
37             {
38                 for(int j =s[i];j <=200000+s[i];j++ )
39                     if(dp[j-s[i]]>-INF)
40                     {
41                         dp[j] = max(dp[j],dp[j-s[i]]+t[i]);
42                     }
43 
44             }
45         }
46         long long max1 = 0;
47         for(int i = 100000;i <=200000;i++)
48             if(dp[i]>0&&dp[i]+i-100000)
49             max1 = max(max1,dp[i]+i-100000) ;
50         cout<<max1<<endl;
51     }
52 
53     return 0;
54 }