Cow Exhibition
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 13578 | Accepted: 5503 |
Description
"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.
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.
* 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.
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.
01背包dp
设f[i]表示TS为i时TF的最大值。
因为TS可能为负数，所以将TS值+100000处理。
要注意当前si为正和为负时转移顺序不同，详见代码
1 #include<iostream> 2 #include<cstring> 3 #include<cstdio> 4 #include<cstdlib> 5 #include<cmath> 6 #include<algorithm> 7 using namespace std; 8 int n; 9 int f[200005]; 10 int a[101],b[101]; 11 int main() 12 { 13 scanf("%d",&n); 14 for(int i=1;i<=n;i++) scanf("%d%d",&a[i],&b[i]); 15 memset(f,-5,sizeof(f)); 16 int ans=0,m1=0,m2=0; 17 f[100000]=0; 18 for(int i=1;i<=n;i++) 19 { 20 if(a[i]>0) 21 for(int j=200000;j>=a[i];j--) 22 { 23 f[j]=max(f[j],f[j-a[i]]+b[i]); 24 if(j-100000>=0&&f[j]>=0&&j-100000+f[j]>ans)ans=j-100000+f[j]; 25 } 26 if(a[i]<0) 27 for(int j=0;j<=200000+a[i];j++) 28 { 29 f[j]=max(f[j],f[j-a[i]]+b[i]); 30 if(j-100000>=0&&f[j]>=0&&j-100000+f[j]>ans)ans=j-100000+f[j]; 31 } 32 } 33 cout<<ans; 34 }