poj2184 Cow Exhibition（带负数的背包问题）(关于背包问题的精髓可以去百度背包九讲)
Cow Exhibition
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 7634 | Accepted: 2775 |
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.
要两边的和都大于零，并且求出最大值，其实就是背包问题，只不过带了负数，取100000处为原点就可
Memory: 1488 KB
Time: 141 MS
Language: G++
Result:
Accepted
#include
int c[1050],w[1050],f[201000];
#define A 1000000000
int main()
{
int i,j,k,n,v,m,x,max;
while(scanf("%d",&n)!=EOF)
{
for(i=0;i<=200000;i++)
{
f[i]=-A;
}//printf("%d ",w[0]);
for(i=0;i0)
for (v = 200000; v >=c[i]; --v)//c[i]可优化为bound,bound = max {V - sum c[i,...n],c[i]}//正数的是从后往前的
{
if(f[v-c[i]]>-A)
if(f[v] < f[v - c[i]] + w[i])
{
f[v] =f[v - c[i]] + w[i];
}
}
else for (v = c[i];v<=200000+c[i]; v++)//注意啦，负数的递推方程是从前往后的，为的是避免重复加上一个状态
{
if(f[v-c[i]]>-A)
if(f[v] < f[v - c[i]] + w[i])
{
f[v] =f[v - c[i]] + w[i];
}
}
}
max=-A;
for(i=100000;i<=200000;i++)
{
if(f[i]>=0)
{
//printf("giuie");
x=f[i]+i-100000;
if(max 下面再贴一份学长写的16ms的程序，比我的快十倍啊
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